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
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:
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
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.
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.
|
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 ÞLevel 1: Beginning Adult Numeracy
Strand Þ Number
Sense
Learners engage in problem solving within adult contextual
situations by communicating, reasoning, and connecting to:
|
Standard
Þ
|
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
Þ
Assessment
(See
page 10)
Þ
|
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
|
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
|
|
|
|
Ý
Enabling skill
|
Ý 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.”
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:
- 2 refers to the Proficiency Level 2
- P- refers to the Strand, Patterns, Functions and Algebra (N
for Number Sense, and so on)
- 3 refers to the Standard (Recognize and use algebraic
symbols to model mathematical and contextual situations)
- 4 refers to the Benchmark (Read and understand positive
and negative numbers as showing direction and change)
- 1 refers to the Enabling Knowledge and Skills (Know
that positive refers to values greater than zero)
How to use This Document in
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
Þ
Assessment
Þ
(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
|
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.
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.
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 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
|
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?
|
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
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-1.3.1
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
|
|
|
|
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
|
|
|
|
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-1.2.1
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-1.2.1
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-3.2.1
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
|
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
|
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
¸ 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 ¸ 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 ¸ 4 ¹ 4 ¸ 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 ¸ 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.
|
|
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 +, -, ´, ¸,
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 ¸
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 ¸ 2= ð
¸ 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-1.1.1
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
|
|
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-3.2.1
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
|
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 42
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.
|
|
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
|
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-2.2.2
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
|
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 +, -, ´, ¸, 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 ¸
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 ¸
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
|
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-1.1.1
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-4.1.1
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
|
|
Reading advertisements
to make choices
|
|
3S-4.11
Identify obvious misstatements.
|
3S-4.11.1
Recognize where to look for numbers representing relevant quantities
|
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
|
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
|
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