Massachusetts Adult Basic Education

 

Curriculum Framework

 

For

 

 

Mathematics and Numeracy

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Massachusetts Department of Education

Adult and Community Learning Services

October, 2005

 

TABLE OF CONTENTS

 

 

Acknowledgments. 4

Introduction.. 5

The Development of the Massachusetts ABE Curriculum Framework   5

What is Numeracy?  A Definition of Numerate Behavior.. 7

How to use This Document (Teacher's Guide) 8

Connecting Curriculum, Instruction, and Assessment.. 10

Core Concepts. 12

Guiding Principles. 14

Habits of Mind.. 15

Content Strands and Learning Standards. 16

The Strand Number Sense. 17

The Strand Patterns, Functions, and Algebra.. 17

The Strand Statistics and Probability.. 19

The Strand Geometry and Measurement.. 19

Outline of Learning Levels. 21

Level 1. Beginning Adult Numeracy.. 21

Strand:  Number Sense. 21

Strand: Patterns, Functions, and Algebra. 23

Strand: Statistics and Probability. 25

Strand: Geometry and Measurement 26

Level 2: Beginning ABE Mathematics. 29

Strand: Number Sense. 29

Strand: Patterns, Functions and Algebra. 34

Strand: Statistics and Probability. 35

Strand: Geometry and Measurement 37

Level 3: Intermediate ABE Mathematics. 41

Strand: Number Sense. 41

Strand: Patterns, Functions, and Algebra. 46

Strand: Statistics and Probability. 48

Strand: Geometry and Measurement 53

Level 4: Pre-GED / ABE Standards. 56

Strand: Number Sense. 56

Strand: Patterns, Functions and Algebra. 61

Strand: Statistics and Probability. 64

Strand: Geometry and Measurement 69

Level 5: ASE / GED Standards. 74

Strand: Number Sense. 74

Strand: Patterns, Functions, and Algebra. 77

Strand: Statistics and Probability. 79

Strand: Geometry & Measurement 84

Level 6: ASE / Bridge to College Standards. 87

Strand: Number Sense. 87

Strand: Patterns, Functions, and Algebra. 89

Strand: Statistics and Probability. 91

Strand: Geometry and Measurement 97

Appendices. 99

Appendix A. Suggested Readings. 99

Appendix B. Sample Instructional Units. 100

Appendix C. Instructional Resources and Materials. 100

Adult Numeracy Curriculum.. 100

Number Sense. 100

All Strands 101

Problem-Solving. 101

GED Preparation. 101

Learning Differences and Disabilities 102

Internet Resources 102

Appendix D. Criteria for Evaluating Instructional Materials and Programs. 103

Appendix E. Massachusetts Common Core of Learning.. 105

Thinking and Communicating. 105

Gaining and Applying Knowledge. 106

Working and Contibuting. 107

Appendix F.  Equipped for the Future Role Maps and Domain Skills  108

Parent/Family Role Map. 108

Worker Role Map. 109

Citizen/Community Member Role Map. 110

Lists of Skills from the Four Domains in the EFF Standards 112

Content Framework for EFF Standards 113

 

 

 

 

 

 

 

 

 

Acknowledgments

 

Special thanks are due to the team who have contributed to the development of the Massachusetts ABE Curriculum Framework for Mathematics and Numeracy over the past number of years:

 

Patricia Donovan*

Barbara Goodridge*

Robert Foreman

Roberta Froelich*

Esther D. Leonelli*

Andrea (Drey) Martone

Marilyn Moses*

Jenifer Mullen*

Mary Jane Schmitt*

Jane Schwerdtfeger

Ruth Schwendeman*

Judith Titzel

 

* Denotes members of the original Math Curriculum Framework Development Team

 

 

Massachusetts Adult Basic Education Curriculum Framework for Mathematics and Numeracy                      4                                   

Massachusetts Department of Education, Adult and Community Learning Services, October 2005

 
In addition, we would like to recognize the ABE practitioners, students, business representatives, and other stakeholders from across the Commonwealth who shared their valuable time and talent through developmental working groups, field trials, and revisions that were essential in bringing the ABE Curriculum Framework for Mathematics and Numeracy to the level of quality that is reflected in this edition.


Introduction

 

The Development of the Massachusetts ABE Curriculum Framework

for Mathematics and Numeracy

 

Over the past number of years, several initiatives have set the stage for writing the Massachusetts ABE Curriculum Frameworks for Mathematics and Numeracy.

 

The First Version: Changing the Way We Teach Math

 

In 1989, the National Council of Teachers of Mathematics (NCTM) published the Curriculum and Evaluation Standards for School Mathematics, a document that served as a template for reforming and improving K-12 mathematics education across the nation.  In 1994, sixteen Massachusetts ABE/GED teachers formed a team and studied the Massachusetts K-12 standards to see how some of the ideas might play out in their adult education classrooms.  After a year of action research in their classes, these teachers published two documents: a set of adult education math standards and stories of what changes looked like in their classrooms.  Their adult math standards were incorporated into the Massachusetts ABE Math Standards (1995) and were the first set of ABE frameworks to hit the press.  As such, they served as an early template for the Massachusetts ABE Curriculum Frameworks in other subjects that were subsequently developed.

 

In 1996, in the wake of education reform and a national science and math initiative in the state (which included Adult Basic Education), the Massachusetts ABE Math Standards were subsumed into the document, Massachusetts Curriculum Frameworks: Achieving Mathematical Power (1996).  This state curriculum framework was to be used for both grades K-12 and for Adult Basic Education.  In 2000, when the Massachusetts K-12 frameworks were revised, it was decided that the adult education math framework should be rewritten and revised, and developed as a separate document. This current version of the Massachusetts ABE Mathematics Curriculum Frameworks is a second revision of that first framework, but it is heavily influenced by developments in the adult education field since then, both nationally and internationally.

 

National Influences: The Adult Numeracy Frameworks and Equipped for the Future

 

In March 1994, the first national Conference on Adult Mathematical Numeracy, co-sponsored by the National Council of Teachers, the National Center on Adult Literacy (NCAL), and the U.S. Department of Education/Office of Vocation and Adult Education, brought policy makers, researchers, publishers, and practitioners together to discuss the issues of adult numeracy needs and mathematical education.  Out of this conference came at least two significant events: the formation of the Adult Numeracy Network (ANN), a national network of practitioners, and the development of the “honest list: what math we should be teaching adults.”

 

In October 1995, the ANN was granted one of eight planning grants for system reform and improvement, funded by the National Institute for Literacy as part of the Equipped for the Future (EFF) project.  Over the course of a year, through teacher-led focus groups of learners, business, and other state policy stakeholders in five states (including Massachusetts), and an on-line virtual study group, the ANN expanded upon the “honest list” developed from the conference.  The teacher teams studied, among other documents, the teacher-developed Massachusetts ABE math standards, the report of the Secretary’s Commission on Achieving Necessary Skills (SCANS, 1991), and Equipped for the Future.  Out of their research and focus groups, the teams developed seven themes which serve as the foundation for adult numeracy standards: Relevance/Connections, Problem-Solving/Reasoning/Decision-Making, Communication, Number and Number Sense, Data, Geometry: Spatial Sense and Measurement, Algebra: Patterns and Functions. In 1996, they published A Framework for Adult Numeracy Standards: The Mathematical Skills and Abilities Adults Need to be Equipped for the Future (1996).

 

As a result of this work, mathematics was included in the Equipped for the Future Content Standards: What Adults Need to Know for the 21st Century (Stein, 2000), a framework for adult instruction that is grounded in data gathered from adults on their roles as workers, parents, and community members.  Of the sixteen EFF standards, one specifically addresses numeracy or mathematics: listed under Decision-Making Skills, it is Use Math to Solve Problems and Communicate

 

International Influences: Looking at Adult Numeracy

 

In addition to studying state and national mathematics curriculum frameworks, the ABE Math Frameworks 2001 Development Team considered several numeracy frameworks from other countries, including Australia, the United Kingdom, and the Netherlands, as well as the numeracy framework developed for the Adult Literacy and Lifeskills Survey (ALL), an international, large-scale comparative survey of basic skills in the adult populations of participating countries.

 

The term numeracy is a word that was first used in 1959 in Great Britain and is used more often internationally than in this country.  Numeracy has been described as the mirror image of literacy (Crowther Report, 1959) and is often thought to deal just with “numbers.”  But since the 1980’s, work by adult educators in Australia, the UK, and other countries, has expanded the notion that numeracy refers just to the ability to perform basic calculations.  For example, in the Australian curriculum frameworks, numeracy denotes the ability to perform a wider range of math skills, such as measuring and designing, interpreting statistical information, and giving and following directions, as well as using formulas and other advanced topics to pursue further knowledge. Moreover, numeracy and literacy are presented as interconnected and on an equal footing.  The frameworks are written so as to address the purposes for learning mathematics and do not proceed from a school-based mathematics curriculum model so much as looking at the mathematics that is used in the context of adult lives.  The Massachusetts ABE Curriculum Frameworks for Mathematics and Numeracy incorporate some of these ideas in the current revision.


What is Numeracy?  A Definition of Numerate Behavior

 

For purposes of this framework, the following definition is incorporated for describing numeracy and what it means to be a numerate adult:

 

 

 

Numerate behavior involves:

 

Managing a situation or solving a problem in a real context

everyday life

work

societal

further learning

 

by responding

identifying or locating

acting upon

interpreting

communicating about

 

to information about mathematical ideas

quantity and number

dimension and shape

pattern and relationships

data and chance

change

 

that is represented in a range of ways

objects and pictures

numbers and symbols

formulae

diagrams and maps

graphs

tables

texts

 

and requires activation of a range of

enabling knowledge, behaviors, and processes.

mathematical knowledge and understanding

mathematical problem-solving skills

literacy skills

beliefs and attitudes.

 

 

 

 

Source:  Gal, I., van Groenestijn, M., Manly, M., Schmitt, M.J., and Tout, D. (1999). Adult Literacy and Lifeskills Survey Numeracy Framework Working Draft. Ottawa: Statistics Canada.

 

 


How to use This Document (Teacher's Guide)

 

The Mathematics Frameworks presents four learning strands: Number Sense; Patterns, Functions, and Algebra; Statistics and Probability; Geometry and Measurement which are described beginning on page 16 (in the Section on Content Strands and Learning Standards.) In order to present a document that makes sense practically, as well as theoretically, the Outline of Learning Levels on page 21 presents each of the strands and their standards at six performance levels:

§         Level 1: Beginning Adult Numeracy

§         Level 2: Beginning ABE Mathematics

§         Level 3: Intermediate ABE Mathematics

§         Level 4: Pre-GED/ABE Mathematics

§         Level 5: ASE/GED Mathematics

§         Level 6: ASE/Bridge to College Mathematics

 

At each level the strands are given in a chart, as shown below.

 

 Level      ŽLevel 1: Beginning Adult Numeracy

Strand       Ž Number Sense

Learners engage in problem solving within adult contextual situations by communicating, reasoning, and connecting to:

 

Standard     Ž

Standard 2P-3. Recognize and use algebraic symbols to model mathematical and contextual situations

 

 

 

Benchmark: At this level an adult will be expected to:

Enabling Knowledge and Skills

Examples of Where Adults Use It

Benchmark          Ž

 

 

 

Assessment

(See page 10)

Ž

 

2P-3.4 Read and understand positive and negative numbers as showing direction and change.

 

 

 

Assessed by 3P-3.7

2P-3.4.1 Know that positive refers to values greater than zero

 

2P-3.4.2 Know that negative refers to values less than zero

 

2P-3.4.3 Use a horizontal or vertical number line to show positive and negative values

Reading thermometers

 

Riding an elevator below ground level

Staying "in the black" or going "into the red" on bill paying

 

 

2P-3.5 Use a number line to represent the counting numbers.

2P-3.5.1 Demonstrate an understanding that a horizontal number line moves from left to right using lesser to greater values

 

Reading and interpreting scales

 

 

 

 

Ż Enabling skill

 Ż Application

 

Benchmark Column (e.g. At this level an adult will be expected to:)

Benchmarks describe the set of skills learners need to develop and achieve in order to meet the more broadly stated standards.  By providing more detailed information on the specific skills and contexts for learners to meet the standard, benchmarks show teachers and learners what a standard “looks like” at each of the six levels.

 

The strands and standards are arranged by performance levels so that each level can build on the previous ones. At each level, the four strands and their standards are outlined with the skills appropriate for that level.  The skills defined at each level are ones to be achieved while working through the level.  The teacher can use the frameworks as a curriculum guide. Each level builds on the previous levels, so it is recommended that teachers familiarize themselves not only with the level of their own class, but with the preceding levels as well.

 

Enabling Knowledge and Skills Column

The study of mathematics is developmental, but many adult learners have gaps in their learning of math.  At times a learner may struggle with a skill because he or she has not grasped an enabling skill on which it is based.   To present problems and practice with a skill, we must first lay the proper groundwork. Since not all adult education teachers have experience teaching math at an elementary level, the skills needed for the development of each performance skill are outlined.

 

Examples of Where Adults Use It Column

Teaching mathematics to adults is different than teaching it to children. As stated in the Common Chapters for the Massachusetts Adult Basic Education Curriculum Frameworks, “Adult learners value education and the power it has, but they rarely see it as an end in and of itself.  Rather, education is seen as a means to other kinds of opportunities and achievements.”[1] Adult learners need to know that what they are learning in the classroom is relevant to the lives and goals outside of the classroom.  For this reason, we have included an application for each skill by giving an example of using the skill in an adult context.

 

It is our expectation that this format will be a useful tool for:

 

§         Lesson planning

§         Curriculum development

§         Presenting practical applications for adult use of the math skills

§         Assessing student math levels for placement, informal classroom instruction, and for pre- and post-test assessment

§         Connecting pre- and post-test assessment to curriculum and instruction

 

The standards and benchmarks for each level are ambitious. They set the bar to be reached by learners, not the expectation of what is covered in a given class in a given year. However, the Framework does assume that the teaching of numeracy and mathematics be given a significant amount of time and attention in a program’s class offerings and curriculum.

 

Mathematical understanding progresses from the concrete (counting two groups of blocks) to the representative (adding numbers presented in pictorial or verbal problems) to the abstract (using symbols and graphs).  Presenting adults with problems or situations that allow them to develop their own approach to an inquiry model gives learners opportunities to talk about, write about, and represent math situations.  During such inquiry, a learner can experience this progression in his or her own thinking.   This affords an opportunity to see interconnections within math and between math and other disciplines.

 

The numbering system used with the Standards and benchmarks was developed so the specific benchmarks or enabling skills can be referred to (e.g. in a lesson plan, curriculum, or scope and sequence). In the number 2P-3.4.1, for example, the system is as follows:

 

 

 

How to use This Document in

Connecting Curriculum, Instruction, and Assessment

 

The University of Massachusetts Center for Educational Assessment, working with the Adult and Community Learning Services of the Massachusetts Department of Education, has developed an assessment to measure adult learners’ skills as outlined in the Massachusetts ABE Curriculum Framework for Math and Numeracy. 

 

The ABE Curriculum Framework for Math and Numeracy is not an end in itself but a part of the broader goal of aligning curriculum, instruction and assessment.  To this end, Adult and Community Learning Services and ABE practitioners have worked closely with the University of Massachusetts’ Center of Educational Assessment to develop a math and numeracy assessment that is designed to measure the skills outlined in the Framework.  This assessment will be capable of measuring more accurately and capturing more comprehensively, the skills that adult learners have acquired or need to acquire through the instruction provided in adult basic education classes.   Both the ABE Curriculum Framework for Math and Numeracy and the results of the new math assessment are valuable tools that should be used to inform classroom instruction.

The Frameworks provide teachers with Standards, Benchmarks and Examples that describe what it is adult learners need to know and be able to do, while the new math assessment will help identify how well students are acquiring the skills and knowledge as well as their ability to apply the skills and knowledge outlined in the Frameworks.  By using the Frameworks and assessment results to inform instruction, programs and teachers can achieve the goal of aligning curriculum, instruction and assessment.

 

The skill numbers in the frameworks directly correspond with the skill numbers on the math test.  The skills within each level are assessed at that level unless otherwise noted as shown in the example on page 8, and below.

 

 

 

At this level an adult will be expected to:

Enabling Knowledge and Skills

Examples of Where Adults Use It

Skill           Ž

 

 

Assessment Ž

(See page 11)

2P-3.4 Read and understand positive and negative numbers as showing direction and change

 

Assessed by 3P-3.7

2P-3.4.1 Know that positive refers to values greater than zero

 

2P-3.4.2 Know that negative refers to values less than zero

 

2P-3.4.3 Use a horizontal or vertical number line to show positive and negative values.

Reading thermometers

 

Riding an elevator below ground level

Staying "in the black" or going "into the red" on bill paying

 

 

 

The math frameworks endeavor to expose students at all levels to the four strands: N-Number Sense; P-Patterns, Functions, and Algebra; S-Statistics and Probability; and G-Geometry and Measurement with the realization that some material introduced at one level might need to be expanded on in a later level.  For this reason, there is overlap between the levels.  Positive and negative numbers, for example, may be discussed with basic applications at Level 2, but the learner will not be expected to demonstrate knowledge and skill with the topic until Level 3 as shown above with the reference to 3P-3.7

 

Adult learners come to our classes with a wide range of prior learning, but often they have gaps in their knowledge. A student who is well-read may be familiar with interpreting graphs and tables, but struggle to understand the principles of area and volume relating to home decor.  Some adults who are very capable with computation may have developed a mental block against algebraic notation.   The Frameworks, therefore; encourages multi-level exploration within the classroom while more clearly defining skills to be demonstrated at each assessment level.

 

 

 

 


Core Concepts

 

 

 

Adults develop numeracy skills and mathematical fluency through actions involving problem solving, reasoning, decision-making, communicating and connecting in curriculums that link to their own mathematics knowledge, experiences, strategies and goals. Fluency is enhanced by instruction that requires learners to strive for a constant interplay of accuracy, efficiency and flexibility in their work.

 

 

Problem solving is an important key to independence for adults.  Problem solving enables learners to:

 

§         reach their own solutions,

§         generalize problem solving strategies to a wide range of significant and relevant problems,

§         use appropriate problem solving tools including real objects, calculators, computers, and measurement instruments.

 

Mathematical reasoning provides adults with access to information and the ability to orient themselves to the world.  It enables learners to:

 

§         validate their own thinking and intuition,

§         pose their own mathematical questions,

§         evaluate their own arguments, and

§         feel confident as math problem solvers.

 

Success as an adult involves decision-making as a parent, citizen and worker.  Mathematical decision-making enables learners to:

 

§         determine the degree of precision required by a situation,

§         define and select data to be used in solving a problem, and

§         apply knowledge of mathematical concepts and procedures to figure out how to answer a question, solve a problem, make a prediction, or carry out a task that has a mathematical dimension.

 

The ability to communicate mathematically means having an expanded voice and being heard in a wider audience.  Mathematical communication enables learners to:

 

§         interact with others,

§         define everyday, work-related or test-related mathematical situations using concrete, pictorial, graphical or algebraic methods,

§         reflect and clarify their own thinking about mathematical outcomes, and

§         make convincing arguments and decisions based on discussion and reflection.

 


Connecting everyday life with mathematics helps adults access essential information and make informed decisions.  Mathematical connections enable the learner to:

 

§         view mathematics as an integrated whole that is connected to past learning, the real world, adult life skills, and work-related settings, and

§         apply mathematical thinking and modeling to solve problems that arise in other disciplines, as well as in the real world and work-related settings.

 

The thinking skills of accuracy, efficiency and flexibility are essential tools for success in a rapidly changing world.  In mathematics, such fluency enables the learner to:

 

§         develop a sense of the appropriate ballpark for a solution,

§         be able to keep track of how a solution is reached,

§         develop the practice of double-checking results,

§         use robust strategies that work efficiently for solving different kinds of problems, and

§         take more than one approach to solving a class of problems.

 

 

 

 


Guiding Principles

 

The Guiding Principles summarize a broad vision of adult numeracy that guides all instructional efforts.  They address the specific and unique characteristics of both the subject of math and the adult mathematics learner.

 

Curriculum: A real life context for mathematical concepts and skills across mathematical content areas is the driving force behind curriculum development.  Within that setting, mathematics instruction transcends textbook-driven computation practice to include experiences in understanding and communicating ideas mathematically, clarifying one’s thinking, making convincing arguments, and reaching decisions individually and as part of a group.

 

Assessment: Mathematical assessment occurs in a framework of purposes for learning relevant to the successful performance of a variety of everyday adult mathematical tasks and the pursuit of further education.  Learners are active partners in identifying these purposes, in setting personal learning goals, and in defining measures of success.

 

Equity: Adult numeracy learners at every level of instruction have access to all mathematics domains (number sense, patterns, relations and functions, geometry and measurement, probability and statistics).

 

Life Skills: Adult mathematics literacy education strives to create instruction that helps learners become less fearful and more confident in tasking risks, voicing their opinions, making decisions, and actively participating in today’s world.

 

Teaching: Mathematics instruction mirrors real-life activity through the use of both hands-on and printed instructional materials, group as well as individual work, and short-term and long-term tasks.

 

Technology: Adult numeracy instruction offers all learners experience with a broad range of technological tools (such as calculators, rulers, protractors, computer programs, etc.) appropriate to a variety of mathematical settings.

 


 

 

Habits of Mind

 

Habits of Mind are practices that strengthen learning.  In numeracy instruction, habits of mind involve reflection, inquiry and action.  They are developed by teachers and programs that offer challenging mathematical tasks in settings that support learners’ curiosity, respect for evidence, persistence, ownership, and reflection about what is learned and how it is learned.  These habits flourish in instructional environments that favor uncovering mathematical concepts and connections rather than mimicking algorithms.

 

The following chart defines the habits of mind crucial to adults’ numeracy development.  It also lists questions students and teachers may share to assess their own mathematical habits.

 

 

Habits of Mind
Habit
Learner Question
Curiosity

A curious and open attitude towards the presentation of new ideas or ways of approaching problems, even when confusion arises, facilitates learning.

 

 

 

Do I ask “Why,” “How,” or “What If” questions?

Respect for Evidence

To evaluate reasoning, it is essential to see evidence.  Reasoning is demonstrated by the appropriate use of verbal and visual mathematical evidence to support solutions and ideas.

 

 

Do I listen carefully for others’ use of

evidence, and do I include evidence to support my solutions and ideas?

Persistence

Solutions in mathematics are not always apparent at first glance.  Persistence is necessary to work through challenging problems that stretch our understanding.

 

 

 

Do I keep going when I feel lost or discouraged while solving problems?

Ownership

What we own has meaning for us, and taking ownership of our work encourages us to do our best.  Although someone else might assign a mathematical task to us, we must treat the problem as important to us, as though it was our own, if we are to produce high quality work and learn from experience.

 

 

 

 

In what ways do I show that my work is purposeful and important to me?

Reflection

To become an autonomous learner, it is necessary to think about how our learning happens.  We need to consider how we learn from mathematical experiences.

 

 

 

Do I notice and analyze how and what I learn?

 

 

 

 

Content Strands and Learning Standards

 

 

Following is a chart that outlines the content strands and learning standards for the Mathematics and Numeracy curriculum framework.  After this chart, you will find a more detailed explanation of each content strand and the learning standards that go along with it.

 

 

Strands

Standards  

Learners will demonstrate the ability to…

 

Number Sense

 

 

N-1  Represent and use numbers in a variety of equivalent

         forms in contextual situations

N-2  Understand meanings of operations and how they relate

         to one another

N-3  Compute fluently and make reasonable estimates

 

 

Patterns, Functions and Algebra

 

 

P-1  Explore, identify, analyze, and extend patterns in

        mathematical and adult contextual situations

P-2  Articulate and represent number and data relationships

        using words, tables, graphs, rules, and equations

P-3  Recognize and use algebraic symbols to model

        mathematical and contextual situations

P-4  Analyze change in various contexts

 

 

Statistics and Probability

 

 

S-1  Collect, organize, and represent data

S-2  Read and interpret data representations

S-3  Describe data using numerical descriptions, statistics, and

        trend terminology

S-4  Make and evaluate arguments and statements by applying

        knowledge of data analysis, bias factors, graph

       distortions, and context

S-5   Know and apply basic probability concepts

 

 

Geometry and Measurement

 

 

G-1  Use and apply geometric properties and relationships to

         describe the physical world and identify and analyze the

         characteristics of geometric figures

G-2  Use transformations and symmetry to analyze

         mathematical situations

G-3  Specify locations and describe spatial relationships using

         coordinate geometry and other representational systems

G-4  Understand measurable attributes of objects and the

         units, systems, and processes of measurement and apply

         appropriate techniques, tools, and formulas to determine

         measurements

 

 

 

 

The Strand Number Sense

 

Number Sense is the foundation of numeracy.  Sound number sense enables us to interpret and represent the world in which we live.  It is evident in all we do, whether in complex examples such as the Gross National Product, basic issues such as the family budget, or as personal as a blood pressure reading.  Mathematical intuition grows with a strong basic understanding of numbers and, with that, our ability to do mathematical problem solving.

 

To be efficient workers or consumers in today's world, adults must have a strongly developed conceptual understanding of arithmetic operations, as well as the procedural knowledge of computation and number facts.  They must be able to perceive the idea of place value and be able to read, write, and represent numbers and numerical relationships in a wide variety of ways.  Simple paper-and-pencil computation skills are not enough.  Adults must be able to make decisions regarding the best method of computation (mental math, paper-and-pencil, or calculator/computer) to use for a particular situation.  Knowledge of numbers, operations and computation must include both a well-developed number sense and the ability to use basic mathematics-related technologies.

 

Number sense promotes accuracy in estimation and flexibility and efficiency in mental math. While calculators and computers are used to do most of the complex computations in today’s world, the ability to estimate is critical for lifelong learners. Adults use informal measurements in life skill activities such as cooking, shopping, buying clothes, or estimating the time required for daily tasks.  Estimation is a valuable skill for checking the reasonableness of computation or accuracy in problem solving, and is an aid in timed-test situations such as the GED.  It builds on adult experience and knowledge.  Good estimators use a variety of strategies and techniques for computational estimation that can be explored and shared by learners.

 

 

Learners engage in problem solving within adult contextual situations by communicating, reasoning, and connecting to:

 

§         Standard N-1. Represent and use numbers in a variety of equivalent forms in contextual situations,

§         Standard N-2. Understand meanings of operations and how they relate to one another, and in

§         Standard N-3. Compute fluently and make reasonable estimates.

 

 

The Strand Patterns, Functions, and Algebra

 

Mathematics has been defined as the study of patterns.  Learning to recognize, analyze, describe, and represent patterns and number relationships connects math to the world and helps us to appreciate fully the intrinsic value of such pleasures as poetry, art, music, and science.  Math concepts formerly taught only in basic algebra courses are increasingly part of the culture and vocabulary of modern life. Headlines and news reports speak of exponential growth of the national debt, a variable rate mortgage, or a balanced budget, while medical literature uses terms like “HIV-positive,” or “RH-negative.”

 

Being able to see and use patterns has been identified as a fundamental skill needed for developing mathematical understanding.  The Patterns, Functions, and Algebra strand is positioned after the Number Sense strand because of the importance of building pre-number skills such as patterning which, in turn, enable adult learners to learn multiplication tables and number relationships necessary for efficient and fluent computation skills.  The strand also encompasses skills that are necessary for developing concepts in the Data and Geometry and Measurement strands.

 

Algebra serves as a bridge between arithmetic and more broadly generalized mathematical situations.  These generalizations can be expressed in words, tables and charts, the notation of formulas, and graphs.  Life experience has afforded adult basic education learners with a broad base of real-world ties that can be readily linked to the concepts of equation, function, variable, and graph.  From baby formulas to chemical formulas, algebra offers a succinct way to define real-world situations that can aid adults in the home and in the workplace.

 

Algebra impacts the competency of workers, parents and citizens, and algebraic thinking skills are crucial if adults are to compete in the global economy.  Workplace skills requiring competencies in “information,” “systems,” and “technology” stress the need for organizing, interpreting and communicating information and employing computers as a tool for those tasks, as well as the ability to “discover a rule or principle underlying the relationship between two or more objects and apply it in solving a problem.”  Identifying and expressing pattern, relation and function are the algebraic skills imbedded within these competencies.  

 

 

Learners engage in problem solving within adult contextual situations by communicating, reasoning, and connecting to:

 

§         Standard P-1. Explore, identify, analyze, and extend patterns in mathematical and adult contextual situations,

§         Standard P-2. Articulate and represent number and data relationships using words, tables, graphs, rules, and equations, 

§         Standard P-3. Recognize and use algebraic symbols to model mathematical and contextual situations, and

§         Standard P-4. Analyze change in various contexts.

 

 

 

 


The Strand Statistics and Probability

 

The Statistics and Probability strand links numeracy and literacy learning.  Numbers, logical reasoning, and texts interweave to describe phenomena visually, numerically and verbally in what we term data, which is the heart of this strand. 

 

Data is a wide-ranging topic that touches on many areas of academic study and tells us much about our world.  For instance, we learn about preferences, predilections and group characteristics when we read and interpret data.  We learn about the power of evidence as we develop the skills to make statements and evaluate arguments based on data.  We learn the power of the question and the framer of the question when we collect and represent data, and we learn that sometimes true, sometimes false, pictures are created when we compress data into statistics. Data is a powerful descriptive tool.

 

So powerful is data that agencies of authority often use it to generate, promote and, sometimes, evaluate decisions.  Citizens, therefore, must understand the ways of data in order to exercise their collective and individual intelligence by responding to the expanding presence of this dense expression of information.  

 

The learning standards in the Statistics and Probability strand provide adult learners with the tools for dealing with data.

 

 

Learners engage in problem solving within adult contextual situations by communicating, reasoning, and connecting to:

 

§         Standard S-1. Collect, organize and represent data,

§         Standard S-2. Read and interpret data representations,

§         Standard S-3. Describe data using numerical descriptions, statistics and trend terminology,

§         Standard S-4. Make and evaluate arguments or statements by applying knowledge of data analysis, bias factors, graph distortions and context, and

§         Standard S-5. Know and apply basic probability concepts

 

 

 

 

The Strand Geometry and Measurement

 

Geometry and measurement help us represent in an orderly fashion what we see in our world. Whether we are cooking or cartooning, shopping or shipping, painting a canvas or a wall, designing an addition for a house or a play yard for preschool, we continually bump up against these mathematical organizers. Lifelong learners should know and understand these interconnected and symbiotic mathematical domains.

 

Adult learners who attend basic mathematics classes at any level share a wealth of pragmatic experience surrounding geometric and spatial concepts.  They have probably built a bookcase, laid out a garden, applied wallpaper or tiled a floor, all the while discovering informally the rules which formally govern the study of geometry itself

 

Geometry and measurement often spark a renewed interest in mathematics for those students who have been turned off for some reason or heretofore have felt unsuccessful with mathematics learning. Investigating problems that involve geometry and measurement broadens all students' mathematical understanding and engages them as they explore mathematical ideas.

 

Hands-on, interactive investigations using nonstandard and standard units help adult basic education students develop an understanding of the many measurable attributes of physical objects. Measurement sense including length, time, temperature, capacity, weight, mass, area, volume, and angle will benefit from this approach. This realistic approach helps build an accessible measurement vocabulary and a meaningful comprehension of what it means to measure.

 

 

 

Learners engage in problem solving within adult contextual situations by communicating, reasoning, and connecting to:

 

§         Standard G-1. Use and apply geometric properties and relationships to describe the physical world and identify and analyze the characteristics of geometric figures,

§         Standard G-2. Use transformations and symmetry to analyze mathematical situations,

§         Standard G-3. Specify locations and describe spatial relationships using coordinate geometry and other representational systems,

§         Standard G-4. Understand measurable attributes of objects and the units, systems, and processes of measurement and apply appropriate techniques, tools and formulas to determine measurements.

 

 


 

 

Outline of Learning Levels

 

Level 1. Beginning Adult Numeracy

See “How to Use This Document (Teacher’s Guide) and (Connecting Curriculum, Instruction and Assessment),” pages 8-10.

At this time, the Massachusetts ABE Test for Math does not assess students’ knowledge at Level 1.

 

Strand:  Number Sense

Learners engage in problem solving within adult contextual situations by communicating, reasoning, and connecting to the following standards:

 

Standard 1N-1. Represent and use numbers in a variety of equivalent forms in contextual situations

Benchmark: At this level an adult will be expected to:

Enabling Knowledge and Skills

Examples of Where Adults Use It

1N-1.1 Count reliably forward and backward up to 20 items.

 

 

 

1N-1.1.1 Demonstrate an understanding that if items are rearranged, the numbers stay the same

 

1N-1.1.2 Count forward and backward from ten or less

 

1N-1.1.3 Count forward and back from 11-20

Counting children in a group to make sure no one is missing

 

Counting dollar bills to pay for a purchase

 

Counting items at the grocery express line

 

Using the remote channel tuner for a TV

 

Watching a digital timer on a microwave count down the time

1N-1.2 Recognize odd and even numbers up to 100.

 

1N-1.2.1 Demonstrate an understanding that even numbers represent amounts that can be paired

 

1N-1.2.2 Demonstrate an understanding that odd numbers represent amounts that when paired have one remaining

Identifying the number of possible couples at a dance or a dinner party

 

Recognizing when house numbers go up in odd or even numbers

 

Finding a room in a hospital or hotel

 

1N-1.3 Read, write, and compare numbers from 0 up to 100.

1N-1.3.1 Explain how the position of a digit signifies its value

 

1N-1.3.2 Demonstrate an understanding of directionality in reading numbers and comparisons from left to right.

 

1N-1.3.3 Explain what each digit in a two-digit number represents, including the use of zero as a place holder

 

1N-1.3.4 Distinguish between greater than and less than, and recognize between-ness when comparing numbers

Telling which address falls in a given block, knowing the first number on the block

 

Writing a money order for a whole dollar amount (no change)

1N-1.4 Using a 100 chart, skip count by 2’s, 5’s, and 10’s.

 

1N-1.4.1 Know the multiples of 2, 5, and 10 to 100

Counting nickels and dimes

 

Finding the amount of money in a small stack of $2, $5, or $10 bills

 

Standard 1N-2. Understand meanings of operations and how they relate to one another

Benchmark: At this level an adult will be expected to:

Enabling Knowledge and Skills

Examples of Where Adults Use It

1N-2.1 Demonstrate an understanding of different meanings of addition (e.g. counting on, combining) of numbers up to 20.

 

 

1N-2.1.1 Add by counting on (e.g. four objects plus three objects can be totaled by counting on three more than four (or five, six, seven), or counting on four more than three (or four, five, six, seven)

Demonstrate an understanding that combining two amounts into one larger total is adding.

 

1N-2.1.2 Use objects, pictures, or tallies to show addition

 

1N-2.1.3 Demonstrate the ability to visualize grouping of objects

Paying a twelve dollar amount by using a ten dollar bill and two ones

 

Figuring hours of work or sleep by using fingers to count

 

Figuring hours of sleep by joining the hours slept before and after midnight

 

 

1N-2.2 Demonstrate an understanding of subtraction as taking away or separating from numbers up to 20.

 

1N-2.2.1 Subtract by counting back (e.g. taking away four of seven objects by counting back--six, five, four, three)

 

Figuring how much of $20 is left while paying out $14

 

1N-2.3 Demonstrate an understanding of how addition and subtraction relate to each other.

1N-2.3.1 Add back to check subtraction (e.g. 10 – 6 = 4, 6 + 4 = 10)

Making change (e.g. for a twenty dollar bill, by counting on from the price to $20)

 

Standard 1N-3. Compute fluently and make reasonable estimates

Benchmark: At this level an adult will be expected to:

Enabling Knowledge and Skills

Examples of Where Adults Use It

1N-3.1 Know all pairs of numbers with a total of 10.

1N-3.1.1 Combine amounts that add to 10 without having to count

Adding using mental math

1N-3.2 Add numbers with totals to 20.

1N-3.2.1 Use the operation of addition and related vocabulary (e.g., add, sum of, total, plus, etc.)

Calculating totals, e.g., five reams of paper in a full box plus three packs on the shelf

1N-3.3 Subtract single-digit numbers from numbers up to 20.

 

 

 

 

1N-3.3.1 Use the operation of subtraction and related vocabulary (e.g. difference, take away, less than)

 

1N-3.3.2 Know subtraction facts for pairs of numbers with totals to 10 (e.g. 10 – 6 = 4)

 

1N-3.3.3 Know how to add back to check subtraction (e.g. 10 – 6 = 4, and 6 + 4 = 10)

Working out the shortfall in numbers, e.g. eggs for a recipe, plants to fill a display tray, cups to serve visitors

 

 

 

 

 

 

1N-3.4 Double whole numbers to 10.

1N-3.4.1 Know doubles of numbers to 10

Finding the cost of tickets for an amusement ride for two children.

 

Planning fare for round trip subway travel at $1 a token

1N-3.5 Finding half of whole numbers up to 20.

1N-3.5.1 Know doubles of numbers to 10

 

1N-3.5.2 Demonstrate the ability to separate amounts in two piles

Sharing the cost of pizza between two people.

1N-3.6 Use a calculator to check calculations using whole numbers.

 

 

1N-3.6.1 Identify the signs for addition, subtraction, equals

 

1N-3.6.2 Recognize the numerals 0 – 9

 

1N-3.6.3 Demonstrate an understanding of the order to key in numbers and operators

 

1N-3.6.4 Demonstrate the ability to clear the display, and recognize that this should be done before starting a new calculation

Finding the total score for a card game

 

Finding the total price of 3 items ordered from a menu

 

Finding the change for a purchase

 

 

 

Strand: Patterns, Functions, and Algebra

Learners engage in problem solving within adult contextual situations by communicating, reasoning, and connecting to the following standards:

 

Standard 1P-1. Explore, identify, analyze, and extend patterns in mathematical and adult contextual situations

Benchmark: At this level an adult will be expected to:

Enabling Knowledge and Skills

Examples of Where Adults Use It

1P-1.1 Sort up to 20 objects or lists by color, shape, number, letter, or size.

 

1P-1.1.1 Identify attributes of objects and classify such as shape, size, number and/or size

Sorting laundry

 

Sorting bottles for recycling facility

 

Sorting telephone numbers by area code and figuring which are long distance calls

 

Shelving stock

1P-1.2 Recognize and create simple repeating patterns (e.g. color, rhythmic, shape, number, and letter) and identify the unit being repeated.

1P-1.2.1 Count forward and back by 1's from 1 to 20

 

1P-1.2.2 Read and write whole numbers from 1 to 100

 

1P-1.2.3 Skip count by 2’s, 5’s, and 10’s from 1 to 100

 

1P-1.2.4 Identify odd and even

Knowing on which side of the hall or street a room or a house is

 

Counting pennies or 1 dollar bills

 

Counting nickels or five dollar bills

 

Counting things 2 at a time

 

Counting dimes or 10 dollar bills

 

Counting beats in music

 

Designing a necklace and describing the assembly rule

 

Laying tile on a floor

 

Standard 1P-2. Articulate and represent number and data relationships using words, tables, graphs, rules, and equations

Benchmark: At this level an adult will be expected to:

Enabling Knowledge and Skills

Examples of Where Adults Use It

1P-2.1 Explore basic number relationships (e.g., find all the ways numbers to 10 can be written as sums).

 

1P-2.1.1 Know all pairs of numbers with totals to 10

 

1P-2.1.2 Decompose numbers into sums of smaller numbers 17 = 10 + 7

 

1P-2.1.3 Demonstrate an understanding that 2 + 3 and 3 + 2 yield the same sum; therefore, they are counted once in a list

Playing card games

 

Preparing for further study

 

Standard 1P-3.  Recognize and use algebraic symbols to model mathematical and contextual situations

Benchmark: At this level an adult will be expected to:

Enabling Knowledge and Skills

Examples of Where Adults Use It

1P-3.1 Use and interpret  +, -, and = to represent combining, taking away, and equivalence.

1P-3.1.1 Demonstrate recognition that + represents operations of combining

 

1P-3.1.2 Demonstrate recognition that  - represents operations of separation

 

1P-3.1.3 Demonstrate recognition that = represents vocabulary such as: is equal to, is the same as, and gives you.

 

Using a four-function calculator to find the total whole dollar amount of a grocery bill

 

Using a calculator to find how much change you get from a $20.00 bill

 

Helping children with homework.


 

1P-3.2 Understand simple number sentences such as: 9 + 1 = 10 and ___ + 5 = 10  and 8 - 3 = ___ where the ___ represents a missing amount.

 

1P-3.2.1 Demonstrate an understanding that an underlined blank space represents a missing value in addition and subtraction equations

Helping children with homework.

 

Test taking when seeking employment

1P-3.3 Make statements of inequality e.g.:

2 is less than 10

10 is greater than 8

99 is less than 100

6 + 5 ¹ 10

1P-3.3.1 Explain that directionality of reading numbers and expressions moves from left to right

Helping children with homework

 

Test-taking when seeking employment

 

Standard 1P-4. Analyze change in various contexts

Benchmark: At this level an adult will be expected to:

Enabling Knowledge and Skills

Examples of Where Adults Use It

1P-4.1 Describe qualitative change, such as lengthening or decreasing hours of daylight, or rising or falling of temperature over time.

 

1P-4.1.1 Observe physical change over time

 

1P-4.1.2 Compare changes which go up or increase with those which go down or decrease

Discussing weather patterns

 

Describing seasons, daylight savings time, or tides

 

 

Strand: Statistics and Probability

Learners engage in problem solving within adult contextual situations by communicating, reasoning, and connecting to the following standards:

 

Standard 1S-1. Collect, organize and represent data

Benchmark: At this level an adult will be expected to:

Enabling Knowledge and Skills

Examples of Where Adults Use It

1S-1.1 Gather data to answer posed questions.

1S-1.1.1 Demonstrate that observing and asking relevant questions and counting gathered responses can produce answers

Planning a neighborhood party

 

Planning what kind of pizza or sandwiches to order for an employee luncheon

1S-1.2 Group objects or responses by a single criterion.

1S-1.2.1 Demonstrate an understanding of the concept of categories by grouping items by shape, size, color, or yes or no responses

 

1S-1.2.2 Know how to count each category for subtotals up to 20

Keeping track of who will or will not attend party

 

Sorting stock by size

 

 

Standard 1S-2. Read and interpret data representations

Benchmark: At this level an adult will be expected to:

Enabling Knowledge and Skills

Examples of Where Adults Use It

1S-2.1 Identify graphs in available resources.

1S-2.1.1 Explain how graph is a visual representation

Reading a graph in an ad or poster


 

1S-2.2 Extract simple information from a list or two-column table.

 

1S-2.2.1 Identify how lists can be ordered in different ways (e.g. alphabetically, numerically, or randomly)

 

1S-2.2.2 Make a 1-1 correspondence within a row in charts with two columns

Checking items against a stock list

1S-2.3 Read values on a bar graph up to 100.

1S-2.3.1 Skip-count by 2, 5, or 10

 

1S-2.3.2 Demonstrate an understanding and that the height of the bar is equal to the amount on the axis across from it

Reading a nutrition graph in a health poster

1S-2.4 Make comparative statements about relative values on a bar graph.

 

1S-2.4.1 Explain how comparative statements such as greater than or less than can be made based on the height of the bars

Conversing about information contained in newspapers and magazines

1S-2.5 Connect simple graphs and tables to arguments or statements.

1S-2.5.1 Demonstrate how to locate titles

 

1S-2.5.2 Explain that titles indicate subject matter

Reading a chart or graph in a health pamphlet.

 

Standard 1S-3. Describe data using numerical descriptions, statistics, and trend terminology

 

 

 

Not applicable at this level.

 

 

Standard 1S-4. Make and evaluate arguments and statements by applying knowledge of data analysis, bias factors, graph distortions, and context

 

 

 

Not applicable at this level.

 

 

 

Standard 1S-5. Know and apply basic probability concepts

Benchmark: At this level an adult will be expected to:

Enabling Knowledge and Skills

Examples of Where Adults Use It

1S-5.1 Discuss events as likely or unlikely.

1S-5.1.1 Develop an understanding that while some events are impossible, some are certain to happen, and in other events some are more likely to occur than others

Deciding whether or not to carry an umbrella

 

Making the call when flipping a coin

 

 

 


Strand: Geometry and Measurement

Learners engage in problem solving within adult contextual situations by communicating, reasoning, and connecting to the following standards:

 

Standard 1G-1. Use and apply geometric properties and relationships to describe the physical world and identify and analyze the characteristics of geometric figures

Benchmark: At this level an adult will be expected to:

Enabling Knowledge and Skills

Examples of Where Adults Use It

1G-1.1 Recognize, name, describe and compare common basic 2-D shapes (square, circle, rectangle, triangle) using everyday language (straight, curved, etc.).

1G-1.1.1 Identify the names of shapes

 

1G-1.1.2 Demonstrate an understanding that shape is independent of size and orientation

 

1G-1.1.3 Show two triangles or two rectangles in different positions and sizes

Identifying things (e.g. a curved road, a straight highway, a rotary)

 

Recognizing the shape and meaning of a triangular yield sign and other shapes in buildings and everyday structures

1G-1.2 Understand the conventions for naming a rectangle by its length and width.

1G-1.2.1 Demonstrate an understanding that the longer side is called the length.

 

1G-1.2.2 Demonstrate an understanding that the shorter side is called the width.

Purchasing window shades or coverings

 

Describing a rectangular photo or frame; or a room size by its length and width

 

Standard 1G-2. Use transformations and symmetry to analyze mathematical situations

Benchmark: At this level an adult will be expected to:

Enabling Knowledge and Skills

Examples of Where Adults Use It

1G-2.1 Estimating where a line of symmetry falls in a basic shape.

1G-2.1.1 Demonstrate an understanding concepts of sameness or half-ness

 

1G-2.1.2 Divide a figure in half

Cutting a cake in half

 

Folding objects

 


Standard 1G-3. Specify locations and describe spatial relationships using coordinate geometry and other representational systems

Benchmark: At this level an adult will be expected to:

Enabling Knowledge and Skills

Examples of Where Adults Use It

1G-3.1 Use the cardinal directions to describe where one location is relative to another.

1G-3.1.1 Know the convention that is North is the opposite direction from South and that East and West are opposite

 

1G-3.1.2 Explain the difference between vertical and horizontal

Reading a road sign or route sign which uses north or south, east or west

 

Making a simple map with cardinal directions

 

Locating offices, apartments that are labeled with cardinal directions

1G-3.2 Understand and use location prepositions and everyday language of position appropriately.

1G-3.2.1 Know the meaning of terms such as left, right, bottom, top, down, up, behind, over, through, etc.

Assembling a piece of furniture from a diagram

 

Giving oral directions for getting from one place to another

Standard 1G-4. Understand measurable attributes of objects and the units, systems, and processes of measurement and apply appropriate techniques, tools, and formulas to determine measurements

Benchmark: At this level an adult will be expected to:

Enabling Knowledge and Skills

Examples of Where Adults Use It

1G-4.1 Show equivalent amounts of money using different bills and coins.

1G-4.1.1 Know coin & bill names and values

Getting out money to pay at the register

 

Verifying change given at a store

1G-4.2 Read, record, and use date concepts in common formats.

1G-4.2.1 Know the months and corresponding numbers, days of week

Completing forms (birth date, etc.)

 

1G-4.3 Read, record, and understand time of the day.

1G-4.3.1 Count to 60 by 5’s and 10’s

Reading a bus schedule that uses AM and PM

1G-4.4 Read analog and digital clocks.

1G-4. 4.1 Demonstrate an understanding that each hour of digital time is read to 59 minutes

Looking at clock outside a bank and know if one is on time

1G-4.5 Compares familiar quantities, length, mass, capacity, time, temperature, using informal comparative language and methods (e.g. taller, heavier, smallest).

1G-4.5.1 Explain how the suffixes –er, -est, and how, more, less, and too will change the quantity

Sorting by size to organize a kitchen cabinet

 

Understanding a child’s growth chart

1G-4.6 Read a ruler to the nearest whole inch.

1G-4.6.1 Line up the edge of a ruler to measure an object

 

Measuring the length and width of photo

1G-4.7 Begins to develop personal reference points of measure (one’s height, weight).

1G-4.7.1 Demonstrate a general recognition of common heights and weights for women, men and children

Give one’s height or weight on a medical form

1G-4.8 Find the perimeter of rectangles up to 20 units.

1G-4.8.1 Know that the two lengths are of equal measure and the two widths are of equal measure

 

1G-4.8.2 Know that the perimeter of a rectangle is equal to the total of the four sides

Buying weather stripping

 

Buying wood for a picture frame or baseboard

 

Finding the length of fencing around a garden

 

 


Level 2: Beginning ABE Mathematics

See “How to use This Document (Teacher’s Guide) and (Connecting Curriculum, Instruction and Assessment),” pages 8-10.

 

Strand: Number Sense

Learners engage in problem solving within adult contextual situations by communicating, reasoning, and connecting to the following standards:

 

Standard 2N-1. Represent and use numbers in a variety of equivalent forms in contextual situations

Benchmark: At this level an adult will be expected to:

Enabling Knowledge and Skills

Examples of Where Adults Use It

2N-1.1 Count, read, write, order, and compare two and three-digit numbers.

 

2N-1.1.1 Know that the position of a digit signifies its value

 

2N-1.1.2 Know what each digit in a three-digit number represents, including the use of zero as a place holder

 

2N-1.1.3 Count on or back in 10s or 100s starting from any two-digit or three-digit number, up to 1,000

Carrying out a stock inventory

 

Finding items for an order from bin numbers

 

Checking grocery receipt against purchases

 

2N-1.2 Distinguish between odd and even numbers up to 1,000.

 

2N-1.2.1 Recognize that even numbers end in 0, 2, 4, 6, or 8

 

2N-1.2.2 Recognize that odd numbers end in 1, 3, 5, 7, or 9

 

Telling which side of a street a house will be on from its number

 

Knowing on what days lawn watering is permitted under rationing by odd or even house number

2N-1.3 Read, write, and compare halves and quarters of quantities.

 

2N-1.3.1 Know the words, half, fourth and the symbols 1/2, 1/4 

 

2N-1.3.2 Demonstrate an understanding that 1/2 means one group or unit separated into 2 equal parts

 

2N-1.3.3 Demonstrate an understanding that two halves make one whole

 

2N-1.3.4 Demonstrate an understanding that 1/4 means one group or unit separated into 4 equal parts and that four quarters make one whole

 

2N-1.3.5 Demonstrate an understanding that two fourths and one half are equivalent

Sharing money or brownies

 

 

2N-1.4 Use 50% as equivalent for one-half.

2N-1.4.1 Understand that 100% represents the whole of something

 

2N-1.4.2 Understand that 50% means separating a set or dividing an amount into two equal parts

Buying something discounted at 50% off

 

 

2N-1.5 Skip count forward or backward by 2’s, 5’s, or 10’s.

 

 

2N-1.5.1 Know the multiples of 2, 5, and 10

Checking two-sided copies for missing or out of order pages

 

Counting five and ten dollar bills

 

Standard 2N-2. Understand meanings of operations and how they relate to one another

2N-2.1 Demonstrate an understanding of different meanings of addition (counting on, combining) of two- and three-digit numbers.

 

 

 

2N-2.1.1 Know that adding can be done by counting on by ones, tens, or hundreds

 

2N-2.1.2 Demonstrate an understanding that when combining two amounts the total will be the same for   2 + 4   as for   4 + 2 (commutative property)

 

2N-2.1.3 Know that 4 + 2 + 3 gives the

same total as 3 + 2 + 4

 

2N-2.1.4 Demonstrate an understanding that adding zero leaves a number unchanged

Paying an amount in the hundreds using ten dollar bills

 

Checking totals by adding again in a different order.

 

Figuring how many coffees are needed for a group that includes non-coffee drinkers

2N-2.2 Demonstrate an understanding of efficient and flexible strategies of subtraction of two and three digit numbers.

2N-2.2.1 Know that subtracting can be done by counting back by ones, tens, or hundreds

 

2N-2.2.2 Know that subtraction can be used to answer the questions: How much more or less? (Comparing)

 

2N-2.2.3 Demonstrate an understanding that subtracting zero leaves a number unchanged

 

2N-2.2.4 Demonstrate an understanding that having 4 and giving away 2 is not the same as having 2 and giving away 4. (Subtraction is not commutative)

Figuring out how much is left of an amount in the hundreds by counting back as ten dollar bills are paid out

 

Balancing a checkbook

 

Finding the difference between two distances or amounts.

2N-2.3 Demonstrate an understanding of how addition and subtraction relate to each other for numbers up to 1,000.

2N-2.3.1.1 Know how to add back to check, e.g. 10 – 6 = 4  because  6 + 4 = 10

Making change of whole dollar amounts by counting on from the price to the amount given

2N-2.4 Demonstrate an understanding of different meanings of multiplication of numbers up to 12 (repeated addition, grouping, and arrays).

 

2N-2.4.1 Know that multiplication is a shorter way to do repeated addition, (e.g. 3 ´ 4 = 3 + 3 + 3 + 3)

 

2N-2.4.2 Relate skip counting to multiplication

 

2N-2.4.3Know how to use multiplication to find groups of items numbering 2 – 12.

 

2N-2.4.4 Use area models to build arrays to show multiplication

 

2N-2.4.5 Use an area model to demonstrate distributive property by adding two rectangles (e.g. 8 ´ 12 = (8 ´ 10) + (8 ´ 2)

Checking delivery of goods in small batches

 

Finding price of 2 cartons of milk or 6 bottles of soda.

 

Calculating total number (e.g. three days a week for four weeks)

 

Generating results using mental methods of multiplication when solving problems

 

In shopping, when you buy 2 different items with different prices.

2N-2.5 Demonstrate an understanding of different meanings of division (separating into equal groups, discovering the number of equal groups contained within).

 

 

2N-2.5.1 Know that division is a shorter way to do repeated subtraction (e.g.

12 ø 4 = 3 because 12 – 4 – 4 – 4 = 0)

 

2N-2.5.2 Know how to find how many groups of a given number of items when given the total of items (e.g. . 6 ø 3 means 6 candies shared by three people or 6 candies given  (or dealt) 3 to each person

 

2N-2.5.3 Know that division means partitioning into groups of equal size

 

2N-2.5.4 Demonstrate an understanding of the concept that division is not commutative (e.g.. that 12 ø 4 ¹ 4 ø 12)

 

Working out how many cars are needed to transport a group of people

 

Finding how many pairs of socks when given a total number of socks

 

Finding how many dozens in a given amount of eggs (e.g. 24 eggs)

 

Knowing that order of entry is critical when using a calculator to perform division

 

2N-2.6 Demonstrate an understanding of how multiplication and division of one and two digit numbers relate to each other.

 

2N-2.6.1 Demonstrate an understanding of the relation between doubling and halving 

 

2N-2.6.2 Know how to multiply to check division (e.g., 12 ø 4 = 3 because 3 ´ 4 = 12)

Generating the solution to a division problem by using guess and check with multiplying

 


 

Standard 2N-3.  Compute fluently and make reasonable estimates

Benchmark: At this level an adult will be expected to:

Enabling Knowledge and Skills

Examples of Where Adults Use It

2N-3.1 Add two- and three-digit whole numbers flexibly, efficiently, and accurately.

 

2N-3.1.1Know how to align numbers in column addition

 

2N-3.1.2 Know that regrouping occurs when the total in a column exceeds 9

 

2N-3.1.3 Recall addition facts to 20

 

2N-3.1.4 Compose and decompose numbers to aid addition (e.g. 97 + 23 = 90 + 20 + 7 + 3)

 

2N-3.1.5 Demonstrate that there are different strategies for adding

 

2N-3.1.6 Demonstrate an understanding that there are different methods of checking answers (e.g. adding in a different order, using inverses, collecting 10's, and using a calculator)

 

2N-3.1.7 Estimate answers to addition

Calculating the production shortfall from a daily target

 

 

Performing mental addition

 

 

Verifying deposits in a checking account.

2N-3.2 Estimate to the nearest 10 or 100 in numbers up to 1,000.

2N-3.2.1 Know benchmark numbers of 5 and 50 are halfway in intervals of 10 and 100  (e.g. 35 is halfway between 30 and 40 and 250 is halfway between 200 and 300)

 

2N-3.2.2 Tell whether a number is greater than benchmark numbers of 5 and 50

 

2N-3.2.3 Demonstrate an understanding of rounding to the nearest 10 or 100 using algorithm

Estimating amount of purchase to nearest 10 dollars.

 

Estimating distances between cities.

 

Giving ballpark figures for numbers in a crowd.

2N-3.3 Subtract using two- and three-digit whole numbers flexibly, efficiently, and accurately.

 

2N-3.3.1 Know how to align numbers in column subtraction

 

2N-3.3.2 Know that "borrowing" is regrouping

 

2N-3.3.3 Recall subtraction facts to 20

 

2N-3.3.4 Estimate answers 

 

2N-3.3.5 Compose and decompose numbers to aid subtraction (e.g. 107 - 83 = 100 - 80 + 7 – 3) 

 

2N-3.3.6 Demonstrate an understanding of strategies or methods for subtraction such as borrowing or counting up

Performing mental subtraction

 

 

2N-3.4 Multiply two-digit whole numbers by numbers 1,2,3,4,5,10 and 11.

 

2N-3.4.1 Use doubling or repeated addition when multiplying by 2 or 4, e.g. To find 26 x 4, do 26 + 26, 52 + 52

 

2N-3.4.2 Demonstrate an understanding the operation of multiplication and related vocabulary (e.g. multiplied by, times, lots of)

 

2N-3.4.3 Recall multiplication facts

(e.g. multiples of  2, 3, 4, 5, 10)

 

2N-3.4.4 Recognize two- and three-digit multiples of 2, 5, or 10 and three-digit multiples of 50 and 100

 

2N-3.4.5 Know that multiplication can be performed in any order, so that 2(3)(4) = 4(2)(3)

Calculating the total number of items in batches (e.g. 5 crates with 16 boxes to a crate)

 

 

 

2N-3.5 Know halves of even numbers up to 100.

2N-3.5.1 Double one- and two-digit numbers up to 50

Separating members into two groups

2N-3.6 Divide two-digit whole numbers by single-digit whole numbers.

 

2N-3.6.1 Demonstrate an understanding that division is the inverse of multiplication

 

2N3.6.2 Recall multiplication facts

 

Working out the number of cars needed to transport a group of people

 

Finding the number of pairs that can form in class or on a dance floor

2N-3.7 Approximate by rounding to the nearest tens or hundreds in numbers up to 1,000.

2N-3.7.1 Demonstrate an understanding of place value for units, tens, hundreds

Rounding numbers to make approximate calculations

 

2N-3.8 Use a calculator to check calculations using whole numbers.

 

 

2N-3.8.1 Demonstrate an understanding of the order to enter a two-digit number

 

2N-3.8.2 Demonstrate an understanding of the order to key in numbers and operators

 

2N-3.8.3 Know how to clear the display and cancel a wrong entry

Performing any calculations at this level

 

 


Strand: Patterns, Functions and Algebra

Learners engage in problem solving within adult contextual situations by communicating, reasoning, and connecting to the following standards:

 

Standard 2P-1. Explore, identify, analyze, and extend patterns in mathematical and adult contextual situations

Benchmark: At this level an adult will be expected to:

Enabling Knowledge and Skills

Examples of Where Adults Use It

2P-1.1 Complete simple repeating number patterns up to 1,000 and identify the unit being repeated.

2P-1.1.1 Skip count forward or backward by 2’s, 3's, 4's, 5’s, and 10’s

Seeing if pages are missing or out of order in a duplicating job

 

Estimating how many exits there are on the highway

 

2P-1.2 Recognize and create repeating patterns and identify the unit being repeated.

2P-1.2.1 Isolate smallest unit of repetition

 

 

Laying tile on a floor

 

Designing a tiled floor and describing the pattern

 

Knitting

 

Standard 2P-2. Articulate and represent number and data relationships using words, tables, graphs

Benchmark: At this level an adult will be expected to:

Enabling Knowledge and Skills

Examples of Where Adults Use It

2P-2.1 Create tables to show the patterns inherent in addition and multiplication of number pairs from 0 to 12.

2P-2.1.1 Know addition and multiplication facts

 

2P-2.1.2 Recognize and extend patterns

Helping children with homework

 

Preparing for further study

 

Standard 2P-3. Recognize and use algebraic symbols to model mathematical and contextual situations

Benchmark: At this level an adult will be expected to:

Enabling Knowledge and Skills

Examples of Where Adults Use It

2P-3.1 Use and interpret +, -, ´, ø, and = to represent combining, comparing, separating and equivalence.

 

Assessed by 2P-3.6

2P-3.1.1 Demonstrate an understanding that + represents operations of combining

 

2P-3.1.2 Demonstrate an understanding that - represents operations of separation or comparison

 

2P-3.1.3 Demonstrate an understanding that ´ stands for combining multiples

 

2P-3.1.4 Demonstrate an understanding that ø means separating into equal groups or discovering the number of equal groups contained within

 

2P-3.1.5 Demonstrate an understanding that = represents vocabulary such as: is equal to, is the same as, and gives you

Using a four-function calculator to find the total of a grocery bill

 

Using a calculator to find how much change you get from a $20.00 bill

 

Using a four function calculator to find hourly rate given weekly pay or to find weekly pay given hourly rate

 

Helping children with homework

2P-3.2 Read and write simple number sentences such as n + 5 = 10, 

8 - 3 = ,  5 ´ ¸ = 10, 8 ø 2= š

¸ ø 3 = 5 where the ¸ represents a missing amount or n = a missing number

2P-3.2.1 Demonstrate an understanding that n or  ¸ represents a missing value in addition and subtraction equations

Helping children with homework.

 

Test-taking when seeking employment

2P-3.3 Write statements of inequality for numbers up to 1,000.

 

2P-3.3.1 Demonstrate an understanding that > stands for greater than

 

2P-3.3.2 Demonstrate an understanding that < stands for less than

Selecting filter for data entry

 

2P-3.4 Read and understand positive and negative numbers as showing direction and change.

 

Assessed by 3P-3.7

2P-3.4.1 Know that positive refers to values greater than zero

 

2P-3.4.2 Know that negative refers to values less than zero

 

2P-3.4.3 Use a horizontal or vertical number line to show positive and negative values

Reading thermometers

 

Riding an elevator below ground level

 

Staying "in the black" or going "into the red" on bill paying

 

2P-3.5 Use a number line to represent the counting numbers.

2P-3.5.1 Demonstrate an understanding that a horizontal number line moves from left to right using lesser to greater values

 

2P-3.5.2 Demonstrate an understanding that intervals on a number line must follow a consistent progression

Reading and interpreting scales

 

 

2P-3.6 Write a simple expression or equation representing a verbal expression to demonstrate an understanding of the four operations and the equal sign.

2P-3.6.1Translate simply worded problems into simple equations (e.g. Write a number sentence for the sum of four and five is nine)

Entering an expression in a spread sheet

 

Standard 2P-4. Analyze change in various contexts

Benchmark: At this level an adult will be expected to:

Enabling Knowledge and Skills

Examples of Where Adults Use It

2P-4.1 Describe qualitative change, such as lengthening hours of daylight or increasing heat.

2P-4.1.1 Observe steady change over time

Reporting and planning in accordance with weather changes

2P-4.2 Describe quantitative change, such as saving 3 cents a day for one month.

2P-4.2.1 Record and save data

 

2P-4.2.2 Know basic arithmetic skills

Following the growth in height or weight of babies and young children

 

 


Strand: Statistics and Probability

Learners engage in problem solving within adult contextual situations by communicating, reasoning, and connecting to the following standards:

 

Standard 2S-1. Collect, organize and represent data

Benchmark: At this level an adult will be expected to:

Enabling Knowledge and Skills

Examples of Where Adults Use It

2S-1.1 Gather data to answer posed questions.

2S-1.1.1 Know that answers can be found by observing and asking relevant questions and counting responses

Planning a party or meeting

 

 

2S-1.2 Group objects or responses by a single criterion.

2S-1.2.1 Demonstrate an understanding of categories such as shape, size, color, or yes or no responses

 

2S-1.2.2 Know how to count each category for subtotals

Sorting stock by size

 

Keeping track of who will or will not attend a party

2S-1.3 Represent information so that it makes sense to others (e.g. using a list, table or diagram).

2S-1.3.1 Demonstrate an understanding that information can be represented in different ways such as in a list, table, or a diagram

 

2S-1.3.2 Demonstrate an understanding of the importance of labeling information in a list, table, or diagram

Reporting on responses to party or meeting

 

Keeping records for a club

2S-1.4 Find a total from subtotaled categories of two- or three-digits to verify inclusion of all data.

2S-1.4.1 Demonstrate an understanding that when objects or responses are divided into categories all data must be included

Checking monthly totals against weekly totals

 

Standard 2S-2. Read and interpret data representations

Benchmark: At this level an adult will be expected to:

Enabling Knowledge and Skills

Examples of Where Adults Use It

2S-2.1 Identify graphs and tables in available resources.

2S-2.1.1 Demonstrate an understanding that a graph is a visual representation

Reading newspapers and magazines

2S-2.2 Find graphs and tables from external sources.

2S-2.2.1 Recognize that graphs can be found in many publications

Reading advertisements.

2S-2.3 Extract simple information from a list or table.

 

2S-2.3.1 Demonstrate an understanding that lists can be ordered in different ways such as alphabetically, numerically, or randomly

 

2S-2.3.2 Demonstrate an understanding that tables are arranged in rows and columns

 

2S-2.3.3 Demonstrate an understanding that titles, labels, etc. provide essential information

Using the yellow pages

 

Checking items against a stock list

2S-2.4 Read values on a bar graph up to 1,000.

2S-2.4.1 Demonstrate an understanding that the height of the bar is equal to the amount on the axis across from it

Reading newspapers and magazines

2S-2.5 Make numerical comparisons about relative values on a bar graph.

 

2S-2.5.1 Demonstrate an understanding that comparative statements such as greater than or less than can be made based on the height of the bars

 

2S-2.5.2 Demonstrate an understanding of relative numerical terms such as twice or half

Conversing about information contained in newspapers and magazines

Standard 2S-3. Make and evaluate statements by applying knowledge of data

Benchmark: At this level an adult will be expected to:

Enabling Knowledge and Skills

Examples of Where Adults Use It

2S-3.1 Match graphs and tables to statements.

 

 

2S-3.1.1 Know how to locate titles

 

2S-3.1.2 Titles indicate subject matter

 

2S-3.1.3 Know what to look for to connect data representations with statements

Reading a newsletter from the health service

2S-3.2 Determine whether or not a graph connects to an argument/ statement using title, labels and percent matches.

 

Assessed by 4S-4.1

2S-3.2.1 Know how to locate data labels in tables and graphs to verify they match arguments/statements 

 

2S-3.2.2 Locate and connect percent numbers in graphs and arguments

Reading insurance documents

2S-3.3 Support simple statements with data.

2S-3.3.1 Know that data can be collected to verify statements such as ‘more people in class walk than drive to class’

 

2S-3.3.2 Know how to keep track of collected data

Taking political action to institute changes in the community

2S-3.4 Visually identify ‘who has more’ and identify obvious misstatements.

 

2S-3.4.1 Recognize that bar heights and circle wedges show quantity

 

2S-3.4.2 Knowing to connect bar heights and wedge sizes with statements/arguments to verify accuracy

Reading ads with bar graphs in newspaper article

 

Standard 2S-4. Know and apply basic probability concepts

Benchmark: At this level an adult will be expected to:

Enabling Knowledge and Skills

Examples of Where Adults Use It

2S-4.1 Discuss events as likely or unlikely.

2S-4.1.1 Demonstrate an understanding that while some events are impossible, some are certain to happen, and in other events some are more likely to occur than others

Deciding whether or not to carry an umbrella

 

Making the call when flipping a coin

 

2S-4.2 Give the probability of a single outcome in simple concrete situations such as tossing a coin or rolling a die.

 

Assessed by 3S-5.2

2S-4.2.1 Demonstrate an understanding that probability depends on the total number of possibilities

Tossing a coin

 

Rolling dice

 

 

Strand: Geometry and Measurement

Learners engage in problem solving within adult contextual situations by communicating, reasoning, and connecting to the following standards:

 

Standard 2G-1. Use and apply geometric properties and relationships to describe the physical world and identify and analyze the characteristics of geometric figures

Benchmark: At this level an adult will be expected to:

Enabling Knowledge and Skills

Examples of Where Adults Use It

2G-1.1 Name, order, and group two- dimensional shapes by properties.

2G-1.1.1 Demonstrate familiarity with terms and concepts such as: Curved vs. straight lines, equal lengths, number of sides

parallel, square corners

Sorting 2D and 3D shapes

 

Matching patterns for home decorating by design and shape

2G-1.2 Investigate and explain common uses of shapes in the environment.

2G-1.2.1 Identify the names of basic 2D shapes (square, circle, rectangle, triangle) using everyday language (straight, curved, etc.)

 

2G-1.2.2 Demonstrate an understanding that shape is independent of size and orientation

Comparing use of shapes in house construction or room design

 

Standard 2G-2. Use transformations and symmetry to analyze mathematical situations

Benchmark: At this level an adult will be expected to:

Enabling Knowledge and Skills

Examples of Where Adults Use It

2G-2.1 Estimate where a line of symmetry falls in a basic shape.

 

Assessed by 3G-2.3

2G-2.1.1 Demonstrate an understanding of concepts of sameness or half-ness

Creating designs

 

Writing certain letters (e.g. A, C, D, E, H, etc.)

2G-2.2 Show more than one line of symmetry in a basic shape.

 

Assessed by 3G-2.3

2G-2.2.1 Demonstrate an understanding of concepts of sameness or half-ness

Creating holiday designs for greetings cards or crafts

 

Standard 2G-3. Specify locations and describe spatial relationships using coordinate geometry and other representational systems

Benchmark: At this level an adult will be expected to:

Enabling Knowledge and Skills

Examples of Where Adults Use It

2G-3.1 Use the compass rose on a map with secondary (SW, NE, etc.) directions.

2G-3.1.1 Know the convention that is North is the opposite direction from South and that East and West are opposite

 

2G-3.1.2 Explain the difference between vertical and horizontal

 

2G-3.1.3 Demonstrate an understanding of diagonal direction between vertical and horizontal

 

2G-3.1.4 Demonstrate an understanding that secondary directions lie halfway between the cardinal directions (e.g. northeast is the diagonal direction between north and east

Appreciating wind directions stated during a weather forecast

 

Reading directions from a map

2G-3.2 Use a street directory or a map with a coordinate grid (C5, etc.).

 

Assessed by 3G-3.1

2G-3.2.1 Explain the difference between vertical and horizontal

 

Finding and explaining the route to a familiar place, or locating own street on map

 

Standard 2G-4. Understand measurable attributes of objects and the units, systems, and processes of measurement and apply appropriate techniques, tools, and formulas to determine measurements

Benchmark: At this level an adult will be expected to:

Enabling Knowledge and Skills

Examples of Where Adults Use It

2G-4.1 Calculate the total cost of many items and the change from a whole dollar amount.

2G-4.1.1 Use whole number addition

 

2G-4.1.2 Know the meaning and symbols used for money

Making everyday purchases

2G-4.2 Read, record, and understand time formats of quarter and half, with a digital and 12hour analog clock.

2G-4.2.1 Familiarity with quarter and half concepts

Telling time on various clocks

2G-4.3 Estimate, measure, and compare lengths, weights, capacity using standard and non-standard units.

2G-4.3.1 Ability to read scales such as a 12- inch ruler to ¼ inch, general knowledge of weight and capacity vocabulary and concepts

 

2G-4.3.2 Know that 2/4 = ½

 

2G-4.3.3 Know that 3/4 is greater than ½

Following a recipe

2G-4.4 Use simple instruments graduated in familiar units (e.g. inches, feet, yards, pounds, fluid ounces, and centimeters).

 

Assessed by 3G-4.12

2G-4.4.1 Know appropriate scales for familiar measures

Reading thermometer, scales

2G-4.5 Know the relationship of familiar units (e.g. 12 inches in a foot, 3 feet in a yard, 4 cups in a quart).

2G-4.5.1 Demonstrate how to find equivalent measures with rulers, yard sticks, and cup measures

Measuring a baby’s length in inches

 

Expressing a person’s height in feet and inches

 

Doubling or halving a recipe

2G-4.6 Read and compare positive temperatures in Fahrenheit.

 

 

2G-4.6.1 Read scale and digital read-outs

 

2G-4.6.2 Read and compare numbers

Understanding a weather chart and being able to describe the temperature in a given location using appropriate vocabulary (hot, warm, freezing, etc.)

2G-4.7 Develop personal benchmarks for temperatures.

2G-4.7.1 Read a thermometer

Knowing that a child has a fever when reading thermometer

2G-4.8 Find the perimeter of rectangles.

2G-4.8.1 Know that the two lengths are of equal measure and the two widths are of equal measure

 

2G-4.8.2 Know that the perimeter of a rectangle is equal to the total of the four sides

Buying weather-stripping

2G-4.9 Find the area of rectangles.

 

Assessed by 3G-4.11

2G-4.9.1 Know that area measures the space within a figure in square units

Buying carpeting, tiles, or wall paper

 

 

 


Level 3: Intermediate ABE Mathematics

See “How to use This Document (Teacher’s Guide) and (Connecting Curriculum, Instruction and Assessment),” pages 8-10.

 

Strand: Number Sense

Learners engage in problem solving within adult contextual situations by communicating, reasoning, and connecting to the following standards:

 

Standard 3N-1.  Represent and use numbers in a variety of equivalent forms in contextual situations

Benchmark: At this level an adult will be expected to:

Enabling Knowledge and Skills

Examples of Where Adults Use It

3N-1.1 Read, write, order, and compare numbers up to 1,000,000.

 

 

 

 

3N-1.1.1 Demonstrate an understanding that the position of a digit signifies its value

 

3N-1.1.2 Know what each digit represents in a number up to six digits, including the use of zero as a place holder

 

3N-1.1.3 Demonstrate an understanding of the symbols for greater than, less than

Filing plans in numerical order

 

Reading route numbers on delivery labels

3N-1.2 Read, write and compare common fractions (e.g. thirds, halves, and quarters).

 

 

 

 

3N-1.2.1 Demonstrate an understanding that the denominator indicates the number of equal parts in the whole

 

3N-1.2.2 Demonstrate an understanding that the numerator identifies how many of these equal parts are shown

 

3N-1.2.3 Demonstrate an understanding that a unit fraction is one part of a whole divided into equal parts  (e.g. 1/4 indicates one of four equal parts is shown)

 

3N-1.2.4 Demonstrate an understanding that non-unit fractions are several equal parts of a whole, indicated by the numerator (e.g. 3/4 = 1/4 + 1/4 + 1/4)

 

3N-1.2.5 Demonstrate an understanding that the size of the fraction changes as the numerator and denominators change

Using a 1/4 cup measure to add 3/4 of a cup of flour to a recipe

 

Reading fractions used in sale signs and special offers (e.g. 1/2 off)

 

 

3N-1.3 Recognize and use equivalent forms of common fractions (e.g.1/2 = 5/10).

 

Assessed by 4N-1.11

3N-1.3.1 Demonstrate an understanding that equivalent fractions look different but have the same value

 

3N-1.3.2 Demonstrate an understanding that when the top and bottom number of a fraction are the same, the fraction is equivalent to 1

In the context of measures, recognizing relationships (e.g. that 2/8 inch = 1/4 inch)

3N-1.4 Read, write and compare decimals up to two decimal places in practical contexts ( money in decimal notation, e.g. $10.35).

 

 

3N-1.4.1 Demonstrate an understanding that the decimal point separates dollars and parts of a dollar

 

3N-1.4.2 Demonstrate an understanding that a dime is a tenth of a dollar

 

3N-1.4.3 Demonstrate an understanding that a penny is a hundredth of a dollar

 

3N-1.4.4 Demonstrate an understanding of the use of zero as a placeholder

 

3N-1.4.5 Demonstrate an understanding of the use of a leading zero (e.g. $0.76)

Reading price tags

 

Understanding prices on a menu

 

Counting and recording total value of change received at a rummage sale

 

 

 

 

3N-1.5 Recognize fraction, decimal, and percent equivalents for a half and one quarter.

3N-1.5.1 Know ½ = 0.5 = 50% and 1/4 = 0.25 = 25%

Ordering a half pound at a deli that uses a digital scale

 

Recognizing 50% off and half-price as the same

3N-1.6 Read, write, and compare positive and negative numbers in practical contexts.

 

Assessed by 4N-1.2

 

3N-1.6.1 Demonstrate an understanding of the words positive and negative

 

3N-1.6.2 Demonstrate an understanding that a negative temperature is below zero

 

3N-1.6.3 Demonstrate an understanding that a negative amount of money represents money owed

Understanding wind-chill information

 

Reading a thermometer

 

 

 

 

3N-1.7 Read, write, and compute squares and cubes of whole numbers.

3N-1.7.1 Read and write 4 (4) as 4

 

3N-1.7.2 Recognize that any value taken to the second power will form a square

 

3N-1.7.3 Read and write 4 (4)(4) as 43

 

3N-1.7.4 Recognize that any value taken to the third power will form a cube

Reading pollen count per cubic meter

 

 

3N-1.8 Understand that percent represents a ratio of a part to a whole where the whole is 100.

 

3N-1.8.1 Know that percent means per hundred

 

3N-1.8.2 Demonstrate an understanding of the percent ratio as a comparison based

on division by 100

 

3N-1.8.3 Know that 100% of one dollar is one dollar and that 50% of a dollar is 50 cents out of one dollar

Figuring a 5% sales tax on a one dollar item


 


Standard 3N-2. Understand meanings of operations and how they relate to one another

Benchmark: At this level an adult will be expected to:

Enabling Knowledge and Skills

Examples of Where Adults Use It

3N-2.1 Demonstrate an understanding that multiplying a whole number by a unit fraction is the same as dividing the whole number by that fraction’s denominator.

 

3N-2.1.1 Know that multiplying a whole number by a unit fraction can be seen as adding the fraction to itself that many times (e.g. 4 ´ 1/2 = 1/2 + 1/2 + 1/2 + 1/2  = 2), or as adding the whole number to itself the fractional number of times (e.g. 4 taken 1/2 times or 4 ø 2 = 2)

Generating solutions using mental mathematics in situations involving common unit fractions

3N-2.2 Demonstrate an understanding of how squaring and taking the square root are related.

 

Assessed by 4N-2.5

 

3N-2.2.1 Know that to square a number one multiplies the number by itself

 

3N-2.2.2 Know that to find the square root of an amount, one finds the number that multiplied by itself produces that amount

3N-2.2.3 Because 4 (4) = 16, Ö16 = 4

Finding the area of a square room from the length of a side or to find the length of a side from the area

3N-2.3 Demonstrate an understanding of how addition and subtraction relate to each other for numbers up to 1,000,000.

3N-2.3.1 Know how to add back to check, e.g. 1,000 – 250 = 750 because 250 + 750 = 1,000

Checking the balance in a checkbook

3N-2.4 Choose the correct operation for solving a one-step narrative problem.

3N-2.4.1 Demonstrate an understanding that addition is combining, subtraction is separating or comparing, multiplication is repeated addition, and division is repeated subtraction

Taking a standardized or employment test

3N-2.5 Understand and use exponents to represent repeated multiplication.

3N-2.5 Recognize that exponents indicate the number of times that the base is written as a factor

Computing with formulas on a standardized test

 

Standard 3N-3. Compute fluently and make reasonable estimates

Benchmark: At this level an adult will be expected to:

Enabling Knowledge and Skills

Examples of Where Adults Use It

3N-3.1 Divide by two and three-digit whole numbers and interpret remainders.

 

Assessed by 3N-3.11

 

 

 

 

3N-3.1.1 Demonstrate an understanding of the concept of remainder, and that remainders need to be interpreted in context when solving problems

 

3N-3.1.2 Demonstrate an understanding of when the context requires one to round off to a whole number

 

3N-3.1.3 Demonstrate an understanding of when to express remainders as decimals or fractions

Finding the average number of hotdogs per person sold at an event

 

Finding how many buses are needed to transport three classes of children for a field trip

3N-3.2 Carry out calculations with three-digit whole numbers using efficient written methods.

 

Assessed by 3N-3.10 and 3.11

 

 

3N-3.2.1 Demonstrate an understanding that there are different strategies for carrying out each of the four operations

 

3N-3.2.2 Demonstrate an understanding that there are different ways to check answers

Using written methods to generate results when solving problems with three-digit whole numbers

3N-3.3 Multiply and divide whole numbers by 10 and 100.

 

 

3N-3.3.1 Demonstrate an understanding of place value for whole numbers and to two-decimal places

 

Changing dollar amounts to dimes and pennies and vice versa

 

Changing meters to centimeters and vice versa

3N-3.4 Carry out basic calculations with money.

3N-3.4.1 Demonstrate an understanding of place value for whole numbers and to two-decimal places

 

Balancing a checkbook

 

Figuring one share of a restaurant bill that is divided equally

3N-3.5 Approximate by rounding numbers up to 1,000,000 to the nearest tens, hundreds, or thousands

3N-3.5.1 Demonstrate an understanding place value for units, tens, hundreds, thousands

Rounding numbers to make approximate calculations

3N-3.6 Find common parts of whole number quantities or measurements (e.g. ¾ of 12, 2/3 of 15).

 

 

 

3N-3.6.1 Demonstrate an understanding of the relationship between unit fractions and division when finding parts

 

3N-3.6.2 Demonstrate an understanding that there are different strategies for finding fractional parts

Reducing the quantities in a recipe

 

 

 

 

 

3N-3.7 Use equivalencies between common fractions and percentages to find part of whole-number quantities.

3N-3.7.1 Know common fraction and percent equivalents (e.g. 50% = ½, 25% = ¼, 75% = ¾)

Estimating savings using mental mathematics strategies at a percentage off sale

3N-3.8 Find squares, square roots, and cubes of whole-number quantities

 

Assessed by 3N-1.7

 

3N-3.8.1 Know that a number is squared by multiplying it by itself

 

3N-3.8.2 Know that a number is cubed by multiplying it by itself three times

 

3N-3.8.3 Know that squaring and finding the square root are inverse operations

 

3N-3.8.4 Know the calculator keys that generate squares, square roots, and cubes of numbers

Finding the area of a square room

 

Finding the volume of a square room

3N-3.9 Use a calculator to calculate whole numbers and decimals to two places to solve problems in context, and to check calculations.

 

 

 

3N-3.9.1 Know how to key in and interpret money calculations (e.g. key in 85 cents as $0.85, interpret 8.2 as $8.20)

 

3N-3.9.2 Demonstrate an understanding that a calculator will sometimes display a string of digits after the decimal point, and that it is only necessary (at this level) to read the first two (e.g. 1.333333 is $1.33)

 

3N-3.9.3 Know how to find the square and cube of a number

 

3N-3.9.4 Know how to key in a square root calculation

 

3N-3.9.5 Know and use strategies to check answers obtained with a calculator

Finding the total charge on a purchase

 

Multiplying the monthly cable charge by twelve to find the annual charge

 

Finding the area of a square room

 

 

3N-3.10 Carry out calculations using addition and subtraction with numbers up to 1,000,000 using efficient written methods, including ways to check answers.

3N-3.10.1 Compose and decompose numbers to aid addition (e.g. 1240 + 2040 = 1,000 + 2000 + 100 + 40 + 40)

 and estimate answers to addition

 

3N-3.10.2 Demonstrate that there are different strategies for adding

 

3N-3.10.3 Demonstrate an understanding that there are different methods of checking answers (e.g. adding in a different order, using inverses, collecting 10's and using a calculator)

 

3N-3.10.4 Know how to align numbers in column subtraction

 

3N-3.10.5 Know that “borrowing” is regrouping

 

3N-3.10.6 Can compose and decompose numbers to aid subtraction (e.g. 1007 - 803 =1,000 - 800 + 7 – 3) 

 

3N-3.10.7 Demonstrate an understanding of strategies or methods for subtraction such as borrowing or counting up

Calculating the production shortfall from a daily target

 

 

Performing mental addition

 

 

Checking deposits in a checking account

3N-3.11 Carry out calculations using multiplication and division with two and three digit numbers using efficient written methods, including ways to check answers and interpret remainders.

 

3N-3.11.1 Demonstrate an understanding that division is the inverse of multiplication and that the answer to a division problem can be checked by multiplication

 

3N-3.11.2 Demonstrate the ability to determine the placement of the decimal points in multiplication of decimal numbers of up to two places

 

3N-3.11.3 Demonstrate an understanding of the concept of remainder, and that remainders need to be interpreted in context when solving problems

 

3N-3.11.4 Demonstrate an understanding of when the context requires one to round off to a whole number

 

3N-3.11.5 Demonstrate an understanding of when to express remainders as decimals or fractions

Calculating miles per gallon that a car attains

 

Estimating travel time in hours based on distance and speed

3N-3.12 Compute percentages when part and whole are given using friendly numbers (e.g. 10%, 25%, 50%, and 75%).

 

3N-3.12.1 Know percent and fraction equivalents for benchmark numbers (e.g. 10%, 25%, 50%, and 75%)

 

3N-3.12.2 Demonstrate an understanding of part-whole relationship inherent in fractions and percents

Calculating a percent increase in pay or demographics

 

 

Strand: Patterns, Functions, and Algebra

Learners engage in problem solving within adult contextual situations by communicating, reasoning, and connecting to the following standards:

 

Standard 3P-1. Explore, identify, analyze, and extend patterns in mathematical and adult contextual situations

Benchmark: At this level an adult will be expected to:

Enabling Knowledge and Skills

Examples of Where Adults Use It

3P-1.1 Complete number sequences with whole numbers involving two-step progressions.

3P-1.1.1 Know multiplication tables

Using rate tables for postage

 

3P-1.2 Recognize and create repeating patterns and identify the unit being repeated.

 

Assessed by 3P-1.1

3P-1.2.1 Isolate smallest unit of repetition

 

3P-1.2.2 Use a notation system to record patterns

Creating Sales Tax tables

 

Using mental math strategies

 

3P-1.3 Given a table of amounts, generalize the relationship between the quantities using simple patterns such as doubling.

3P-1.3.1 Read tables

 

3P-1.3.2 Recognize and verbalize patterns

Using rate tables for prices

 

 


Standard 3P-2. Articulate and represent number and data relationships using words, tables, graphs

Benchmark: At this level an adult will be expected to:

Enabling Knowledge and Skills

Examples of Where Adults Use It

3P-2.1 Write an expression or equation representing verbal situations with one or two operations.

3P-2.1.1 Translate simple worded problems involving unknown quantities into simple equations

Entering an expression in a spreadsheet

 

3P-2.2 Develop and use simple formulas from tables with one or two arithmetical steps for real life contexts.

3P-2.2.1 Discover patterns in an “in-out” table

 

3P-2.2.2 Verbalize a rule for finding values in an “in-out” table

 

3P-2.2.3 Write a general expression for finding values in an “in-out” table

 

3P-2.2.4 Write an equation

 

3P-2.2.5 Decide on the effectiveness of a developed formula by substituting known values

Converting temperature between Celsius and Fahrenheit

 

Finding interest on a loan from a table

 

Standard 3P-3. Recognize and use algebraic symbols to model mathematical and contextual situations

Benchmark: At this level an adult will be expected to:

Enabling Knowledge and Skills

Examples of Where Adults Use It

3P-3.1 Use and interpret +, -, ´, ø, and = to represent combining, comparing, and equivalence.

 

Assessed by 3P-3.2

 

 

 

 

 

 

3P-3.1.1 Demonstrate an understanding that + represents operations of combining

 

3P-3.1.2 Demonstrate an understanding that – represents operations of separation or comparison

 

3P-3.1.3 Demonstrate an understanding that ´ stands for combining multiples

 

3P-3.1.4 Demonstrate an understanding that ø means separating into equal groups or discovering the number of equal groups contained within

 

3P-3.1.5 Demonstrate an understanding that = represents vocabulary such as is equal to, is the same as, and gives you

Using a four-function calculator to find the total of a grocery bill

 

Using a calculator to find how much change you get from a $20.00 bill

 

Using a four function calculator to find hourly rate given weekly pay, or to find weekly pay given hourly rate

 

Helping children with homework

3P-3.2 Read, write, and solve expressions using algebraic notation for addition, subtraction, multiplication, division, and parentheses with one or two operations.

 

 

3P-3.2.1 Read and write 5 (10) for 5 ´ 10

 

3P-3.2.2 Read and write 10 for 10 ø 2

                                                   2

3P-3.2.3 Know that the contents of parentheses must be worked out first

Following convention in notation and order of operation

 

Test-taking when seeking employment

3P-3.3 Substitute the value for the variable in one-step expressions using whole numbers when the value is given, such as finding x + 4 and

 10 – x when x has a value of 1

3P-3.3.1 Demonstrate an understanding that a variable represents a missing value in addition and subtraction expressions

Preparing for further study

3P-3.4 Find the value of the variable in one-step equations with whole numbers e.g.:

x + 25 = 100

x – 16 = 42

3y = 42

y/5 = 200.

 

3P-3.4.1 Recognize that addition and subtraction are inverse operations

 

3P-3.4.2 Recognize that multiplication and division are inverse operations

 

3P-3.4.3 Know the unknown of a one-step equation can be found by using the inverse of the operation present

Preparing for further study

3P-3.5 Use a number line to represent the counting numbers.

 

Assessed within 4P-3.9

 

 

 

3P-3.5.1 Demonstrate an understanding that a horizontal number line moves from left to right using lesser to greater values

 

3P-3.5.2 Demonstrate an understanding that intervals on a number line must follow a constant progression by values including positive numbers and common fractions and decimals

Reading and interpreting scales

 

 

3P-3.6 Write statements of inequality for numbers up to 1,000,000.

3P-3.6.1 Demonstrate an ability to use the symbols > and < in number statements with larger numbers.

Using mathematical language and symbols to compare and order (e.g. less than, greater than, at most, at least, <, >, =) in place of longer spoken/written sentence.

3P-3.7 Read and understand positive and negative numbers as showing direction and change on both horizontal and vertical number lines.

3P-3.7.1 Demonstrate an understanding that a horizontal number line moves from left to right using lesser to greater values

 

3P-3.7.2 Demonstrate an understanding that a vertical number line moves from the bottom up using lesser to greater values.

Viewing an automotive electrical gauge to determine if the battery is charging or discharging.

 

 

 

Standard 3P-4. Analyze change in various contexts

Benchmark: At this level an adult will be expected to:

Enabling Knowledge and Skills

Examples of Where Adults Use It

3P-4.1 Investigate how a change in one variable relates to a change in a second variable.

 

3P-4.1.1 Record data

 

3P-4.1.2 Represent data in graphical form

Tracking wages when paid an hourly rate on a variable work schedule

3P-4.2 Identify and describe situations with constant or varying rates of change and compare them.

3P-4.2.1 Record data in table form

 

3P-4.2.2 Represent data in graphical form

Following monthly bills (e.g. rent, heating and telephone, in order to budget)

 

 


Strand: Statistics and Probability

Learners engage in problem solving within adult contextual situations by communicating, reasoning, and connecting to the following standards:

 

Standard 3S-1. Collect, organize and represent data

Benchmark: At this level an adult will be expected to:

Enabling Knowledge and Skills

Examples of Where Adults Use It

3S-1.1 Pose questions about themselves and their surroundings and gather data to answer posed questions.

 

Assessed by  2S-1.1

3S-1.1.1 Know that answers can be found by observing and asking relevant questions and counting responses.

Planning a party or meeting

 

Conducting a political survey

3S-1.2 Group objects or responses by a single criterion.

 

Assessed by 2S-1.2

3S-1.2.1 Demonstrate an understanding of the concept of categories, such as shape, size, color, or yes or no responses

 

3S-1.2.2 Know how to count each category for subtotals

Keeping track of who will or will not attend party.

 

Sorting stock by size

3S-1.3 Represent information so that it makes sense to others.

3S-1.3.1 Demonstrate an understanding that information can be represented in different ways such as a list, table, or a diagram.

 

3S-1.3.2 Demonstrate an understanding of the importance of labeling information in a list, table, or diagram

Reporting on responses to party or meeting

 

Keeping records for a club

3S-1.4 Find a total from subtotaled categories to verify inclusion of all data.

3S-1.4.1 Demonstrate an understanding that when objects or responses are divided into categories all data must be included in one and only one category; therefore, categories must identify distinct sets

Checking monthly totals against weekly totals

3S-1.5 Represent categorical data on a line plot.

3S-1.5.1 Demonstrate an understanding that each X in a line plot represents one and only one item or response; therefore, it is verifiable that the number of responses is equal to the number of X’s

Keeping a visual tally of responses by category

 

Standard 3S-2. Read and interpret data representations

Benchmark: At this level an adult will be expected to:

Enabling Knowledge and Skills

Examples of Where Adults Use It

3S-2.1 Identify graphs and tables in available resources.

 

Assessed by 2S-2.1

3S-2.1.1 Demonstrate an understanding that a graph is a visual representation

 

3S-2.1.2 Demonstrate an understanding that a table arranges information in rows and columns

Reading newspapers and magazines

3S-2.2 Find graphs and tables in external sources.

 

Assessed by 2S-2.2

3S-2.2.1 Recognize that graphs and tables can be found in many publications

Reading advertisements

Finding current interest rates

3S-2.3 Sort graphs and tables by type.

3S-2.3.1 Know that a bar graph uses bars of various heights to display amount

 

3S-2.3.2 Know that line graphs use lines to display changes in amount

 

3S-2.3.3 Know that a circle or pie graph represents the whole 

Participating in conversations about represented data

3S-2.4 Extract simple information from a list or table.

 

Assessed by 2S-2.3

3S-2.4.1 Demonstrate an understanding that lists can be ordered in different ways such as alphabetically, numerically, or randomly

 

3S-2.4.2 Demonstrate an understanding that tables are arranged in rows and columns

 

3S-2.4.3 Demonstrate an understanding that titles, labels, etc provide essential information

Using the yellow pages

 

Checking items against a stock list

3S-2.5 Read values on a bar or line graph up to 1,000,000.

3S-2.5.1 Demonstrate an understanding that the height of the bar is equal to the amount on the axis across from it.

 

3S-2.5.2 Know how to read a scale on an axis

 

3S-2.5.3 Demonstrate an understanding that specific data points on a line graph correspond with the labels on both axes.

Reading newspapers and magazines

3S-2.6 Make numerical comparisons about relative values on a bar graph.

 

3S-2.6.1 Demonstrate an understanding that comparative statements such as greater than or less than can be made based on the height of the bars.

 

3S-2.6.2 Demonstrate an understanding of relative numerical terms such as twice or half.

Conversing about information contained in newspapers and magazines

 

Standard 3S-3. Describe data using numerical descriptions, statistics and trend terminology

Benchmark: At this level an adult will be expected to:

Enabling Knowledge and Skills

Examples of Where Adults Use It

3S-3.1 Identify the minimum, maximum, spread and shape of data.

 

Assessed by 5S-3.1

3S-3.1.1 Be familiar with terms-minimum, maximum, and spread.

Recognition of gaps, holes, and clusters in the data set to determine where data is missing and where it is heavily represented.

Reading temperature charts

3S-3.2 Use “most of” statements to describe data.

3S-3.2.1 Recognize that values in the data set can be repeated and some values may be repeated more frequently than others.

Analyzing results of a survey or group consensus


 

3S-3.3 Find the average (mean) and range for a data set.

3S-3.3.1 Know that mean is “average” and that average in this case is about equal distribution.

 

3S-3.3.2 Know that the average can be found by adding all values in the data set and dividing by the number of values in the set.

Estimating one’s daily expenses.

3S-3.4 Find the median.

 

Assessed by 4S-3.4

3S-3.4.1 Know that median is the middle value.

 

3S-3.4.2 Know that when there is an even number of values in the data set, the median is found by calculating the mean of two middle values.

Explaining the median salary or median years worked in company statistics

 

Standard 3S-4. Make and evaluate arguments or statements by applying knowledge of data analysis

Benchmark: At this level an adult will be expected to:

Enabling Knowledge and Skills

Examples of Where Adults Use It

3S-4.1 Match more than one graph or table with statements.

 

Assessed by 2S-3.1

3S-4.1.1 Know how to locate titles

 

3S-4.1.2 Titles indicate subject matter

 

3S-4.1.3 Know what to look for to connect data representations with statements

Presenting information to children or co-workers

3S-4.2 Determine whether or not a graph/table connects to a statement using title, data labels and percent matches.

 

Assessed by 4S-4.1

3S-4.2.1 Know how to locate data labels in tables and graphs to verify they match statements

 

3S-4.2.2 Locate and connect percent numbers in graphs and statements

Reading insurance documents to decide if the what they state matches what they show

3S-4.3 Visually identify “who has more,” and use some numbers to compare quantities.  

 

Assessed by 2S-3.4

 

 

3S-4.3.1 Recognize bar heights and circle wedges show quantity

 

 

Understanding graphic presentations in newspapers and magazines

3S-4.4 Support simple statements with data.

3S-4.4.1 Know that data can be collected to verify statements such as “more people in class walk than drive to class.” Know how to keep track of collected data

Taking political actions to institute changes in the community

3S-4.5 Use “most of” statements to support arguments.

 

Assessed by 3S-4.4

 

 

3S-4.5.1 Know ways to compare numbers

Discussing numbers with peers and co-workers

3S-4.6 Know statements using “double” and “half” or fifty percent are accurate.

3S-4.6.1 Double and halving numbers

 

3S-4.6.2 Fifty percent equals one half

Reading and/or responding to consumer materials

3S-4.7 Know when percent figures don’t add up to 100%.

 

Assessed by 4S-4.6

 

 

3S-4.7.1 Awareness that circle graphs usually represent 100%, and all figures in them should add to 100 or statements based on the graph are suspect

Reading budget reports

3S-4.8 Recognize that mean and median numbers are considered “averages,” and that averages represent numbers typical of the data that can support an argument.

 

Assessed by 4S-3.4

3S-4.8.1 Awareness that what are termed “averages” are numbers supposedly “typical” of data

 

3S-4.8.2 Know ways in which “averages” are “typical” of data – median is the middle value and mean implies equal distribution of all data

Debating proposed rent increases

3S-4.9 Recognize that bar widths can provide misleading information.

3S-4.9.1 Visual messages are given by bar widths – thin relays message of “less” and wide relays message of “more.”  Visual messages can contradict or enhance evidence

Reading advertisements to make choices

3S-4.10 See where authors of data reports can manipulate data to benefit themselves or malign others in provided materials.

 

Assessed by 5S-4.7

3S-4.10.1 Know how to recognize who produced a data report and how their interests might affect the report – conflict of interest

Reading advertisements to make choices

3S-4.11 Identify obvious misstatements.

3S-4.11.1 Recognize where to look for numbers representing relevant quantities

 

3S-4.11.2 Knowing to connect numbers with statements/arguments to verify accuracy

Reading newspaper articles and deciding if what they state accurately matches what they show

3S-4.12 Use statements that refer to “double” and “half” or fifty percent of the data.

 

3S-4.12.1 Demonstrate and ability to double and find half of numbers

 

3S-4.12.2 Demonstrate and awareness that fifty percent equals one half

Calculating the cost of items marked “one-half” off.

 

Calculating the down payment for an item requiring 50% down

 

Standard 3S-5. Know and apply basic probability concepts

Benchmark: At this level an adult will be expected to:

Enabling Knowledge and Skills

Examples of Where Adults Use It

3S-5.1 Discuss events as likely or unlikely using benchmarks.

3S-5.1.1 Demonstrate an understanding that while some events are impossible, some are certain to happen and some are more likely to occur than others.

Making decisions about how weather may affect outdoor plans

 

Predicting the outcome of a sporting event based on a team’s past performance.

3S-5.2 Give the probability of a single outcome in simple concrete situations such as tossing a coin or rolling a die.

3S-5.2.1 Demonstrate an understanding that probability depends on the total number of possibilities

Tossing a coin

 

Rolling dice

 

3S-5.3 State probability as a ratio in multiple forms (colon, words, and fractions) with simple scenarios.

3S-5.3.1 Know that probability is the ratio of the potential successful outcomes to total possibilities

 

3S-5.3.2 Know that such ratios can be written in fraction form

 

3S-5.3.3 Know that ratio fractions can be simplified

Determining the chances of winning a prize in a drawing

 


Strand: Geometry and Measurement

Learners engage in problem solving within adult contextual situations by communicating, reasoning, and connecting to the following standards:

 

Standard 3G-1. Use and apply geometric properties and relationships to describe the physical world and identify and analyze the characteristics of geometric figure

Benchmark: At this level an adult will be expected to:

Enabling Knowledge and Skills

Examples of Where Adults Use It

3G-1.1 Use informal visual methods to describe and compare shape, dimension, perimeter, area, angles and sides in two dimensional and 3-D objects.

 

3D objects – Assessed by 4G-1.3

3G-1.1.1 Be able to solve practical problems using the properties of 2D and 3D figures

 

3G-1.1.2 Demonstrate an understanding that that area is conserved, but perimeter is not when 2-D objects are combined

 

3G-1.1.3 Build 3D figures using 2-D plans and blocks

Organizing a closet

 

Packing a trunk

 

Covering a package with paper

 

Tying string around a package

3G-1.2 Identify properties, locations, and functions of right angles.

3G-1.2.1 Know that a right angle is 90 degree or a quarter turn, that two right angles make a straight line, and four right angles fill a space

Creating tiling patterns

 

Standard 3G-2. Use transformations and symmetry to analyze mathematical situations

Benchmark: At this level an adult will be expected to:

Enabling Knowledge and Skills

Examples of Where Adults Use It

3G-2.1 Estimate where a line of symmetry falls in a basic shape.

 

Assessed by 3G-2.3

3G-2.1.1 Demonstrate an understanding of concepts of sameness or half-ness

Cutting cake in half

 

Folding objects

3G-2.2 Show more than one line of symmetry in a basic shape.

 

Assessed by 3G-2.3

3G-2.2.1 Demonstrate an understanding of concepts of sameness or half-ness

Designing and making a quilt

 

3G-2.3 Identify where a line of symmetry falls in a basic shape.

3G-2.3.1 Demonstrate an understanding of concepts of sameness or half-ness

Recognizing patterns and symmetry in design and architecture

 

Standard 3G-3. Specify locations and describe spatial relationships using coordinate geometry and other representational systems

Benchmark: At this level an adult will be expected to:

Enabling Knowledge and Skills

Examples of Where Adults Use It

3G-3.1 Use direction, distance, coordinates, simple scales, labels, symbols, and keys to read and use maps and plans.

3G-3.1.1 Use the compass rose on a map with secondary (SW, NE, etc) directions

 

3G-3.1.2 Demonstrate an understanding of latitude and longitude, or horizontal and vertical indices on a map

Planning an automobile trip

 

Finding a city on a globe

3G-3.2 Draw 2 dimensional (2-D) shapes in different orientations on a grid.

 

Assessed by 4G-3.3

3G-3.2.1 Use graph paper to draw 2-D shapes

 

3G-3.2.2 Be able to change the orientation and copy object.

Creating a pattern for a model plane


 

Standard 3G-4. Understand measurable attributes of objects and the units, systems, and processes of measurement and apply appropriate techniques, tools and formulas to determine measurements

Benchmark: At this level an adult will be expected to:

Enabling Knowledge and Skills

Examples of Where Adults Use It

3G-4.1 Add, subtract, multiply and divide sums of money including decimal notation.

3G-4.1.1 Demonstrate an understanding of place value for whole numbers and to two-decimal places

 

3G-4.1.2 Know how to round off thousandths (mils) to the nearest hundredths (cents)

 

3G-4.1.3 Know how to use a calculator

Balancing a checkbook

 

Figuring one’s share of a restaurant bill being divided equally

 

Finding cost of multiples units of an item

3G-4.2 Demonstrate a general understanding of inter-relatedness of distance, time, and speed.

3G-4.2.1 Investigate how a change in one variable (speed) relates to a change in a second variable (time, distance)

 

3G-4.2.2 Identify and describe situations with constant or varying rates of change and compare them (e.g. acceleration, slowing down, stopping)

Estimating time of arrival with slower or faster speeds

3G-4.3 Read and interpret scales with marked and unmarked labels.

 

Assessed by 4G-3.1

3G-4.3.1 Skip counting by 5, 10, 100, 500

 

3G-4.3.2 Making visual estimates of lengths

Inferring distances on a road map

3G-4.4 Measures with a ruler to 1/8inch and metric ruler in cm and mm.

 

3G-4.4.1 Know that a foot equals 12 inches

Knowing when more exact measure is needed (e.g. woodworking project)

3G-4.5 Can make informal comparisons between inches and centimeters.

3G-4.5.1 Demonstrate an understanding of making a one-to-one correspondence between different rulers and units.

 

3G-4.5.2 Make visual estimates of the number of centimeters per inch.

 

3G-4.5.3 Create physical (bodily) benchmarks for units (e.g. fingernail = 1 cm; thumb joint = 1 inch.)

Using a ruler with both inches and centimeter scales

 

Selecting the appropriately sized wrench when working on a European-made car

 

Mixing cleaning chemicals in the correct proportions by comparing metric to standard liquid measure

 

Measuring correct doses of medication.

3G-4.6 Can convert units of measure in the same systems.

3G-4.6.1 Know the relationship of familiar units (e.g. 12 inches in a foot, 3 feet in a yard, 4 cups in a quart)

 

3G-4.6.2 Know when to multiply and when to divide when converting units of measure

Substituting the use of foot rulers for a yardstick or a one cup measure for a quart measure

 

Doing home repairs and carpentry projects

 

3G-4.7 Use and apply concepts of weight and capacity to solve problems.

 

 

3G-4.7.1 Know the difference between weight and capacity

 

 

Correctly loading a washing machine to maintain balance throughout the cycle

Reading the capacity of a liquid to near exact measure

3G-4.8 Use, read, and compare positive and negative Fahrenheit temperatures.

3G-4.8.1 Demonstrate an understanding that temperature increases as it goes up and decreases as it goes down

 

3G-4.8.2 Know that the sign of the temperature changes when crossing the zero degree point

Reading weather forecasts

 

Understanding wind-chill factor

3G-4.9 Use and interpret the 24 hour clock.

3G-4.9.1 Demonstrate an understanding of standard notation for A.M and P.M.

 

3G-4.9.2 Addition and multiplication facts to 12

 

3G-4.9.3 Familiarity with quarter and half concepts

Matching 12 and 24 hour times

3G-4.10 Calculate times using the appropriate value and converting between time formats (including elapsed time).

3G-4.10.1 Know equivalencies for hours, seconds, minutes, days, weeks, months, decades, and centuries.

 

3G-4.10.2 Know multiplication and division by 2-digit numbers

 

3G-4.10.3 Use mental math skills

Understanding that 2 centuries is 200 years to appreciate past events and their place in history

3G-4.11 Directly measures perimeter in linear units and area in square units (sq. in., sq. ft., sq. cm.).

3G-4.11.1 Use a ruler to measure length and width

 

3G-4.11.2 Compare two figures by laying them on top of each other to determine larger area

 

3G-4.11.3 Cover a figure with square units and count the units

 

3G-4.11.4 Use addition and multiplication skills to aid in counting units

Planning renovations or paint for a room

 

Making a cover for a counter top

 

Sewing a chair cover

3G-4.12 Estimate, measure, and compare whole number weights using simple instruments, graduated in familiar units (ounces and pounds) and know when to use appropriate measures.

3G-4.12.1 Use a scale to measure weight

 

3G-4.12.2 Compare two figures holding them to determine which is heavier

 

3G-4.12.3 Place two objects on a balance scale

 

3G-4.12.4 Use addition and multiplication skills to aid in counting units

Placing objects of various weights on shelves or hanging them on walls

 

Shopping for fresh vegetables in a market

 

 


Level 4: Pre-GED / ABE Standards

See “How to use This Document (Teacher’s Guide) and (Connecting Curriculum, Instruction and Assessment),” pages 8-10.

 

Strand: Number Sense

Learners engage in problem solving within adult contextual situations by communicating, reasoning, and connecting to the following standards:

 

Standard 4N-1. Represent and use numbers in a variety of equivalent forms in contextual situations

Benchmark: At this level an adult will be expected to:

Enabling Knowledge and Skills

Examples of Where Adults Use It

4N-1.1 Read, write, order and compare numbers, including large numbers (millions or billions).

 

 

 

4N-1.1.1 Demonstrate an understanding that the position of a digit signifies its value

 

4N-1.1.2 Know what each digit represents in a number up to seven digits, including the use of zero as a place holder

 

4N-1.1.3 Demonstrate an understanding of the symbols for greater than and less than

Filing plans in numerical order

 

Reading route numbers on delivery labels

4N-1.2 Recognize positive and negative numbers in practical contexts.

 

 

 

 

4N-1.2.1 Demonstrate an understanding of the words positive and negative

 

4N-1.2.2 Demonstrate an understanding that a negative temperature is below zero

 

4N-1.2.3 Demonstrate an understanding that a negative amount of money represents money owed

Reading wind-chill chart

 

Reading a thermometer

4N-1.3 Read, write, order, and compare fractions and mixed numbers.

 

 

 

4N-1.3.1 Know common equivalent fractions (e.g. equivalent to a half, quarters, thirds, fifths, tenths)

 

4N-1.3.2 Demonstrate an understanding that in unit fractions, the larger the denominator, the smaller the fraction

 

4N-1.3.3 Demonstrate an understanding that non-unit fractions must be ordered by their closeness to the whole

Reading fractions used in recipes

 

Comparing interest rates (e.g. 1 ¼% versus 1 ½%)

4N-1.4 Read, write, order, and compare decimals up to three decimal places.

 

 

 

 

 

 

4N-1.4.1 Demonstrate an understanding that the position of a digit signifies its value

 

4N-1.4.2 Know that the decimal point separates whole numbers from decimal fractions

 

4N-1.4.3 Know what each digit represents, including the use of zero as a place holder

Reading and comparing gas prices

 

Reading and comparing metric measurements

 

 

 

 

4N-1.5 Recognize and use equivalencies between fractions and decimals.

 

4N-1.5.1 Know any fraction is equivalent to a decimal that ends or has a repeating pattern, and vice versa

Understanding how to read adigital scale when placing a fraction order at the deli

4N-1.6 Can convert fractions to decimals and decimals to fractions.

4N-1.6.1 Demonstrate an understanding that a fraction can be converted to an equivalent decimal by dividing the numerator of a fraction by the denominator

 

4N-1.6.2 Demonstrate an understanding that a decimal can be converted to an equivalent fraction by writing the decimal value over 10, 100, or 1,000 and reducing to simplest form

 Understanding how the scale works at the deli counter

 

Using an electronic calculator to make volume and area computations based on measurements made by a standard tape measure

4N-1.7 Read, write, order, and compare simple percentages.  

 

4N-1.7.1 Demonstrate an understanding of percentage as the number of parts in every 100

 

4N-1.7.2 Know that 100% is the whole

Finding 20% off in a sale

 

4N-1.8 Demonstrate an understanding of simple percentage of increase and decrease.

 

Assessed by 5N-1.4

 

4N-1.8.1 Demonstrate an understanding of percentage as the number of parts in every 100

 

4N-1.8.2 Know that 100% is the whole

 

4N-1.8.3 Demonstrate an understanding that a 10% pay increase is more than a 5% pay increase, but the actual increase depends on the number operated on

Finding a price increase of 10%

 

Finding a cost-of-living salary increase

4N-1.9 Recognize equivalencies between common fractions, percentages and decimals (e.g. 50% = ½, 0.25 = ¼) and use these to find part of whole-number quantities.

 

Assessed by 5N-1.5

 

4N-1.9.1 Know common fraction equivalents (e.g. half, quarter, fifths, tenths)

 

4N-1.9.2 Recognize 50% off and half-price as the same

 

4N-1.9.3 Know ½ as 0.5 when solving a problem with a calculator

Computing discounts efficiently and flexibly using percents or fraction equivalencies

 

Finding 25% discount by dividing by 4

 

Finding a tip using mental math

4N-1.10 Use ratio and proportion to solve one-step percent problems.

4N-1.10.1 Demonstrate an understanding that equal ratios are equal fractions

 

4N-1.10.2 Recognize the term proportion for a statement of equal ratios

 

4N-1.10.3 Calculate for the missing term in a proportion by a variety of methods

Adjusting a recipe for a larger or smaller  number of servings

 

Converting measurements from one standard to another (e.g. miles per hour to feet per second)

 


 

4N-1.11 Recognize and use equivalent forms of common fractions (e.g. ½ = 5/10).

4N-1.11.1 Demonstrate an understanding that equivalent fractions look different but have the same value

 

4N-1.11.2 Demonstrate an understanding that when the top and bottom number of a fraction are the same, the fraction is equivalent to 1

Calculating the size of a container required to hold a variety of portions (e.g. ¼ cup of x plus ¼ cup of y plus ½ cup of z)

 

Standard 4N-2. Demonstrate an understanding meanings of operations and how they relate to one another

Benchmark: At this level an adult will be expected to:

Enabling Knowledge and Skills

Examples of Where Adults Use It

4N-2.1 Choose the correct operation for solving a multi-step narrative problem.

4N-2.1.1 Demonstrate an understanding that addition is combining, subtraction is separating or comparing, multiplication is repeated addition, and division is repeated subtraction

Taking a standardized test

4N-2.2 Perform multiplication operations reliably, accurately, and efficiently.

4N-2.2.1 Demonstrate an understanding that multiplication is commutative, but that in context changing order changes meaning

Knowing that taking two tablets four times a day is different from taking four tablets twice a day

4N-2.3 Use ratios to describe the relationship between two sets of objects.

4N-2.3.1 Know when something is separated into equal groups

 

4N-2.3.2 Demonstrate an understanding of ratio as comparison based on division

Recognizing when a solution can be generated by the use of proportion

4N-2.4 Read, write, and compute with exponents.

 

4N-2.4.1 Be familiar with the terms square, cube, and square root

 

4N-2.4.2 Recognize that any value taken to the second power will form a square and that any value taken the third power will form a cube

 

4N-2.4.3 Recognize that exponents represent repeated multiplication

 

4N-2.4.4 Recognize that exponents indicate the number of times that the base is written as a factor

 

4N-2.4.5 Read and write expressions such as 6(6) (6) (6) (6) (6) (6) as 67

Preparing for further study

 

Understanding exponential growth of bacteria or virus such as HIV

4N-2.5 Calculate square roots of perfect squares, estimate within range of square root value, and demonstrate an understanding of how squaring and taking the square root are related.

4N-2.5.1 Know that a number is squared by multiplying it by itself

 

4N-2.5.2 Know the values of perfect squares up to 152

 

4N-2.5.3 Know that square root is the inverse of squaring

 

4N-2.5.4 Know the square roots of perfect squares up to the square root of 225

 

4N-2.5.5 Know that the square roots of values which are not perfect squares fall between two whole numbers

Estimating the number of 12-inch tiles needed to cover a rectangular floor.

 

Standard 4N-3. Compute fluently and make reasonable estimates

Benchmark: At this level an adult will be expected to:

Enabling Knowledge and Skills

Examples of Where Adults Use It

4N-3.1 Round decimals in practical contexts and verbal problems.

4N-3.1.1 Know how to read decimals up to four decimal places

 

4N-3.1.2 Recognize that rounding a decimal to a particular decimal place requires analyzing the digit in the following decimal place

Performing estimations of mathematical problems to check work

4N-3.2 Add, subtract, multiply, and divide decimals up to three places.

 

 

 

4N-3.2.1 Know and use strategies to check answers (e.g. approximate calculations using whole numbers)

 

4N-3.2.2 Know how to align numbers for column addition and subtraction

 

4N-3.2.3 Know how to multiply decimal factors to produce decimal placement in product

 

4N-3.2.4 Know how to multiply divisor and dividend by the same value to determine quotient

Working out the total amount due for an order

 

Working out change needed from a purchase (e.g. $20 less $14.99)

4N-3.3 Evaluate one number as a fraction of another.

 

 

4N-3.3.1 Demonstrate an understanding of equivalent fractions

 

4N-3.3.2 Demonstrate an understanding of simplest form

 

4N-3.3.3 Know how to bring a fraction to its simplest form (e.g. by recognizing equivalent fractions, by using factors to “cancel”)

 

4N-3.3.4 Recognize prime numbers (e.g. numbers that can’t be canceled)

 

4N-3.3.5 Demonstrate an understanding that quantities must be in the same units to evaluate one as a fraction of another

Changing minutes to fractions of an hour to fill in a time sheet

 

Representing the outcome of observations as a fraction

4N-3.4 Use fractions to add, subtract, multiply, and divide amounts or quantities.

 

 

 

4N-3.4.1 Know some common addition and subtraction facts (e.g. ½ + ¼ = ¾, ¾ – ½ = ¼)

 

4N-3.4.2 Demonstrate an understanding of how to change fractions to equivalent fractions for the purpose of adding and subtracting

 

4N-3.4.3 Know some common multiplication and division facts (e.g. ½ x ½ = ¼, ¼ ø ½ = ½)

Adding hours on a time sheet that includes fractions

 

Finding time-and-a-half pay rate when working overtime

 

 

4N-3.5 Work out simple ratio and direct proportion.

 

 

4N-3.5.1 Demonstrate an understanding of simple ratio as the number of parts (e.g. three parts to one part)

 

4N-3.5.2 Demonstrate an understanding of direct proportion as the same rate of increase or decrease (e.g. double, half)

Diluting a liquid in a given ratio (e.g. weed killer, paint)

 

Changing quantities in a recipe to make twice as much

4N-3.6 Follow order of operations in evaluating number sentences with more than one operation.

 

Assessed by 3P-3.2

4N-3.6.1 Applies the rule for order in a horizontal notation

 

Solving algebra equations containing multiple operations

4N-3.7 Add and subtract integers.

4N-3.7.1 Demonstrate an understanding of positive and negative numbers

 

Balancing a checkbook.

4N-3.8 Estimate answers to calculations.

 

 

4N-3.8.1 Know how to make approximate calculations

 

4N-3.8.2 Demonstrate an understanding that knowledge of context enables ‘guessing’ at answers (e.g. it should be about…), or judging if answers are sensible (e.g. that’s far too big; it doesn’t make sense to have an answer less than 1, etc.)

Estimating to check that answers are reasonable

4N-3.9 Use a calculator to calculate efficiently using whole numbers, fractions, decimals, and percentages.

 

 

 

4N-3.9.1 Know how to change a fraction to a decimal

 

4N-3.9.2 Know how to change a percentage to a decimal

 

4N-3.9.3 Know how to interpret a rounding error such as 6.9999999 as 7

 

4N-3.9.4 Know and use strategies to check answers obtained with a calculator

Doing any calculations at this level

4N-3.10 Carry out calculations using addition and subtraction with numbers of any size using efficient written methods including ways to check answers.

4N-3.10.1 Know and use strategies to check answers (e.g. approximate calculations, estimation)

Using mental and written methods of calculation to generate results when solving problems using whole numbers of any size

4N-3.11 Carry out calculations using multiplication and division using efficient written methods including ways to check answers.

4N-3.11.1 Demonstrate an understanding of the words multiple and factor and relate them to multiplication and division facts

 

4N-3.11.2 Demonstrate an understanding of the word prime and know prime numbers up to 20

 

Using mental and written methods of calculation to generate results when solving problems using whole numbers of any size

 


 

4N-3.12 Multiply whole numbers and decimals by 10, 100, and 1,000 to understand the impact on place value.

4N-3.12.1 Recognize the impact on place value of zeros added to whole numbers

 

4N-3.12.2 Recognize the impact on place value as the position of the decimal point changes

Simplifying large numbers to estimate products

4N-3. 13 Divide whole numbers and decimals by 10, 100, and 1,000 to understand the impact on place value.

4N-3.13.1 Recognize the impact on place value of zeros are cancelled in whole numbers

 

4N-3.13.2 Recognize the impact on place value as the position of the decimal point changes

Simplifying large numbers to estimate quotients

 

 

Strand: Patterns, Functions and Algebra

Learners engage in problem solving within adult contextual situations by communicating, reasoning, and connecting to the following standards:

 

Standard 4P-1. Explore, identify, analyze, and extend patterns in mathematical and adult contextual situations

Benchmark: At this level an adult will be expected to:

Enabling Knowledge and Skills

Examples of Where Adults Use It

4P-1.1 Complete number sequences (all whole numbers, simple fractions and decimals) involving two-step progressions.

4P-1.1.1 Know multiplication tables

Using rate tables for postage

 

4P-1.2 Recognize and create repeating patterns, identify the unit being repeated, and generalize.

4P-1.2.1 Isolate smallest unit of repetition

 

4P-1.2.2 Use a notation system to record patterns

Creating Sales Tax tables

 

Using mental math strategies

4P-1.3 Given a table of amounts, generalize the relationship between the quantities.

4P-1.3.1 Read tables

 

4P-1.3.2 Recognize and verbalize patterns

Using rate tables for prices

 

 

Standard 4P-2. Articulate and represent number and data relationships using words, tables, graphs

Benchmark: At this level an adult will be expected to:

Enabling Knowledge and Skills

Examples of Where Adults Use It

4P-2.1 Write a simple expression or equation representing verbal situations including multiple operations, fractions, exponents, and parentheses.

4P-2.1.1 Translate simple worded problems involving unknown quantities into simple equations

Entering an expression in a spreadsheet

 


 

4P-2.2 Develop and use simple formulas from tables with one or two arithmetical steps for real life contexts.

4P-2.2.1 Discover patterns in an “in-out” table

 

4P-2.2.2 Verbalize a rule for finding values in an “in-out” table

 

4P-2.2.3 Write a general expression for finding values in an “in-out” table

 

4P-2.2.4 Write an equation

 

4P-2.2.5 Decide on the effectiveness of the developed formula by substituting known values

Converting temperature between Celsius and Fahrenheit

 

Finding interest on a loan

 

Standard 4P-3. Recognize and use algebraic symbols to model mathematical and contextual situations

Benchmark: At this level an adult will be expected to:

Enabling Knowledge and Skills

Examples of Where Adults Use It

4P-3.1 Use and interpret the +, -, x, ø, and = to represent combining, comparing, and equivalence.

 

Assessed by 4P-3.2

4P-3.1.1 Demonstrate an understanding that + represents operations of combining

 

4P-3.1.2 Demonstrate an understanding that – represents operations of separation or comparison

4P-3.1.3 Demonstrate an understanding that ´ stands for combining multiples

 

4P-3.1.4 Demonstrate an understanding that ø means separating into equal groups or discovering the number of equal groups contained within

 

4P-3.1.5 Demonstrate an understanding that = represents vocabulary such as is equal to, is the same as, and gives you

Using a four-function calculator to find the total of a grocery bill

 

Using a calculator to balance a checkbook

 

Using a four-function calculator to find hourly rate given weekly pay, or to find weekly pay given hourly rate.

 

Helping children with homework.

4P-3.2 Read and write number operations using algebraic notation for multiplication, division, and parentheses.

 

 

 

4P-3.2.1 Read and write 5 (10) for multiplication of 5 times 10

 

4P-3.2.2 Read and write 10 for 10 ø 2

                                         2

 

 4P-3.2.3 Know that the contents of parentheses must be worked out first

 

4P-3.2.4 Know that exponents and roots are simplified before multiplication or division

Following convention in notation and the order of carrying out operations

 

Test-taking when seeking employment

4P-3.3 Demonstrate appropriate use of the universally accepted “order of operations”.

4P-3.3.1 Read and write number expressions which follow the rule of order for simplifying:

Parentheses

Exponents and roots

Multiplication or division

Addition or subtraction

Helping children with homework

 

Preparing for further study

4P-3.4 Substitute the value for the variable in an addition or subtraction expression when the value is given, such as finding x + 4 and 10 – x when x has a value of 1.

 

4P-3.4.1 Demonstrate an understanding that a variable represents a missing value in addition and subtraction expressions

To prepare for further study

4P-3.5 Substitute the value for the variable in a multiplication or division expression when the value is given (e.g. finding 2x and 8/x when x = 2 including exponents.

 

 

 

4P-3.5.1 Demonstrate an understanding that a variable represents a missing value in a multiplication and division expression

 

4P-3.5.2 Demonstrate an understanding that when there is no operator between a number and a variable or two variables that multiplication is implied

To prepare for further study

4P-3.6 Evaluate expressions and make whole number substitutions in given formula to produce results.

4P-3.6.1 Demonstrate an understanding that when there is no operator between a number and a bracket or parentheses that multiplication is implied

 

4P-3.6.2 Know order of operations

Informally using d = rt to make estimates regarding speed or time of departure

4P-3.7 Read and understand positive and negative integers.

4P-3.7.1 Demonstrate an understanding of the words positive, negative, and zero

 

4P-3.7.2 Know that positive refers to values more than zero

 

4P-3.7.3 Know that negative refers to values below zero

Reading thermometers

Riding an elevator below ground level

 

Staying “in the black” or going “into the red”

 

4P-3.8 Demonstrate an understanding addition and subtraction of integers.

4P-3.8.1 Be able to solve expressions such as: 20 – 30

-6 + 10

Finding temperature change

4P-3.9 Use a number line to represent values.

4P-3.9.1 Demonstrate an understanding that a horizontal number line moves from left to right using lesser to greater values

 

4P-3.9.2 Demonstrate an understanding that intervals on a number line must follow a constant progression between values

 

4P-3.9.3 Demonstrate an understanding that numbers to the left of zero are negative and those to the right of zero are positive

Using a “thermometer” to represent the progress of a fund raiser

 

Preparing for further study in algebra or higher math

4P-3.10 Write statements of inequality for integers of any size e.g.:

2 < 10

10 > 8

99 < 100

1,000 > 999.99

-12 < - 11.

4P-3.10.1 Demonstrate an understanding that > stands for greater than

 

4P-3.10.2 Demonstrate an understanding that < stands for less than

 

Preparing for further study in algebra or higher math

 

Helping children with homework

4P-3.11 Find the value of a variable in multi-step equations e.g.:

3x + 25 = 100

2x – 16 = 42

3y+ 3 = 42

m/5 – 25 = 200.

4P-3.11.1 Recognize that addition and subtraction are inverse operations

 

4P-3.11.2 Recognize that multiplication and division are inverse operations

 

4P-3.11.3 Recognize that using the inverse operation can solve equations

Preparing for further study in algebra or higher math

 

Helping children with homework

 

Standard 4P-4. Analyze change in various contexts

Benchmark: At this level an adult will be expected to:

Enabling Knowledge and Skills

Examples of Where Adults Use It

4P-4.1 Use graphs to analyze the nature of changes in quantities in linear relationships.

 

4P-4.1.1 Know vocabulary to describe linear change (e.g. rises steadily, falls, gradually declines)

 

4P-4.1.2 Know mechanics of making a line graph

Interpreting information presented in graphical form in newspapers or magazines

 

 

Strand: Statistics and Probability

Learners engage in problem solving within adult contextual situations by communicating, reasoning, and connecting to the following standards:

 

Standard 4S-1. Collect, organize and represent data

Benchmark: At this level an adult will be expected to:

Enabling Knowledge and Skills

Examples of Where Adults Use It

4S-1.1 Pose questions about themselves and their surroundings and gather data to answer posed questions.

4S-1.1.1 Know that answers can be found by observing and asking relevant questions and counting responses

Conducting a survey for community planning

4S-1.2 Group objects or responses by single or double criteria.

4S-1.2.1 Demonstrate an understanding of the concept of categories such as shape, size, color or yes or no responses

 

4S-1.2.2 Know how to count each category for subtotals

Organizing findings in a chart or table

4S-1.3 Represent information so that it makes sense to others in any graphical form.

4S-1.3.1 Demonstrate an understanding that information can be represented in different ways such as a list, table, or a line plot

 

4S-1.3.2 Demonstrate an understanding of the importance of labeling information in a list, table, or line plot

Writing a health pamphlet

4S-1.4 Find a total from subtotaled categories to verify inclusion of all data.

 

Assessed by 3S-1.4

4S-1.4.1 Demonstrate an understanding that when objects or responses are divided into categories all data must be included in one and only one category; therefore, categories must identify distinct sets

Estimating the total cost of a variety of products, each of which is priced individually (e.g. corn – 6/$1.00, cucumbers - $.39 each, beans - $.99/pound)


 

4S-1.5 Display categorical data in a bar graph or simple fractions of data in a circle graph.

4S-1.5.1 Demonstrate an understanding that the one axis displays the categories

 

4S-1.5.2 Demonstrate an understanding that the other axis is numbered sequentially

 

4S-1.5.3 Demonstrate an understanding that the height (or length) of the bar is equal to the amount on the corresponding axis

 

4S-1.5.4 Demonstrate an understanding that fractions of data sets (1/4,1/3,1/2, 2/3,3/4) can be represented as wedges of a circle graph

Showing various groups’ responses to school activities or programs

4S-1.6 Convert a bar graph into a circle graph.

4S-1.6.1 Demonstrate an understanding that all data must be included so that the circle graph represents 100% of the data

Participating in class to understand interconnections between graphic representations

4S-1.7 Translate data from a numerical table to a line graph and vice versa.

4S-1.7.1 Demonstrate an understanding that a table can display the same data as a line or bar graph but in rows and columns

 

4S-1.7.2 Demonstrate an understanding of the importance of labeling each axis

 

4S-1.7.3 Demonstrate an understanding that single data points are to be connected by a line to create the line graph

Creating a bar graph to illustrate weight gain/loss over a one-week period

 

Creating a line graph to illustrate temperatures over a one-week period

 


Standard 4S-2. Read and interpret data representations

Benchmark: At this level an adult will be expected to:

Enabling Knowledge and Skills

Examples of Where Adults Use It

4S-2.1 Identify graphs and tables in available resources.

 

Assessed by 2S-2.1

4S-2.1.1 Demonstrate an understanding that a graph is a visual representation

 

4S-2.1.2 Demonstrate an understanding that a table arranges information in rows and columns

Reading newspapers and magazines

4S-2.2 Find graphs and tables in external sources.

 

Assessed by 2S-2.2

4S-2.2.1 Recognize that graphs and tables can be found in many publications

Reading advertisements

Looking up taxes payments

 

Finding current interest rates

4S-2.3 Name and sketch various types of graphs and a table.

4S-2.3.1 Know that a bar graph uses bars of various heights to display amount

 

4S-2.3.2 Know that line graphs use lines to connect data points

 

4S-2.3.3 Know that a circle or pie graph represents the whole or 100%

Participating in a class or working with a child on homework

4S-2.4 Extract simple information from a list or table.

 

Assessed by 2S-2.3

 

4S-2.4.1 Demonstrate an understanding that lists can be ordered in different ways such as alphabetically, numerically, or randomly

 

4S-2.4.2 Demonstrate an understanding that tables are arranged in rows and columns.

 

4S-2.4.3 Demonstrate an understanding that titles, labels, etc. provide essential information

Using the yellow pages

 

Checking items against a stock list

4S-2.5 Read values on a bar, line, or circle graph.

4S-2.5.1 Demonstrate an understanding that the height of the bar is equal to the amount on the axis across from it

 

4S-2.5.2 Know how to read a scale on an axis

 

4S-2.5.3 Demonstrate an understanding that specific data points correspond with the labels on both axes

 

Using car mileage graphs

4S-2.6 Make numerical comparisons about relative values on a bar graph or circle graph.

 

4S-2.6.1 Demonstrate an understanding that comparative statements such as greater than or less than can be made based on the height of the bars or wedge sizes

 

4S-2.6.2 Demonstrate an understanding of relative numerical terms such as twice or half

Creating a circle graph illustrating how earnings are broken down and distributed by categories of expenses

 

Standard 4S-3. Describe data using numerical descriptions, statistics and trend terminology

Benchmark: At this level an adult will be expected to:

Enabling Knowledge and Skills

Examples of Where Adults Use It

4S-3.1 Identify the minimum, maximum, spread and shape of data.

 

Assessed by 5S-3.1

4S-3.1.1 Be familiar with the terms minimum, maximum, and spread.

 

4S-3.1.2 Recognition of gaps, holes, and clusters in the data set to determine where data is missing and where it is heavily represented.

Reading temperature charts

4S-3.2 Use “most of” statements to describe data.

 

Assessed by 3S-3.2

 

 

4S-3.2.1 Recognize that values in the data set can be repeated and some values may be repeated more frequently than others

Using a graph to illustrate the breakdown of household expenses while describing them orally


 

4S-3.3 Find the mean.

4S-3.3.1 Know that mean is “average” and that average in this case is about equal distribution

 

4S-3.3.2 Know that the average can be found by adding all values in the data set and dividing by the number of values in the set

 

4S-3.3.3 Demonstrate an understanding that what are termed “averages” are numbers supposedly “typical” of data

 

Estimating one’s daily expenses

4S-3.4 Find the median and mode.

4S-3.4.1 Know that median is the middle value

 

4S-3.4.2 Know that when there is an even number of values in the data set, the median is found by calculating the mean of two middle values

 

4S-3.4.3 Know that mode is the number or item that occurs most often in a set of data

 

4S-3.4.4 Know ways in which “averages” are supposed to be “typical” of data – median is the middle value and mean implies equal distribution of all data

Explaining the median salary or median years worked in company statistics

 

Examining house sale prices to determine which towns are most likely to have affordable housing stock

4S-3.5 Identify the effect of spread on mean and median.

 

Assessed by 5S-4.5

4S-3.5.1 Know the minimum or maximum value can greatly affect the mean but will not affect the median

Interpreting statistical data accurately

 

Standard 4S-4. Make and evaluate arguments or statements by applying knowledge of data analysis

Benchmark: At this level an adult will be expected to:

Enabling Knowledge and Skills

Examples of Where Adults Use It

4S-4.1 Determine whether or not a graph/table connects to an argument/ statement using title, data labels, and percent matches.

 

4S-4.1.1 Know how to locate data labels in tables and graphs to verify they match arguments/statements

 

4S-4.1.2 Locate and connect percent numbers in graphs and arguments/ statements

Reading insurance documents to decide if the what they state matches what they show

4S-4.2 Visually identify “who has more,” use numbers to compare quantities and identify obvious misstatements.

 

Assessed by 2S-3.4

 

4S-4.2.1 Recognize bar heights and circle wedges show quantity

 

4S-4.2.2 Recognize where to look for numbers representing relevant quantities

 

4S-4.2.3 Knowing to connect numbers with statements/arguments to verify accuracy

Reading newspaper articles and deciding if what they state accurately matches what they show


 

4S-4.3 Make statements about data trends to support or reject arguments/ statements forwarded by others.

 

Assessed by 5S-4.4

4S-4.3.1 Demonstrate an understanding that lines going up mean increase; lines tilting down mean decrease and that they can vary over time

 

4S-4.3.2 Know that a flat line means no change

 

4S-4.3.3 Specific vocabulary to describe trends (e.g. “sharp” increase, “plummeted,” etc.)

Looking at reports on stock market to see if they reflect the trends represented

4S-4.4 Know statements using “double” and “half” or fifty percent are accurate.

 

Assessed by 3S-4.6

 

 

4S-4.4.1 Double and halving numbers

 

4S-4.4.2 Fifty percent equals one half

Using consumer reports to make decisions

4S-4.5 Verify that statements using three times or four times, one fourth or one tenth are accurate.

4S-4.5.1 Know ways to estimate multiples of large numbers

 

4S-4.5.2 Know ways to estimate one fourth or one tenth of a number

Using consumer reports to make decisions

4S-4.6 Know when percent figures don’t add up to 100% and when numbers and percent figures (50%, 25%, 10%) don’t match up.

 

4S-4.6.1 Demonstrate an understanding that circle graphs usually represent 100%, and all figures in them should add to 100

 

4S-4.6.2 Know ways to estimate or easily calculate 50%, 25% and 10% of a number

Reading expenditure reports from local or national governments to determine if money spent is totally accounted for

 

Analyzing income data reports to see if the percents given reflect the amounts represented

4S-4.7 Compare and contrast provided graphs to evaluate for contradictory or unsupported statements.

4S-4.7.1 Recognize that statements or arguments based on data are sometimes generated by comparing or contrasting graphs

 

4S-4.7.2 Recognize that statements or arguments based on one graph are sometimes contradicted in another

Analyzing accident-related data

 


Standard 4S-5. Know and apply basic probability concepts

Benchmark: At this level an adult will be expected to:

Enabling Knowledge and Skills

Examples of Where Adults Use It

4S-5.1 Discuss events as likely or unlikely.

 

Assessed by 3S-5.1

 

 

4S-5.1.1 Demonstrate an understanding that while some events are impossible, some are certain to happen, and in other events some are more likely to occur than others.

Deciding to avoid or use certain products


 

4S-5.2 Give the probability of a single outcome in simple concrete situations such as tossing a coin or rolling a die.

 

Assessed by 3S-5.2

 

4S-5.2.1 Demonstrate an understanding that probability depends on the total number of possibilities

Tossing a coin

 

Rolling dice

 

4S-5.3 State probability as a ratio fraction.

4S-5.3.1 Know that probability is the ratio of the potential successful outcomes to total possibilities.

 

4S-5.3.2 Know that such ratios can be written in fraction form.

 

4S-5.3.3 Know that ratio fractions can be simplified

Determining the chances of winning a prize in a drawing

4S-5.4 Find the probability of independent events.

4S-5.4.1 Know that probability is the ratio of the potential successful outcomes to total possibilities.

 

4S-5.4.2 Know that such ratios can be written in fraction form or as one value compared to another

 

4S-5.4.3 Know that ratio fractions can be simplified

Designing and conducting experiments using 1, 2, 3, and 4 different colored balls to determine the likelihood of randomly selecting a specific color by chance

4S-5.5 State the probability as a percent.

4S-5.5.1 Know that ratio fractions can be expressed as a percent by expressing a proportion with the percent out of 100

Converting a specific set of outcomes as likelihood of the event happening in 100 attempts

 

 

Strand: Geometry and Measurement

Learners engage in problem solving within adult contextual situations by communicating, reasoning, and connecting to the following standards:

 

Standard 4G-1. Use and apply geometric properties and relationships to describe the physical world and identify and analyze the characteristics of geometric figures

Benchmark: At this level an adult will be expected to:

Enabling Knowledge and Skills

Examples of Where Adults Use It

4G-1.1 Directly measure and compare the radius, diameter and circumference of a circle

4G-1.1.1 Use a ruler and string to make measurements

 

4G-1.1.2 Demonstrate an understanding that the radius is half of the diameter

 

4G-1.1.3 Demonstrate an understanding that the circumference is a little more than three diameters and that the ratio is known as pi

Measuring automobile tires

 

Designing circular gardens


 

4G-1.2 Directly measure different angles with a protractor.

 

Assessed by 5G-1.7

4G-1.2.1 Estimate the measure of an angle using benchmarks of 90 degrees and 180 degrees

Cutting molding for a corner

4G-1.3 Use informal visual methods to describe and compare shape, dimensions, perimeters, area, and angles, sides in two-dimensional (2-D) and three-dimensional (3D) objects.

 

 

4G-1.3.1 Be able to solve practical problems using the properties of 2-D and 3-D figures

 

4G-1.3.2 Demonstrate an understanding that that area is conserved, but perimeter is not when 2-D objects are combined

 

4G-1.3.3 Build 3-D figures using 2-D plans and blocks

Organizing a closet

 

Packing a trunk

 

Covering a package with paper

 

Tying string around a package

4G-1.4 Identify shapes that are congruent or similar.

4G-1.4.1 Know that congruent shapes are exactly the same with equal sides and angles

 

4G-1.4.2 Know that similar shapes are the same shape, but different sizes

 

4G-1.4.3 Know that the corresponding angles of congruent and similar shapes are congruent

 

4G-1.4.4 Know that similar shapes are proportional to each other

Assembling items bought unassembled (e.g. toys, exercise equipment, some furniture)

4G-1.5 Identify types of angles such as right, obtuse, acute, and straight.

4G-1.5.1 Know that an acute angle has a measure of less than 90°

 

4G-1.5.2 Know that a right angle has a measure of 90°

 

4G-1.5.3 Know that an obtuse angle has a measure of more than 90 but less than 180°

 

4G-1.5.4 Know that a straight angle has a measure of 180°

Using the basic properties of different types of triangles to prove basic theories and solve problems

4G-1.6 Understand the relationship of angles when you have a system of parallel lines cut by a transversal.

4G-1.6.1 Know that a line that crosses two parallel lines is called a transversal

 

4G-1.6.2 Know that a transversal crosses two lines that are parallel to each crosses both lines at the same angle

 

4G-1.6.3 Know that when a transversal crosses two parallel lines the corresponding angles are equal to each other

Cutting molding at a correct angle so that both ends meet with no space in between


 

4G-1.7 Identify different names of triangles by properties, such as isosceles, right, and equilateral.

4G-1.7.1 Know that the sum of the angles of any triangle is 180°

 

4G-1.7.2 Know that equilateral triangles have three equal sides

 

4G-1.7.3 Know that each of the angles of an equilateral (equiangular) triangle measures 60°

 

4G-1.7.4 Know that any triangle with a 90° angle is a right triangle

 

4G-1.7.5 Know that any triangle with two equal sides is an isosceles triangle

 

4G-1.7.6 Know that the angles opposite the equal sides of an isosceles triangle are called the base angles, and that base angles are equal to each other

Following plans when working on carpentry projects

4G-1.8 Estimate the measure of an angle using benchmarks.

4G-1.8.1 Know the range of the measure for acute, right, obtuse, and straight angles

 

4G-1.8.2 Demonstrate an ability to estimate the measure of an angle based on that knowledge

Estimating where a line of symmetry would fall in a rectangular object

 

Standard 4G-2. Use transformations and symmetry to analyze mathematical situations

Benchmark: At this level an adult will be expected to:

Enabling Knowledge and Skills

Examples of Where Adults Use It

4G-2.1 Estimate where a line of symmetry falls in a basic shape.

4G-2.1.1 Demonstrate an understanding of concepts of sameness or half-ness

Cutting cake in half

Folding objects

4G-2.2 Show more than one line of symmetry in a complex shape.

4G-2.2.1 Demonstrate an understanding of concepts of sameness or half-ness

Creating a “snowflake” or hanging decoration using folded paper and scissors

Standard 4G-3. Specify locations and describe spatial relationships using coordinate geometry and other representational systems

Benchmark: At this level an adult will be expected to:

Enabling Knowledge and Skills

Examples of Where Adults Use It

4G-3.1 Read, interpret, and use a distance scale to find the shortest route between two locations on a map.

4G-3.1.1 Reading a map using horizontal and vertical indices or latitude and longitude

 

4G-3.1.2 Reading a scale

 

4G-3.1.3 Use proportional reasoning

Reading a map to plan a hiking trip

4G-3.2 Measure common three-dimensional (3-D) shapes (e.g. a room) and represent the information on an appropriate diagram drawn to scale.

4G-3.2.1 Demonstrate an understanding of 3-D coordinate graph

 

4G-3.2.2 Locate points in 3-D graphs

 

4G-3.2.3 Use proportional reasoning

Creating plans for building a model

4G-3.3 Draw two-dimensional (2-D) shapes in different orientations on a grid.

4G-3.3.1 Use graph paper to draw 2-D shapes

 

4G-3.3.2 Be able to change the orientation and copy objects

Drawing plans for a carpentry project

 

Creating a pattern for a sewing project

4G-3.4 Use coordinate grid to identify and locate specific points on the x and y axes.

4G-3.4.1 Know that the horizontal axis on a coordinate grid is labeled x

 

4G-3.4.2 Know that the vertical axis on a coordinate grid is labeled y

 

4G-3.4.3 Know that the intersection of the x and y axes is called origin

 

4G-3.4.4 Know that the coordinates of all points on the coordinate grid are given (x, y).

 

4G-3.4.5 Know that the coordinates of all points on the coordinate axes are counted from the origin point (0,0).

Organizing and displaying data to detect patterns and departures from patterns

 

Standard 4G-4. Understand measurable attributes of objects and the units, systems, and processes of measurement and apply appropriate techniques, tools and formulas to determine measurements

Benchmark: At this level an adult will be expected to:

Enabling Knowledge and Skills

Examples of Where Adults Use It

4G-4.1 Convert units of measure in different systems by using own informal methods.

4G-4.1.1 Know common equivalences of measurement units

 

4G-4.1.2 Demonstrate an understanding of proportionality

 

4G-4.1.3 Know how to solve ratio and proportion problems

Estimating number of pints of blood in the human body given the number of liters

4G-4.2 Read, measure, and compare Fahrenheit and Celsius temperatures.

4G-4.2.1 Reading scales

 

4G-4.2.2 Making one-to-one correspondence between scales

 

4G-4.2.3 Estimating distances between markings on a scale

 

4G-4.2.4 Read and compare negative numbers

Reading a thermometer

 

 

4G-4.3 Estimate and approximate an understanding of inter-relatedness of distance, time, and speed.

4G-4.3.1 Investigate how a change in one variable (speed) relates to a change in a second variable (time, distance)

 

4G-4.3.2 Identify and describe situations with constant or varying rates of change and compare them (acceleration, slowing, down, stopping)

Estimating the time a trip will take from point “A” to point “B” traveling at the normal speed limit

4G-4.4 Measure with a ruler to 1/16 inch and metric ruler in cm and mm.

4G-4.4.1 Know that a foot equals 12 inches

 

4G-4.4.2 Know the relationship between the fractions of an inch (16ths, 8ths, 4ths, and halves)

 

4G-4.4.3 Know that the metric numbers on a ruler represent centimeters (cm) and a one-foot ruler is approximately 33 cm long

 

4G-4.4.4 Know that the 10 divisions of a centimeter are called millimeters (mm)

 

4G-4.4.5 Know that a metric length is most commonly represented by a decimal.  For example 4 cm 3mm would be 4.3 cm

Completing a project demanding fairly precise measurements

4G-4.5 Use the language (prefixes) of metric units to describe environment.

4G-4.5.1 Know that meters measure length

 

4G-4.5.2 Know that grams measure mass or weight

 

4G-4.5.3 Know that liters measure volume

 

4G-4.5.4 Know the metric prefixes

milli equal to 1/1,000. centi equal to 1/100, deci equal to 1/10, deca equal to 10, hecto equal to 100, and kilo equal to 1,000

Traveling or communicating with people outside of the United States

4G-4.6 Make informal comparisons between grams and ounces, liters and quarts.

4G-4.6.1 Know that an ounce is approximately equal to 28 grams and that a paper clip weighs approximately 1 gram

 

4G-4.6.2 Know that a kilogram is approximately 2.2 pounds

 

4G-4.6.3 Know that a liter is a little larger than a quart (1.1 qts.)

 

Measuring medications 

 

Replacing automotive fluids

4G-4.7 Estimate, measure, and compare capacity using simple instruments graduated in standard units and know when to use appropriate measures.

4G-4.7.1 Demonstrate familiarity with measures of cups, quarts, gallons, inches, feet, yards, ounces, and pounds

 

4G-4.7.2 Demonstrate familiarity with measures of liters, grams, kilograms, centimeters, meters, and kilometers

Buying beverages for a large group

4G-4.8 Work out simple volumes of cubes, cylinders, and rectangular containers.

4G-4.8.1 Using formulas for volume of cubes, cylinders, and rectangular containers be able to solve for the total

Filling a sand box or garden with mulch

4G-4.9 Find perimeter/area of combination shapes using what you know about rectangles and triangles.

4G-4.9.1 Demonstrate an ability to redefine shapes formed as combinations of rectangles and triangles and calculate the perimeter and area using these smaller parts

Estimating amount of material required to cover a piece of furniture

 


Level 5: ASE / GED Standards

See “How to use This Document (Teacher’s Guide) and (Connecting Curriculum, Instruction, and Assessment),” pages 8-10.

 

Strand: Number Sense

Learners engage in problem solving within adult contextual situations by communicating, reasoning, and connecting to the following standards:

 

Standard 5N-1. Represent and use numbers in a variety of equivalent forms in contextual situations

Benchmark: At this level an adult will be expected to:

Enabling Knowledge and Skills

Examples of Where Adults Use It

5N-1.1 Read, write, order, and compare positive and negative numbers of any size in a practical context.

 

 

 

5N-1.1.1 Explain that the position of a digit signifies its value

 

5N-1.1.2 Know what each digit in a number represents, including the use of zero as a place holder

 

5N-1.1.3 Demonstrate an understanding of the meaning of negative numbers in a practical context (e.g. temperature below zero, loss in trading)

Understanding and comparing government spending figures on public services

 

Understanding and comparing change in the value of stocks

5N-1.2 Read, write, order, and compare fractions and mixed numbers.

5N-1.2.1 Change fractions to equivalent fractions with a common denominator

Comparing overtime rates

 

 

5N-1.3 Read, write, order, and compare decimal numbers of any size.

 

 

 

 

5N-1.3.1 Explain that the position of a digit signifies its value

 

5N-1.3.2 Know that the decimal point separates whole numbers from decimal fractions

 

5N-1.3.3 Describe what each digit represents, including the use of zero as a place holder

Reading and comparing gas prices

 

Reading and comparing metric measurements

 

Comparing currency exchange rates

 

 

5N-1.4 Order and compare percentages and understand percentage of increase and decrease.

 

 

 

 

 

 

5N-1.4.1 Demonstrate an understanding of percentage as the number of parts in every 100

 

5N-1.4.2 Know that 100% is the whole

 

5N-1.4.3 Explain how a 10% pay increase is more than a 5% pay increase, but the actual increase depends on the number operated on

Understanding 20% off in a sale

 

Understanding a price increase of 10%

5N-1.5 Identify and use equivalencies between fractions, decimals and percentages.

 

 

 

 

5N-1.5.1 Show that fractions, decimals, and percentages are different ways of expressing the same thing

 

5N-1.5.2 Know that percentages are fractions out of 100

 

5N-1.5.3 Demonstrate how decimal fractions are expressed in tenths, hundredths, thousandths

Writing fractions of an hour as decimals on a time sheet, (e.g. ¾ hour as 0.75)

 

Recognizing that a deli order for 1/3 pound will read about 0.33 on a digital scale

5N-1.6 Read and write numbers in scientific notation.

5N-1.6.1 Understand positive and negative exponent notation with ten as a base

Using a calculator to compute with small and large numbers

 

5N-2. Understand meanings of operations and how they relate to one another

At this level an adult will be expected to:

Enabling Knowledge and Skills

Examples of Where Adults Use It

 5N-2.1 Demonstrate an understanding of the effects of each operation with fractions.

5N-2.1.1 Represent fractions using number lines and area models

 

5N-2.1.2 Demonstrate conceptual and procedural understanding of operations with fractions

 

5N-2.1.3 Know the meaning of commutative, associative, and distributive properties with whole and fractions numbers

Helping children with homework

5N-2.2 Demonstrate an understanding of the effects of each operation with integers.

5N-2.2.1 Represent integers using a number line.

 

5N-2.2.2 Use area models to demonstrate distributive law of multiplication over addition and subtraction

 

5N-2.2.3 Demonstrate procedural understanding of operations with integers.

 

5N-2.2.4 Know the meaning of commutative, associative, and distributive properties with whole numbers and integers

Helping children with homework

5N-2.3 Demonstrate an understanding that dividing by the denominator of a unit fraction produces the same result as multiplying by the decimal form of the fraction.

5N-2.3.1 Demonstrate procedural knowledge of multiplication and division of fractions and decimals

Finding a discount

5N-2.4 Recognizes equivalent fractions, decimals, and percents and can convert from each form to the other two.

5N-2.4.1 Use number lines and area models to represent fractions and decimals

 

5N-2.4.2 Know equivalences of fractions and decimals

 

5N-2.4.3 Know how to convert between fractions and decimal equivalences

Reading and using manufacturing specifications


 


Standard 5N-3. Compute fluently and make reasonable estimates

Benchmark: At this level an adult will be expected to:

Enabling Knowledge and Skills

Examples of Where Adults Use It

5N-3.1 Add, subtract, multiply and divide decimals of any size.

 

 

5N-3.1.1 Know and use strategies to check answers (e.g. approximate calculations using whole numbers)

 

5N-3.1.2 Align numbers for column addition and subtraction

 

5N-3.1.3 Demonstrate the ability to determine the placement of decimal points in multiplication of decimal numbers

 

5N-3.1.4 Demonstrate the ability to determine the placement of decimal points in division of decimal numbers

Converting sums of money between currencies

5N-3.2 Calculate ratio and direct proportion.

 

 

5N-3.2.1 Explain a ratio written in the form 3:2

 

5N-3.2.2 Know how to work out the number of parts in a given ratio, and the value of one part

Comparing the price of products of different weights or capacities

 

Mixing household or workplace materials

5N-3.3 Add, subtract, multiply, and divide using fractions and mixed numbers.

 

 

 

5N-3.3.1 Demonstrate an understanding of how to change fractions to equivalent fractions for the purpose of adding and subtracting

 

5N-3.3.2 Demonstrate an understanding of how to find a fraction quotient through multiplication

Adding hours on a time sheet that includes fractions

 

 

5N-3.4 Add, subtract, multiply, and divide using integers in practical contexts.

 

5N-3.4.1 Understand how number direction affects the four operations

Finding the average temperature

 

Figuring the net result of banking transactions

5N-3.5 Compute with percentage to solve problems in context.

 

5N-3.5.1 Demonstrate how to use proportion to figure with percentage

Figuring the effect on mortgage payments of a change in interest rates

5N-3.6 Use a calculator to calculate efficiently using whole numbers, integers, fractions, decimals, and percentages.

 

 

5N-3.6.1 Change the sign of a number

 

5N-3.6.2 Change a fraction to a decimal

 

5N-3.6.3 Change a percentage to a decimal

 

5N-3.6.4 Interpret a rounding error such as 6.9999999 as 7

 

5N-3.6.5 Interpret a calculator display employing scientific notation

 

 

5N-3.6.6 Demonstrate an understanding of the use of memory and constant functions

 

5N-3.6.7 Know and use strategies to check answers obtained with a calculator

 

 

Calculating the total price on a item offered at 25 % off with 5% sales tax added

5N-3.7 Determine prime numbers up to 100.

5N-3.7.1 Know that a prime number is a positive integer greater than 1 that has no factors other than 1 and itself

 

Simplifying mathematical problems by factoring out numbers from each side of an equation

 

 

Strand: Patterns, Functions, and Algebra

Learners engage in problem solving within adult contextual situations by communicating, reasoning, and connecting to the following standards:

 

Standard 5P-1. Explore, identify, analyze, and extend patterns in mathematical and adult contextual situations

Benchmark: At this level an adult will be expected to:

Enabling Knowledge and Skills

Examples of Where Adults Use It

5P-1.1 Extend a pattern and when applicable hypothesize reasons, and analyze how both repeating and growing patterns are generated.

 

 

5P-1.1.1 Isolate smallest unit of repetition

 

5P-1.1.2 Use a notation system to record patterns

5P-1.1.3 Make a table using pattern values

 

5P-1.1.4 Verbalize a rule for finding values in the table

 

5P-1.1.5 Write a general expression for finding values in the table

 

5P-1.1.6 Decide on the effectiveness of the expression by substituting known values

Accurately describing patterns of heating bills and explaining the patterns

 

Creating a compound interest table

5P-1.2 Demonstrate an understanding of graphical, tabular, or symbolic representations for a given pattern and/or relationship.

 

5P-1.2.1 Make a table using pattern values

 

5P-1.2.2 Verbalize a rule for finding values in the table

 

5P-1.2.3 Write a general expression for finding values in the table

 

5P-1.2.4 Decide on the effectiveness of the expression by substituting known values

Reading and explaining temperature conversion tables

 

Standard 5P-2. Articulate and represent number and data relationships using words, tables, graphs, rules, and equations

Benchmark: At this level an adult will be expected to:

Enabling Knowledge and Skills

Examples of Where Adults Use It

5P-2.1 Create own equations, rules or sketch graphs from word problems or observed situations.

 

5P-2.1.1 Make a table using pattern values

 

5P-2.1.2 Verbalize a rule for finding values in the table

 

5P-2.1.3 Write a general expression for finding values in the table

 

5P-2.1.4 Decide on the effectiveness of the expression by substituting known values

Working out the standard elements of a household budget

5P-2.2 Convert between different representations, such as tables, graphs, verbal descriptions, and equations.

5P-2.2.1 Recognize that a variety of problem situations may be modeled by the same function or type of function

Presenting results of data exploration

5P-2.3 Develop algebraic expressions, rules, formulae, or sketch graphs to generalize straightforward number patterns or observable relationships between variables.

5P-2.3.1 Demonstrate an understanding of the parts of a graph

 

 

Translating graphic depictions of data into oral or written descriptions to explain relationships

5P-2.4 Draw graphs using techniques such as plotting points, sketching from known main features of algebraic function, or using technology like a graphing calculator or computer package.

5P-2.4.1 Know graphing techniques

 

5P-2.4.2 Understand use of a graphing calculator or spreadsheet

Making visual aids for depicting change patterns in business or industry

5P-2.5 Identify general shapes and major characteristics of linear and simple non-linear graphs and interpret their real world meanings.

5P-2.5.1 Recognize and use direct and indirect variation

 

Interpreting graphic presentations of data to analyze events and make predictions

 

Standard 5P-3. Recognize and use algebraic symbols to model mathematical and contextual situations

Benchmark: At this level an adult will be expected to:

Enabling Knowledge and Skills

Examples of Where Adults Use It

5P-3.1 Find the value of an unknown in equations that require multi-step solutions e.g.:

2x + 4 = 6x -8

0.5y2 - 10 = 40.

 

5P-3.1.1 Recognize that addition and subtraction are inverse operations

 

5P-3.1.2 Recognize that multiplication and division are inverse operations

 

5P-3.1.3 Recognize that using the inverse operation can solve equations

Preparing for further study

 

Helping children with homework

5P-3.2 Evaluate formulas.

 

5P-3.2.1 Know that a variable is replaced by its number value within parentheses when a formula is evaluated

 

5P-3.2.2 Demonstrate an understanding that when there is no operator between a number and a bracket or parentheses that multiplication is implied

 

5P-3.2.3 Know order of operations

Informally using d = rt to make estimates regarding speed or time of departure 

 

 

 

 

 

 

Using a calculator

5P-3.3 Solve linear and quadratic equations.

 

5P-3.3.1 Know the quadratic formula

 

5P-3.3.2 Know how to evaluate formulas

Helping children with homework

 

Preparing for further study


 

Standard 5P-4. Analyze change in various contexts

Benchmark: At this level an adult will be expected to:

Enabling Knowledge and Skills

Examples of Where Adults Use It

5P-4.1 Approximate and interpret rates of change from graphical and numerical data.

 

Assessed by 5G-4.3

 

5P-4.1.1 Understand that slope represents rate of change

 

5P-4.1.2 Know how to find the slope from a line graph or table of data

Looking for trends (e.g. in the price of items, in revenue for a business)

 

 

Strand: Statistics and Probability

Learners engage in problem solving within adult contextual situations by communicating, reasoning, and connecting to the following standards:

 

Standard 5S-1. Collect, organize and represent data

Benchmark: At this level an adult will be expected to:

Enabling Knowledge and Skills

Examples of Where Adults Use It

5S-1.1 Pose both categorical and numerical questions about himself or his environment.

5S-1.1.1 Know that answers can be found by observing and asking relevant questions and counting responses

Working on a playground committee to select equipment

5S-1.2 Collect and organize responses to questions.

 

Assessed by 5S-1.1

5S-1.2.1 Demonstrate an understanding of the concept of categories such as shape, size, country, ethnicity, income level or yes or no responses

Conducting research for travel or relocation purposes

5S-1.3 Choose an appropriate representation to display responses to all types of data.

5S-1.3.1 Demonstrate an understanding that categorical data is usually displayed on bar or circle graphs

 

5S-1.3.2 Demonstrate an understanding that numerical data and change over time is usually displayed on a line graph

 

5S-1.3.3 Know how to choose a suitable scale to fit the data set

 

5S-1.3.4 Calculate percents and find percents and/or fractions of 360 degrees

 

5S-1.3.5 Use a protractor

 

5S-1.3.6 Demonstrate an understanding that a table can be more accurate than a graph when recording precise numerical datum

 

5S-1.3.7 Explain the importance of labeling tables, graphs, and diagrams

Representing findings from data gathering in a manufacturing or business setting

5S-1.4 Collect comparative data on a single given question such as responses grouped by age group vs. responses grouped by gender.

5S-1.4.1 Know that responses grouped by different criteria must be recorded in separate data sets

Gathering data in the workplace and sorting it by criteria

5S-1.5 Display comparative data on a double bar or line graph.

5S-1.5.1 Explain why separate data sets must be identified by different colors or line patterns

 

5S-1.5.2 Demonstrate an understanding that a key to identify each data set must be provided

Comparing gathered work-related data by preparation of appropriate bar or line graphs

 

Standard 5S-2. Read and interpret data representations

Benchmark: At this level an adult will be expected to:

Enabling Knowledge and Skills

Examples of Where Adults Use It

5S-2.1 Identify graphs and tables in available resources.

 

Assessed by 2S-2.1

5S-2.1.1 Explain how a graph is a visual representation

 

5S-2.1.2 Describe how a table arranges information in rows and columns

Reading newspapers and magazines

5S-2.2 Know where graphs and tables are likely to be found.

 

Assessed by 2S-.2.2

5S-2.2.1 Recognize that graphs and tables can be found in newspapers, magazines, research journals, and promotional materials

 

5S-2.2.2 Recognize that a table is an organizing tool used in manuals, tax forms, financial statements etc.

Reading advertisements

Looking up taxes payments

 

Finding current interest rates

 

Reading graphic materials in the workplace

5S-2.3 Infer meaning from gaps, clusters and comparisons of data.

5S-2.3.1 Know ways to compare numbers.

 

5S-2.3.2 Know how to connect the shape and comparisons of data with text or background knowledge to infer causes for such phenomena

Reading exam questions

 

Reading corporate or government reports

5S-2.4 Give a verbal description of bar, line, and circle graphs and tables.

5S-2.4.1 Know that a bar graph uses bars of various heights to display amount

 

5S-2.4.2 Know that line graphs use lines to connect data points

 

5S-2.4.3 Know that a circle or pie graph represents the whole or 100%

 

5S-2.4.4 Know that a table can display the same datum as a graph but in rows and columns

Helping with homework

 

Training co-workers

5S-2.5 Make numerical comparisons about relative values on graphs and tables.

5S-2.5.1 Compare and contrast one set of numbers against another

Comparing prices of vacations represented in a brochure

 


 

Standard 5S-3. Describe data using numerical descriptions, statistics and trend terminology

Benchmark: At this level an adult will be expected to:

Enabling Knowledge and Skills

Examples of Where Adults Use It

5S-3.1 Identify the minimum, maximum, spread, shape, and range of data, mean, median, and mode to understand trends and statements.

 

 

5S-3.1.1 Explain the terms minimum, maximum, and spread

 

5S-3.1.2 Demonstrate an understanding that range is the difference between the smallest and largest values in the data set

 

5S-3.1.3 Recognize gaps, holes, and clusters in the data set to determine where data is missing and where it is heavily represented

Reading temperature charts

 

Discussing with a financial planner the relative value of different retirement investment plans offered at work

5S-3.2 Identify the effect of spread on mean and median.

 

Assessed by 5S-4.5

 

5S-3.2.1 Know the minimum or maximum value can greatly affect the mean but will not affect the median

Determining a grade point average

 

Standard 5S-4. Make and evaluate arguments or statements by applying knowledge of data analysis, bias factors, and graph distortions

Benchmark: At this level an adult will be expected to:

Enabling Knowledge and Skills

Examples of Where Adults Use It

5S-4.1 Choose the best graph to support a position.

5S-4.1.1 Distinguish between graphs by understanding the stories each tells

Working with a group to support or oppose a change in the neighborhood

5S-4.2 Support arguments with data and data representations and use number statements to demonstrate the power of an argument.

 

5S-4.2.1 Demonstrate the ability to collect data to support a conjecture, hypothesis or belief

 

5S-4.2.2 Represent collected data in a line plot, table, line or bar graph with an accurate scale, and circle graph

 

5S-4.2.3 Recognize that the greater the number of data supporting an argument, the more powerful the argument

 

5S-4.2.4 Use subtraction to compare

 

5S-4.2.5 Use division to demonstrate how many more times data support an argument

 

Initiating political actions to institute changes in the community

 

Creating a survey or report to support a plea for changes in one’s community

5S-4.3 Convert tables to graphs to support an argument, and convert graphs to narratives and narratives to graphs to forward a position.

 

 

5S-4.3.1 Show how to organize large sets of data in a table

 

5S-4.3.2 Use a table as the foundation for graphic displays

 

5S-4.3.3 Use appropriate language to describe graphic data in a way to show how the data supports an argument

 

5S-4.3.4 Know how to “read” the stories in graphs in order to state them as support an argument

Preparing or reading academic research

 

Preparing reports favoring a political or social position, or to negotiate salaries

5S-4.4 Make statements about data trends to support or reject arguments/statements forwarded by others.

 

5S-4.4.1 Explain lines going up mean increase; lines tilting down mean decrease and that they can vary over time

 

5S-4.4.2 Explain that a flat line means no change

 

5S-4.4.3 Use specific vocabulary to describe trends (e.g. “sharp” increase, “plummeted,” etc.

Checking reports on stock market or discussing smoking trends with children or peers

 

Understanding changes reported in one’s workplace

5S-4.5 Demonstrate an understanding of the impact of spread on mean and median, and which statistic, mean, median, or mode, is most appropriate for data.

 

5S-4.5.1 Finding the mean, median, and mode

 

5S-4.5.2 Know that mean and median are compressions of data

 

5S-4.5.3 Describe experiences with changes and spread and resulting changes or lack of changes in mean and median

 

5S-4.5.4 Explain why means and medians don’t always represent what is typical, and so aren’t always best used in creating an argument

5S-4.5.5 Describe some inappropriate uses of mean, median or mode

 

5S-4.5.6 Use appropriate statistic to support an argument

Reading advertisements or demographic reports in order to make decisions

 

Negotiating salary increases

 

Reading real estate sales reports; health and fitness data

5S-4.6 Recognize that bar widths, scale, and wedge size distortions can provide misleading information.

 

 

5S-4.6.1 Explain how visual messages are given by bar widths (e.g. thin relays message of  “less” and wide relays message of “more”)

 

5S-4.6.2 Explain why visual messages can contradict or enhance evidence

 

5S-4.6.3 Describe how scales are represented in regular increments

 

5S-4.6.4 Explain why size of the increments used in scales can make changes seem more or less significant

 

5S-4.6.5 Explain why wedge size in circle graphs should correspond roughly to fraction of data represented

Creating promotional materials for social change

 

Reading advertisements

 

Reading environmental and corporate reports on pollution

 

Checking out population preference or conditions’ data to determine if it’s accurate

5S-4.7 Explain where and how authors of data reports can manipulate data to benefit themselves or malign others in mixed materials.

5S-4.7.1 Identify who produced a data report and how their interests might affect the report, resulting in a conflict of interest

Reading advertisements and product studies to make consumer choices

5S-4.8 Understand that different categorizations of data reveal different stories.

 

 

5S-4.8.1 Know how to categorize data in a variety of ways, including aggregate or disaggregate data

 

5S-4.8.2 Know how to make ‘story’ statements about what is seen in data and how these change as categories change

 

5S-4.8.3 Know how to use different categorizations appropriately to support an argument

Following demographic data reports or consumer goods’ data with a critical eye

5S-4.9 Demonstrate an understanding of the impacts of data compression, and when compression helps or hinders an argument.

 

Not assessed, but important to teach at this level

 

 

5S-4.9.1 Explain why data representations do not necessarily show each datum; therefore, individual variations are not visible

 

5S-4.9.2 Explain why personal or regional (subset) variations are sometimes more relevant to arguments/statements than aggregate data

 

5S-4.9.3 Discern the level at which an argument is best stated

Reading consumer preferences’ or selections’ data

 

Preparing documents to advocate for school change

 

Gathering data for statistical process control tasks

5S-4.10 Compare and contrast provided graphs to evaluate contradictory or unsupported statements, or to strengthen an argument.

 

Assessed by 4S-4.7

5S-4.10.1 Explain how statements or arguments based on data are sometimes generated by comparing or contrasting graphs

 

5S-4.10.2 Explain how statements or arguments based on one graph are sometimes contradicted in another

 

5S-4.10.3 Explain how statements or arguments based on multiple graphs can be used to support or enhance each other and one’s position

Comparing accident-related data to make a point concerning safety

 

Comparing work-related progress from month to month

 

Standard 5S-5. Know and apply basic probability concepts

Benchmark: At this level an adult will be expected to:

Enabling Knowledge and Skills

Examples of Where Adults Use It

5S-5.1 Find the probability of both independent and dependent events.

5S-5.1.1 Explain that the probability is independent when the outcome of one event does not influence the outcome of another

 

5S-5.1.2 Explain that the probability is dependent when the outcome of one event directly influences the outcome of subsequent events

Interpreting the odds of contracting breast cancer or being in an airplane accident.

 

 

5S-5.2 Find the number of possible combinations given two or more sets of data.

5S-5.2.1 Know that the total number of possible combinations of items in lists can be found by multiplying the number of items in each list times each other

 

5S-5.2.2 Be able to find all of the possible combinations of a set of letters, digits, or items 

 

 

Determining the number of coordinated outfits possible from a set of slacks and tops.

 

Determining the possible combinations available on a menu.

 

Determining the total number of combinations for a combination lock

 

 

Strand: Geometry & Measurement

Learners engage in problem solving within adult contextual situations by communicating, reasoning, and connecting to the following standards:

 

Standard 5G-1. Use and apply geometric properties and relationships to describe the physical world and identify and analyze the characteristics of geometric figures

Benchmark: At this level an adult will be expected to:

Enabling Knowledge and Skills

Examples of Where Adults Use It

5G-1.1 Apply ratio and proportion in familiar situations that may use scales or magnification.

5G-1.1.1 Demonstrate an understanding of simple ratio as the number of parts (e.g. three parts to one part)

 

5G-1.1.2 Demonstrate an understanding of direct proportion as the same rate of increase or decrease (e.g. double, half)

Mixing various quantities of cleaning fluids based on one set of directions

 

Calculating the proper distance to place a projector from its screen to achieve a particular image size

5G-1.2 Use the language (prefixes) of metric units to describe environment (centi, milli, kilo, micro, mega).

 

Assessed by 4G-4.5

5G-1.2.1 Know definitions of measures of mass (grams), capacity (liters), and length (meter)

 

5G-1.2.2 Know meaning of prefixes

 

5G-1.2.3 Develop informal benchmarks for metric units (e.g. length of thumbnail = 1 cm; 1 meter is approximately 3 feet)

Representing measurement outcomes in the workplace

5G-1.3 Use spatial visualization to describe and analyze geometric figures.

 

Assessed 4G-1.3

5G-1.3.1 Know meaning of horizontal and vertical

 

5G-1.3.2 Develop informal benchmarks for angles

 

5G-1.3.3 Know vocabulary for 2-D shapes and orientation

Identifying and describing objects to be measured

5G-1.4 Develop and use formulae that describe relationships between variables in familiar contexts (area and volume).

5G-1.4.1 Demonstrate an understanding of area and volume of 2-D and 3-D figures

 

5G-1.4.2 Use patterns to generalize

Using a formula to determine material required to build or cover an object

5G-1.5 Use properties of triangles to solve problems.

5G-1.5.1 Demonstrate understanding of congruent and similar triangles

 

5G-1.5.2 Explain the sum of the angles in a triangle in a plane equals 180 degrees

 

5G-1.5.3 Recognize situations where properties of right triangles apply

 

5G-1.5.4 Apply the Pythagorean theorem to right triangles

Building and measuring objects in the manufacturing trades

5G-1.6 Use properties of right triangles and Pythagorean relationship to solve problems.

5G-1.6.1 Know properties of right triangles, including angle measurement

 

5G-1.6.2 Demonstrate an understanding of similarity in triangles

 

5G-1.6.3 Apply proportional reasoning to find corresponding sides

Determining the line of symmetry of a right triangle

5G-1.7 Directly measure different angles with a protractor.

5G-1.7.1 Know how to align a protractor with the rays of an angle

Determining a specific angle of slope for installing housing gutters or drains

 

Standard 5G-2. Use transformations and symmetry to analyze mathematical situations

Benchmark: At this level an adult will be expected to:

Enabling Knowledge and Skills

Examples of Where Adults Use It

5G-2.1 Use coordinates to design and describe geometric figures or translations/rotations of geometric figures.

5G-2.1.1 Demonstrate an understanding of the coordinate graph system

 

5G-2.1.2 Know geometric shapes

Reading scientific diagrams

 

Using CAD/CAM software to design a product

 


 

Standard 5G-3. Specify locations and describe spatial relationships using coordinate geometry and other representational systems

Benchmark: At this level an adult will be expected to:

Enabling Knowledge and Skills

Examples of Where Adults Use It

5G-3.1 Find, use, and interpret the slope of a line, the y-intercept of a line, and the intersection of two lines.

5G-3.1.1 Demonstrate an understanding of the coordinate graph system

 

5G-3.1.2 Know how to create a table of ordered pairs which satisfy an equation

 

5G-3.1.3 Generate a graph from a formula or equation

 

5G-3.1.4 Generate and equation or formula from a graph

 

5G-3.1.5 Identify co-efficients with graph steepness

Using linear modeling to determine optimal pricing

 

Standard 5G-4. Understand measurable attributes of objects and the units, systems, and processes of measurement and apply appropriate techniques, tools and formulas to determine measurements

Benchmark: At this level an adult will be expected to:

Enabling Knowledge and Skills

Examples of Where Adults Use It

5G-4.1 Solve and estimate solutions to problems involving length, perimeter, area, surface area, volume, angle measurement, capacity, weight, and mass.

5G-4.1.1 Explain the meaning of the terms perimeter, area, volume, angle, capacity, weight and mass

Estimating materials needs for a given job

 

Solving problems relating to size, shape and capacity in business and industry

5G-4.2 Predict the impact of changes in linear dimensions on the perimeter, area, and volume of figures.

5G-4.2.1 Know the formulas for perimeter, area, and volume.

 

5G-4.2.2 Know how to list data in a chart or table

 

5G-4.2.3 Know how to graph data from a table

 

5G-4.2.4 Know how to describe and analyze patterns of change in a table or graph

Deciding whether and how suggested increases or decreases in measurement will change a manufacturing or building project

5G-4.3 Calculate and interpret rates of change from graphical and numerical data.

5G-4.3.1 Demonstrate an ability to extrapolate numerical data from graphic presentations

 

5G-4.3.2 Demonstrate an ability to accurately calculate percentages

Determine the rate of increase/decrease of gasoline prices based on newspaper reports

5G-4.4 Solve problems of area involving inscribed figures (e.g.  a circle inscribed in square).

5G-4.4.1 Demonstrate a familiarity with the formulas for area of polygons and circles.

 

5G-4.4.2 Demonstrate an understanding of when areas in an inscribed figure are excluded requiring subtraction

Designing a pattern for a flower garden

 

Determining an arrangement for furniture of various shapes in the home

5G-4.5 Use simplified formula to convert between Fahrenheit and Celsius temperatures.

5G-4.5.1 Demonstrate an understanding of the constants and variables provided in conversion formulas

Determining the temperature reported in an area using either the metric or ASE system

 


Level 6: ASE / Bridge to College Standards

See “How to Use This Document (Teacher’s Guide) and (Connecting Curriculum, Instruction and Assessment),” pages 8-10.  At this time, the Massachusetts ABE Test for Math does not assess students’ knowledge at this level.

 

Strand: Number Sense

Learners engage in problem solving within adult contextual situations by communicating, reasoning, and connecting to the following standards:

 

Standard 6N-1. Represent and use numbers in a variety of equivalent forms in contextual situations

Benchmark: At this level an adult will be expected to:

Enabling Knowledge and Skills

Examples of Where Adults Use It

6N-1.1 Read, write, order and compare positive and negative numbers of any size.

 

 

 

6N-1.1.1 Demonstrate an understanding that the position of a digit signifies its value

 

6N-1.1.2 Know what each digit in a number represents, including the use of zero as a place holder

 

6N-1.1.3 Demonstrate an understanding that the meaning of negative numbers in a practical context (e.g. temperature below zero, loss in trading)

Understanding and comparing government spending figures on public services

 

Understanding and comparing change in the value of stocks

6N-1.2 Read, write, order and compare fractions and mixed numbers.

6N-1.2.1 Change fractions to equivalent fractions with a common denominator

Comparing overtime rates

 

 

6N-1.3 Read, write, order and compare decimal numbers.

 

 

 

 

6N-1.3.1 Demonstrate an understanding that the position of a digit signifies its value

 

6N-1.3.2 Know that the decimal point separates whole numbers from decimal fractions

 

6N-1.3.3 Know what each digit represents, including the use of zero as a place holder

Reading and comparing gas prices

 

Reading and comparing metric measurements

 

Comparing currency exchange rates

6N-1.4 Order and compare percentages and understand percentage increase and decrease.

 

 

 

 

6N-1.4.1 Explain percentage as the number of parts in every 100

 

6N-1.4.2 Describe how 100% is the whole

 

6N-1.4.3 Demonstrate an understanding that a 10% pay increase is more than a 5% pay increase, but the actual increase depends on the number operated on

Understanding 20% off in a sale

 

Understanding a price increase of 10%

6N-1.5 Identify and use equivalencies between fractions, decimals and percentages.

 

 

 

 

6N-1.5.1 Explain how fractions, decimals, and percentages are different ways of expressing the same thing

 

6N-1.5.2 Know that percentages are fractions out of 100

 

 

6N-1.5.3 Express decimal fractions in tenths, hundredths, thousandths

Writing fractions of an hour as decimals on a time sheet (e.g. ¾ hour as 0.75)

 

Recognizing that a deli order for 1/3 pound will read about 0.33 on a digital scale

6N-1.6 Read and write numbers in exponential notation using integer exponents.

 

 

 

 

6N-1.6.1 Demonstrate an understanding that a positive exponent indicates the base is to be multiplied by itself that number of times

 

6N-1.6.2 Demonstrate an understanding that a negative exponent indicates the base is to be divided by itself that number of times

Using a calculator to compute with small and large numbers

 

Using exponential notation for metric conversion

 

 

Standard 6N-2. Understand meanings of operations and how they relate to one another

Benchmark: At this level an adult will be expected to:

Enabling Knowledge and Skills

Examples of Where Adults Use It

 6N-2.1 Demonstrate an understanding that use of the associative and commutative properties of addition and multiplication and the distributive property of multiplication over addition can simplify computations with decimals, fractions, and integers.

6N-2.1.1 Demonstrate conceptual and procedural understanding of operations with decimals, fractions, and integers.

 

6N-2.1.2 Know meaning of commutativity and associativity and distributive properties with whole numbers

Using a scientific calculator

6N-2.2 Demonstrate an understanding that raising a number to a negative integer is repeated division.

 

6N-2.2.1 Demonstrate an understanding of exponents

 

6N-2.2.2 Use rules of exponents for multiplication and division

 

 

Standard 6N-3. Compute fluently and make reasonable estimates

Benchmark: At this level an adult will be expected to:

Enabling Knowledge and Skills

Examples of Where Adults Use It

6N-3.1 Add, subtract, multiply and divide decimals up to three places.

 

 

6N-3.1.1 Use strategies to check answers (e.g. approximate calculations using whole numbers)

 

6N-3.1.2 Know how to align numbers for column addition and subtraction

 

6N-3.1.3 Explain the placement of the decimal point in multiplying decimals

 

6N-3.1.4 Explain the placement of the decimal point when dividing decimals

Converting sums of money between currencies

6N-3.2 Calculate ratio and direct proportion.

 

 

6N-3.2.1 Demonstrate an understanding of a ratio written in the form 3:2

 

6N-3.2.2 Work out the number of parts in a given ratio, and the value of one part

Comparing the price of products of different weights or capacities

6N-3.3 Add, subtract, multiply and divide using fractions.

 

 

 

6N-3.3.1 Change fractions to equivalent fractions for the purpose of adding and subtracting

 

6N-3.3.2 Find a fraction quotient through multiplication

Adding hours on a time sheet that includes fractions

 

 

6N-3.4 Add, subtract, multiply and divide using integers.

 

 

6N-3.4.1 Explain how number direction affects the four operations

Finding the average temperature

 

Figuring the net result of banking transactions

 

Determining profit after totaling costs

6N-3.5 Compute with percentage.

 

 

6N-3.5.1 Demonstrate an understanding of how to use proportion to figure with percentage

Figuring the effect on mortgage payments of a change in interest rates

6N-3.6 Use a calculator to calculate efficiently using whole numbers, integers, fractions, decimals, percentages.

 

 

6N-3.6.1 Change the sign of a number

 

6N-3.6.2 Change a fraction to a decimal

 

6N-3.6.3 Change a percentage to a decimal

 

6N-3.6.4 Interpret a calculator display employing scientific notation

 

6N-3.6.5 Find a trigonometric function of a number (e.g. cos 90°)

 

6N-3.6.6 Interpret a rounding error such as 6.9999999 as 7

 

6N-3.6.7 Demonstrate an understanding of the use of memory and constant functions

 

6N-3.6.8 Use strategies to check answers obtained with a calculator

Any calculations at this level

 

 

Strand: Patterns, Functions, and Algebra

Learners engage in problem solving within adult contextual situations by communicating, reasoning, and connecting to the following standards:

 

Standard 6P-1. Explore, identify, analyze, and extend patterns in mathematical and adult contextual situations

Benchmark: At this level an adult will be expected to:

Enabling Knowledge and Skills

Examples of Where Adults Use It

6P-1.1 Describe, complete, extend, analyze, generalize, and create a wide variety of patterns, including iterative/recursive (e.g. Fibonnacci Numbers), linear, quadratic and exponential functions.

 

 6P-1.1.1 Create and analyze different representations, such as tables, graphs, verbal descriptions, and equations

 

6P-1.1.2 Create algebraic expressions, rules, formulae, or sketch graphs to generalize number patterns or observable relationships between variables

Creating mathematical models


 

6P-1.2 Explain the difference between linear and exponential growth.

 

6P-1.2.1 Identify general shapes and major characteristics of linear and simple non-linear graphs and interpret their real world meanings

 

6P-1.2.2 Draw graphs using techniques such as plotting points; sketching from known main features of algebraic function; or using technology like a graphing calculator or computer package

Reading scientific or economic charts

 

Standard 6P-2. Articulate and represent number and data relationships using words, tables, graphs, rules, and equations

Benchmark: At this level an adult will be expected to:

Enabling Knowledge and Skills

Examples of Where Adults Use It

6P-2.1 Convert between different representations, such as tables, graphs, verbal descriptions, and equations.

6P-2.1.1 Explain how a variety of problem situations may be modeled by the same function or type of function

Connecting visual information from a variety of sources to reach a decision about a process, product or service

6P-2.2 Develop algebraic expressions, rules, formulae, or sketch graphs to generalize straightforward number patterns or observable relationships between variables.

 

6P-2.2.1 Create own equations, rules or sketch graphs from word problems or observed situations

 

6P-2.2.2 Recognize and analyze patterns in number relationships and in charts and tables

Describing growth or change in workplace output

6P-2.3 Draw graphs using techniques such as plotting points; sketching from known main features of algebraic function; or using technology like a graphing calculator or computer package.

 

6P-2.3.1 Create a table of values for relations and functions

 

6P-2.3.2 Demonstrate an understanding of slope

 

6P-2.3.3 Can use slope-intercept form of equations

 

6P-2.3.4 Know spreadsheet conventions

 

6P-2.4 Identify general shapes and major characteristics of linear and simple non-linear graphs and interpret their real world meanings.

6P-2.4.1 Recognize and use direct and indirect variation

Applying graphic information to the decision- making process

 

Standard 6P-3. Recognize and use algebraic symbols to model mathematical and contextual situations

Benchmark: At this level an adult will be expected to:

Enabling Knowledge and Skills

Examples of Where Adults Use It

6P-3.1 Recognize that a variety of problem situations may be modeled by the same function or type of function.

 

6P-3.1.1 Describe experience using common functions

 

6P-3.1.2 Describe observations of similarities between graphs of functions of the same type

Preparing for further study


 

6P-3.2 Convert between different representations, such as tables, graphs, verbal descriptions, and equations.

 

6P-3.2.1 Graph data in table form

 

6P-3.2.2 Form a table from data in graph form

 

6P-3.2.3 Find the equation of a line or how to figure slope and intercept from table data

Presenting findings of data exploration

6P-3.3 Evaluate formulas and functions.

 

6P-3.3.1 Explain that a variable is replaced by its number value within parentheses when a formula or function is evaluated

 

6P-3.3.2 Demonstrate an understanding that when there is no operator between a number and a bracket or parentheses that multiplication is implied

 

6P-3.3.3 Demonstrate knowledge of order of operations

Informally using d = rt to make estimates regarding speed or time of departure

 

Using a scientific calculator

6P-3.4 Solve equations (e.g. linear, quadratic, exponential, trigonometric) and systems of linear equations.

 

6P-3.4.1 Demonstrate fluency working with algebraic expressions

 

6P-3.4.2 Demonstrate experience with a graphing calculator

Preparing for further study

 

Measuring angles in industrial settings

6P-3.5 Recognize and use direct and indirect variation.

 

6P-3.5.1 Describe experience using common functions

 

6P-3.5.2 Describe observations of similarities between graphs of functions of the same type

 

 

Standard 6P-4. Analyze change in various contexts

Benchmark: At this level an adult will be expected to:

Enabling Knowledge and Skills

Examples of Where Adults Use It

6P-4.1 Approximate and interpret rates of change from graphical and numerical data.

 

6P-4.1.1 Demonstrate an understanding that slope represents rate of change

 

6P-4.1.2 Find the slope from a line graph or table of data

Looking for trends (e.g. in the price of items, in revenue for a business, in value of wages)

 

 

Strand: Statistics and Probability

Learners engage in problem solving within adult contextual situations by communicating, reasoning, and connecting to the following standards:

 

Standard 6S-1. Collect, organize and represent data

Benchmark: At this level an adult will be expected to:

Enabling Knowledge and Skills

Examples of Where Adults Use It

6S-1.1 Pose both categorical and numerical questions about himself or his environment.

6S-1.1.1 Demonstrate that answers can be found by observing and asking relevant questions and counting responses

Working on a playground committee to select equipment


 

6S-1.2 Collect and organize responses to posed questions.

6S-1.2.1 Demonstrate an understanding that the concept of categories such as shape, size, color or yes or no responses

Gathering data for a report

6S-1.3 Choose appropriate representation to display responses to all types of data.

6S-1.3.1 Demonstrate an understanding that categorical data is usually displayed on bar or circle graphs

 

6S-1.3.2 Demonstrate an understanding that numerical data and change over time is usually displayed on a line graph

 

6S-1.3.3 Know how to calculate percents and find percents and/or fractions of 360 degrees

 

6S-1.3.4 Demonstrate an understanding that a table can be more accurate than a graph when recording precise numerical data as in decimal values.

Analyzing data from graphs in newspapers or periodicals

6S-1.4 Collect comparative data on a single given question such as responses grouped by age group vs. responses grouped by gender.

6S-1.4.1 Know that responses grouped by different criteria must be recorded in separate data sets

Gathering information regarding taxpayer groups in a community

 

Gathering information regarding target audiences for products

6S-1.5 Display comparative data on a double bar or line graph.

6S-1.5.1 Explain why separate data sets must be identified by different colors or line patterns

 

6S-1.5.2 Demonstrate an understanding that a key to identify each data set must be provided

Showing results of data collection

6S-16 When computers and software are available, know how to use a spreadsheet.

6S-1.6.1 Understand that the rows and columns on a spreadsheet are user defined

 

6S-1.6.2 Understand that cells on the spreadsheet are the intersection of user defined rows and columns

 

6S-1.6.3 Demonstrate an ability to enter formulas for operations on cell data

Entering information on a spreadsheet in the workplace

 

Creating a spreadsheet for personal finance records

 

Standard 6S-2. Read and interpret data representations

Benchmark: At this level an adult will be expected to:

Enabling Knowledge and Skills

Examples of Where Adults Use It

6S-2.1 Identify graphs and tables in available resources.

6S-2.1.1 Demonstrate an understanding that a graph is a visual representation

 

6S-2.1.2 Understand that a table arranges information in rows and columns

Reading graphics in newspapers and magazines


 

6S-2.2 Know where graphs and tables are likely to be found.

6S-2.2.1 Explain that graphs and tables can be found in newspapers, magazines, research journals, and promotional materials

 

6S-2.2.2 Explain that a table is an organizing tool used in manuals, tax forms, financial statements etc.

Reading advertisements

 

Looking up taxes payments

 

Finding current interest rates

 

6S-2.3 Give a verbal description of bar, line, and circle graphs, and tables.

6S-2.3.1 Demonstrate an understanding that a bar graph uses bars of various heights to display amount

 

6S-2.3.2 Demonstrate an understanding that line graphs use lines to connect data points

 

6S-2.3.3 Demonstrate an understanding that a circle or pie graph represents the whole or 100%

Participating in class or work discussions about data representations

6S-2.4 Make numerical comparisons about relative values on graphs and tables.

6S-2.4.1 Demonstrate and ability to use number sense skills

Following changes on sales charts for business trends

6S-2.5 Infer meaning from gaps, clusters, and comparisons of data.

6S-2.5.1 Demonstrate ways to compare numbers

 

6S-2.5.2 Demonstrate how to connect the shape and comparisons of data with text or background knowledge to infer causes for such phenomena

Reading exam questions

 

Reading corporate or government reports

6S-2.6 Infer consequences related to data outcomes.

6S-2.6.1 Project possible consequences from examining data and text and connecting these to similar situations

Reading exam questions

 

Reading corporate or government reports

 

Standard 6S-3. Describe data using numerical descriptions, statistics and trend terminology

Benchmark: At this level an adult will be expected to:

Enabling Knowledge and Skills

Examples of Where Adults Use It

6S-3.1 Identify the minimum, maximum, spread, shape, and range of data.

 

6S-3.1.1 Explain terms minimum, maximum, and spread

 

6S-3.1.2 Demonstrate an understanding that range is the difference between the smallest and largest values in the data set

 

6S-3.1.3 Recognize gaps, holes, and clusters in the data set to determine where data is missing and where it is heavily represented

Reading temperature charts and in discussions with a financial planner about retirement investment plans offered at work.

6S-3.2 Use 'most of' statements to describe data.

6S-3.2.1 Recognize that values in the data set can be repeated and some values may be repeated more frequently than others

 


 

6S-3.3 Find the mean.

6S-3.3.1 Know that mean is “average” and that average in this case is about equal distribution

 

6S-3.3.2 Describe how the average can be found by adding all values in the data set and dividing by the number of values in the set

Estimating one’s daily expenses.

 

Determining a grade point average

6S-3.4 Find the median.

6S-3.4.1 Know that median is the middle value

 

6S-3.4.2 Know that when there is an even number of values in the data set, the median is found by calculating the mean of two middle values

Explaining to someone what it means to say “the median salary is $X per hour,” or that the median years worked at a company is X.”

6S-3.5 Identify the effect of spread on mean and median.

6S-3.5.1 Recognize the minimum or maximum value can greatly affect the mean but will not affect the median

 

6S-3.5.2 Explain how the spread of data can affect the “closeness” of the mean and median values

Discussing with real estate brokers the “true” value of homes in a neighborhood

 

Standard 6S-4. Make and evaluate arguments or statements by applying knowledge of data analysis, bias factors and graph distortions

Benchmark: At this level an adult will be expected to:

Enabling Knowledge and Skills

Examples of Where Adults Use It

6S-4.1 Make statements about data trends to support or reject arguments/statements forwarded by others.

 

6S-4.1.1 Demonstrate an understanding that lines going up mean increase; lines tilting down mean decrease and that they can vary over time

 

6S-4.1.2 Explain that a flat line means no change

 

6S-4.1.3 Define vocabulary to describe trends (e.g. “sharp” increase, “plummeted,” etc.)

Analyzing reports on stock market

 

Describing movement of a product, process or service

6S-4.2 Know when percents given and figures used don’t match

Make accurate statements using percents.

6S-4.2.1 Describe ways for estimating and calculating percents of numbers

 

6S-4.2.2 Explain what it means to have an increase of more than 100 percent

 

6S-4.2.3 Demonstrate an understanding of the significance of large or small percent increases or decreases in various contexts

Analyzing social science reports


 

6S-4.3 Recognize that mean, median, and mode numbers are considered “averages,” and that averages represent numbers typical of the data that can support an argument.

 

 

6S-4.3.1 Explain that what are termed “averages” are numbers supposedly “typical” of data

 

6S-4.3.2 Describe ways in which “averages” are supposed to be “typical” of data; median is the middle value, mean implies equal distribution of all data

Examining house sale prices to determine which towns are most likely to have affordable housing stock

 

Debating rent increases

6S-4.4 Demonstrate an understanding of the impact of spread on mean and median, and therefore, when the choice of statistic is appropriate and know that mean and medians are compressions of data.

6S-4.4.1 Use techniques for finding mean and median

 

6S-4.4.2 Describe with spread changes and resulting changes or lack of changes in mean and median

 

6S-4.4.3 Explain why means and medians don’t always represent what is typical

 

6S-4.4.4 Describe why the choice of statistic is inappropriate or appropriate

Reading advertisements or demographic reports in order to make decisions

 

Negotiating salary increases

6S-4.5 Determine which statistic, mean or median, is appropriate for data.

6S-4.5.1 Describe experience with inappropriate uses of mean and median

 

6S-4.5.2 Use appropriate statistic to support an argument

Consuming health and fitness data to determine a plan of action

6S-4.6 Recognize that bar widths can provide misleading information, and state how those distortions are used to affect the arguments/statements.

6S-4.6.1 Demonstrate an understanding that visual messages are given by bar widths (e.g. thin relays message of  “less” and wide relays message of  “more”)

 

6S-4.6.2 Demonstrate an understanding that visual messages can contradict or enhance evidence

 

6S-4.6.3 Describe scale distortions and relate impacts on arguments/statements

Reading advertisements to make consumer choices

6S-4.7 Recognize scale distortions in research materials, and state how those distortions are used to affect the arguments/statements.

6S-4.7.1 Explain that scales are represented in regular increments

 

6S-4.7.2 Demonstrate an understanding that the size of the increments used in scales can make changes seem more or less significant

 

6S-4.7.3 Describe scale distortions and relate impacts on arguments/statements

Consuming or preparing environmental and/or corporate reports on pollution

6S-4.8 Recognize wedge size distortions, and state how those distortions are used to affect the arguments/statements.

6S-4.8.1 Wedge size in circle graphs should correspond roughly to fraction of data represented

 

6S-4.8.2 Know how to describe wedge distortions and relate impacts on arguments/statements

Working with population preference or condition data; understanding advertisements


 

6S-4.9 Note where authors of data reports can manipulate data to benefit themselves or malign others in mixed materials and state those bias factors.

6S-4.9.1 Determine who produced a data report and how their interests might affect the report  (e.g. as in conflict of interest.) Know how to articulate information about conflicts of interest or bias when noted

Reading advertisements and product reports

6S-4.10 Demonstrate an understanding that different categorizations of data reveal different stories and state how and why such effects relate to arguments/statements.

6S-4.10.1 Categorize data in a variety of ways (e.g. aggregate or disaggregate data)

 

6S-4.10.2 Make “story” statements about what is seen in data and how that changes as categories change

 

6S-4.10.3 Describe possible shifts in data interpretation resulting from the choice of data categorization

Working with demographic data reports or consumer goods’ data to refute a company’s position or to take a stand on an issue

6S-4.11 Demonstrate an understanding of the impacts of data compression and state how and why such effects relate to arguments/statements.

6S-4.11.1 Explain why data representations do not necessarily show every datum; therefore, individual variations are not visible

 

6S-4.11.2 Explain how personal or regional (subset) variations are sometimes more relevant to arguments/statements than aggregate data

 

6S-4.11.3 State source and effects of data compression and relate to arguments/statements forwarded by others

Analyzing consumer preferences’ or selections’ data to determine if it truly reflects what it purports to

 

Using statistical process control information in the workplace

6S-4.12 Compare and contrast graphs to evaluate for contradictory or unsupported statements.

6S-4.12.1 Explain that statements or arguments based on data are sometimes generated by comparing or contrasting graphs

 

6S-4.12.2 Explain that statements or arguments based on one graph are sometimes contradicted in another

 

6S-4.12.3 Where complementary data might be found

Preparing academic research reports

 

Analyzing poll data

6S-4.13 Demonstrate an understanding of simple sample biases.

6S-4.13.1 Explain how sample size reflects on reliability of data. 

 

6S-4.13.2 Explain how sample composition reflects on reliability of data

Preparing academic research reports

 

Analyzing corporate reports

 

Standard 6S-5. Know and apply basic probability concepts

Benchmark: At this level an adult will be expected to:

Enabling Knowledge and Skills

Examples of Where Adults Use It

6S-5.1 Discuss events as likely or unlikely.

6S-5.1.1 Demonstrate an understanding that while some events are impossible, some are certain to happen, and in other events some are more likely to occur than others

Deciding to avoid or use certain products


 

6S-5.2 Give the probability of a single outcome in simple concrete situations such as tossing a coin or rolling a die.

6S-5.2.1 Demonstrate an understanding that probability depends on the total number of possibilities

Tossing a coin or Rolling dice

 

Explaining to children the probability of winning or losing in a competitive activity

6S-5.3 State probability as a ratio fraction.

6S-5.3.1 Describe how probability is the ratio of the potential successful outcomes to total possibilities

 

6S-5.3.2 Know that such ratios can be written in fraction form

 

6S-5.3.3 Know that ratio fractions can be simplified

Playing card games

 

Interpreting the odds at a sporting event

 

Understanding mortality rates related to certain diseases

6S-5.4 State probability as a percent.

6S-5.4.1 Understand that the likelihood of an event is measured on a scale of 0% being impossible and 100% being certain

Interpreting the odds at a sporting event

 

Understanding mortality rates related to certain diseases

6S-5.5 Find the probability of both independent and dependent events.

6S-5.5.1 Demonstrate an understanding that the probability is independent when the outcome of one event does not influence the outcome of another

 

6S-5.5.2 Demonstrate an understanding that the probability is dependent when the outcome of one event directly influences the outcome of subsequent events

Interpreting the odds of contracting breast cancer and being in an airplane accident.