Massachusetts Adult Basic Education
Curriculum Framework
For
Mathematics and Numeracy
Adult and Community Learning Services
October, 2005
The Development of the Massachusetts ABE Curriculum Framework
What is Numeracy? A Definition of Numerate Behavior
How to use This Document (Teacher's Guide)
Connecting Curriculum, Instruction, and Assessment
Content Strands and Learning Standards
The Strand Patterns, Functions, and Algebra
The Strand Statistics and Probability
The Strand Geometry and Measurement
Level 1. Beginning Adult Numeracy
Strand: Patterns, Functions, and Algebra
Strand: Statistics and Probability
Strand: Geometry and Measurement
Level 2: Beginning ABE Mathematics
Strand: Patterns, Functions and Algebra
Strand: Statistics and Probability
Strand: Geometry and Measurement
Level 3: Intermediate ABE Mathematics
Strand: Patterns, Functions, and Algebra
Strand: Statistics and Probability
Strand: Geometry and Measurement
Level 4: Pre-GED / ABE Standards
Strand: Patterns, Functions and Algebra
Strand: Statistics and Probability
Strand: Geometry and Measurement
Strand: Patterns, Functions, and Algebra
Strand: Statistics and Probability
Strand: Geometry & Measurement
Level 6: ASE / Bridge to College Standards
Strand: Patterns, Functions, and Algebra
Strand: Statistics and Probability
Strand: Geometry and Measurement
Appendix A. Suggested Readings
Appendix B. Sample Instructional Units
Appendix C. Instructional Resources and Materials
Learning Differences and Disabilities
Appendix D. Criteria for Evaluating Instructional Materials and Programs
Appendix E. Massachusetts Common Core of Learning
Gaining and Applying Knowledge
Appendix F. Equipped for the Future Role Maps and Domain Skills
Citizen/Community Member Role Map
Lists of Skills from the Four Domains in the EFF Standards
Content Framework for EFF Standards
Special thanks are due to the team who have contributed to the development of the Massachusetts ABE Curriculum Framework for Mathematics and Numeracy over the past number of years:
Patricia Donovan*
Barbara Goodridge*
Robert Foreman
Roberta Froelich*
Esther D. Leonelli*
Andrea (Drey) Martone
Marilyn Moses*
Jenifer Mullen*
Mary Jane Schmitt*
Jane Schwerdtfeger
Ruth Schwendeman*
Judith Titzel
* Denotes members of the original Math Curriculum Framework Development Team
Massachusetts Department of Education, Adult and
Community Learning Services, October 2005
In addition, we would like to
recognize the ABE practitioners, students, business representatives, and other
stakeholders from across the Commonwealth who shared their valuable time and
talent through developmental working groups, field trials, and revisions that
were essential in bringing the ABE Curriculum Framework for Mathematics and
Numeracy to the level of quality that is reflected in this edition.
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.
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.
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.
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:
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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.
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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:
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Standard Þ |
Standard 2P-3. Recognize and use algebraic symbols to model mathematical and contextual situations
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Benchmark: At this level an adult will be expected to: |
Enabling Knowledge and Skills |
Examples of Where Adults Use It |
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Benchmark Þ
Assessment (See page 10) Þ
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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
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Reading thermometers
Riding an elevator below ground level Staying "in the black" or going "into the red" on bill paying
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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
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Reading and interpreting scales
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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.”[1] Adult learners need to know that what they are learning in the classroom is relevant to the lives and goals outside of the classroom. For this reason, we have included an application for each skill by giving an example of using the skill in an adult context.
It is our expectation that this format will be a useful tool for:
§ Lesson planning
§ Curriculum development
§ Presenting practical applications for adult use of the math skills
§ Assessing student math levels for placement, informal classroom instruction, and for pre- and post-test assessment
§ Connecting pre- and post-test assessment to curriculum and instruction
The standards and benchmarks for each level are ambitious. They set the bar to be reached by learners, not the expectation of what is covered in a given class in a given year. However, the Framework does assume that the teaching of numeracy and mathematics be given a significant amount of time and attention in a program’s class offerings and curriculum.
Mathematical understanding progresses from the concrete (counting two groups of blocks) to the representative (adding numbers presented in pictorial or verbal problems) to the abstract (using symbols and graphs). Presenting adults with problems or situations that allow them to develop their own approach to an inquiry model gives learners opportunities to talk about, write about, and represent math situations. During such inquiry, a learner can experience this progression in his or her own thinking. This affords an opportunity to see interconnections within math and between math and other disciplines.
The numbering system used with the Standards and benchmarks was developed so the specific benchmarks or enabling skills can be referred to (e.g. in a lesson plan, curriculum, or scope and sequence). In the number 2P-3.4.1, for example, the system is as follows:
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.
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At this level an adult will be expected to: |
Enabling Knowledge and Skills |
Examples of Where Adults Use It |
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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
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Reading thermometers
Riding an elevator below ground level Staying "in the black" or going "into the red" on bill paying
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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 |
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Habit |
Learner Question |
Curiosity |
Do I ask “Why,” “How,” or “What If” questions? |
Respect for EvidenceTo 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.
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Do I listen carefully for others’ use of evidence, and do I include evidence to support my solutions and ideas? |
PersistenceSolutions in mathematics are not always apparent at first glance. Persistence is necessary to work through challenging problems that stretch our understanding.
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Do I keep going when I feel lost or discouraged while solving problems? |
OwnershipWhat 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.
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In what ways do I show that my work is purposeful and important to me? |
ReflectionTo become an autonomous learner, it is necessary to think about how our learning happens. We need to consider how we learn from mathematical experiences.
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Do I notice and analyze how and what I learn?
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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.
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Strands |
StandardsLearners will demonstrate the ability to… |
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Number Sense
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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
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Patterns, Functions and Algebra
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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
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Statistics and Probability
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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
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Geometry and Measurement
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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
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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.
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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.
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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.
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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.
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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.
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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
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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.
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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.
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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.
Learners engage in problem solving within adult contextual situations by communicating, reasoning, and connecting to the following standards:
Learners engage in problem solving within adult contextual situations by communicating, reasoning, and connecting to the following standards:
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1P-3.2 Understand simple number sentences such as: 9 + 1 = 10 and ___ + 5 = 10 and 8 - 3 = ___ where the ___ represents a missing amount.
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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 |
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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 |
Learners engage in problem solving within adult contextual situations by communicating, reasoning, and connecting to the following standards:
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1S-2.2 Extract simple information from a list or two-column table.
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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 |
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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 |
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1S-2.4 Make comparative statements about relative values on a bar graph.
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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 |
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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 |
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Not applicable at this level. |
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Standard 1S-4. Make and evaluate arguments and statements by applying knowledge of data analysis, bias factors, graph distortions, and context |
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Not applicable at this level. |
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Learners engage in problem solving within adult contextual situations by communicating, reasoning, and connecting to the following standards:
See “How to use This Document (Teacher’s Guide) and (Connecting Curriculum, Instruction and Assessment),” pages 8-10.
Learners engage in problem solving within adult contextual situations by communicating, reasoning, and connecting to the following standards:
Learners engage in problem solving within adult contextual situations by communicating, reasoning, and connecting to the following standards:
Learners engage in problem solving within adult contextual situations by communicating, reasoning, and connecting to the following standards:
Learners engage in problem solving within adult contextual situations by communicating, reasoning, and connecting to the following standards:
See “How to use This Document (Teacher’s Guide) and (Connecting Curriculum, Instruction and Assessment),” pages 8-10.
Learners engage in problem solving within adult contextual situations by communicating, reasoning, and connecting to the following standards:
Learners engage in problem solving within adult contextual situations by communicating, reasoning, and connecting to the following standards:
Learners engage in problem solving within adult contextual situations by communicating, reasoning, and connecting to the following standards:
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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. |
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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 |
Learners engage in problem solving within adult contextual situations by communicating, reasoning, and connecting to the following standards:
See “How to use This Document (Teacher’s Guide) and (Connecting Curriculum, Instruction and Assessment),” pages 8-10.
Learners engage in problem solving within adult contextual situations by communicating, reasoning, and connecting to the following standards:
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4N-1.11 Recognize and use equivalent forms of common fractions (e.g. ½ = 5/10). |
4N-1.11.1 Demonstrate an understanding that equivalent fractions look different but have the same value
4N-1.11.2 Demonstrate an understanding that when the top and bottom number of a fraction are the same, the fraction is equivalent to 1 |
Calculating the size of a container required to hold a variety of portions (e.g. ¼ cup of x plus ¼ cup of y plus ½ cup of z) |
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4N-3.12 Multiply whole numbers and decimals by 10, 100, and 1,000 to understand the impact on place value. |
4N-3.12.1 Recognize the impact on place value of zeros added to whole numbers
4N-3.12.2 Recognize the impact on place value as the position of the decimal point changes |
Simplifying large numbers to estimate products |
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4N-3. 13 Divide whole numbers and decimals by 10, 100, and 1,000 to understand the impact on place value. |
4N-3.13.1 Recognize the impact on place value of zeros are cancelled in whole numbers
4N-3.13.2 Recognize the impact on place value as the position of the decimal point changes |
Simplifying large numbers to estimate quotients |
Learners engage in problem solving within adult contextual situations by communicating, reasoning, and connecting to the following standards:
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4P-2.2 Develop and use simple formulas from tables with one or two arithmetical steps for real life contexts. |
4P-2.2.1 Discover patterns in an “in-out” table
4P-2.2.2 Verbalize a rule for finding values in an “in-out” table
4P-2.2.3 Write a general expression for finding values in an “in-out” table
4P-2.2.4 Write an equation
4P-2.2.5 Decide on the effectiveness of the developed formula by substituting known values |
Converting temperature between Celsius and Fahrenheit
Finding interest on a loan |
Learners engage in problem solving within adult contextual situations by communicating, reasoning, and connecting to the following standards:
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4S-1.5 Display categorical data in a bar graph or simple fractions of data in a circle graph. |
4S-1.5.1 Demonstrate an understanding that the one axis displays the categories
4S-1.5.2 Demonstrate an understanding that the other axis is numbered sequentially
4S-1.5.3 Demonstrate an understanding that the height (or length) of the bar is equal to the amount on the corresponding axis
4S-1.5.4 Demonstrate an understanding that fractions of data sets (1/4,1/3,1/2, 2/3,3/4) can be represented as wedges of a circle graph |
Showing various groups’ responses to school activities or programs |
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4S-1.6 Convert a bar graph into a circle graph. |
4S-1.6.1 Demonstrate an understanding that all data must be included so that the circle graph represents 100% of the data |
Participating in class to understand interconnections between graphic representations |
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4S-1.7 Translate data from a numerical table to a line graph and vice versa. |
4S-1.7.1 Demonstrate an understanding that a table can display the same data as a line or bar graph but in rows and columns
4S-1.7.2 Demonstrate an understanding of the importance of labeling each axis
4S-1.7.3 Demonstrate an understanding that single data points are to be connected by a line to create the line graph |
Creating a bar graph to illustrate weight gain/loss over a one-week period
Creating a line graph to illustrate temperatures over a one-week period |
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4S-3.3 Find the mean. |
4S-3.3.1 Know that mean is “average” and that average in this case is about equal distribution
4S-3.3.2 Know that the average can be found by adding all values in the data set and dividing by the number of values in the set
4S-3.3.3 Demonstrate an understanding that what are termed “averages” are numbers supposedly “typical” of data
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Estimating one’s daily expenses |
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4S-3.4 Find the median and mode. |
4S-3.4.1 Know that median is the middle value
4S-3.4.2 Know that when there is an even number of values in the data set, the median is found by calculating the mean of two middle values
4S-3.4.3 Know that mode is the number or item that occurs most often in a set of data
4S-3.4.4 Know ways in which “averages” are supposed to be “typical” of data – median is the middle value and mean implies equal distribution of all data |
Explaining the median salary or median years worked in company statistics
Examining house sale prices to determine which towns are most likely to have affordable housing stock |
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4S-3.5 Identify the effect of spread on mean and median.
Assessed by 5S-4.5 |
4S-3.5.1 Know the minimum or maximum value can greatly affect the mean but will not affect the median |
Interpreting statistical data accurately |
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4S-4.3 Make statements about data trends to support or reject arguments/ statements forwarded by others.
Assessed by 5S-4.4 |
4S-4.3.1 Demonstrate an understanding that lines going up mean increase; lines tilting down mean decrease and that they can vary over time
4S-4.3.2 Know that a flat line means no change
4S-4.3.3 Specific vocabulary to describe trends (e.g. “sharp” increase, “plummeted,” etc.) |
Looking at reports on stock market to see if they reflect the trends represented |
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4S-4.4 Know statements using “double” and “half” or fifty percent are accurate.
Assessed by 3S-4.6
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4S-4.4.1 Double and halving numbers
4S-4.4.2 Fifty percent equals one half |
Using consumer reports to make decisions |
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4S-4.5 Verify that statements using three times or four times, one fourth or one tenth are accurate. |
4S-4.5.1 Know ways to estimate multiples of large numbers
4S-4.5.2 Know ways to estimate one fourth or one tenth of a number |
Using consumer reports to make decisions |
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4S-4.6 Know when percent figures don’t add up to 100% and when numbers and percent figures (50%, 25%, 10%) don’t match up.
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4S-4.6.1 Demonstrate an understanding that circle graphs usually represent 100%, and all figures in them should add to 100
4S-4.6.2 Know ways to estimate or easily calculate 50%, 25% and 10% of a number |
Reading expenditure reports from local or national governments to determine if money spent is totally accounted for
Analyzing income data reports to see if the percents given reflect the amounts represented |
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4S-4.7 Compare and contrast provided graphs to evaluate for contradictory or unsupported statements. |
4S-4.7.1 Recognize that statements or arguments based on data are sometimes generated by comparing or contrasting graphs
4S-4.7.2 Recognize that statements or arguments based on one graph are sometimes contradicted in another |
Analyzing accident-related data |
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4S-5.2 Give the probability of a single outcome in simple concrete situations such as tossing a coin or rolling a die.
Assessed by 3S-5.2
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4S-5.2.1 Demonstrate an understanding that probability depends on the total number of possibilities |
Tossing a coin
Rolling dice
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4S-5.3 State probability as a ratio fraction. |
4S-5.3.1 Know that probability is the ratio of the potential successful outcomes to total possibilities.
4S-5.3.2 Know that such ratios can be written in fraction form.
4S-5.3.3 Know that ratio fractions can be simplified |
Determining the chances of winning a prize in a drawing |
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4S-5.4 Find the probability of independent events. |
4S-5.4.1 Know that probability is the ratio of the potential successful outcomes to total possibilities.
4S-5.4.2 Know that such ratios can be written in fraction form or as one value compared to another
4S-5.4.3 Know that ratio fractions can be simplified |
Designing and conducting experiments using 1, 2, 3, and 4 different colored balls to determine the likelihood of randomly selecting a specific color by chance |
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4S-5.5 State the probability as a percent. |
4S-5.5.1 Know that ratio fractions can be expressed as a percent by expressing a proportion with the percent out of 100 |
Converting a specific set of outcomes as likelihood of the event happening in 100 attempts |
Learners engage in problem solving within adult contextual situations by communicating, reasoning, and connecting to the following standards:
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4G-1.2 Directly measure different angles with a protractor.
Assessed by 5G-1.7 |
4G-1.2.1 Estimate the measure of an angle using benchmarks of 90 degrees and 180 degrees |
Cutting molding for a corner |
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4G-1.3 Use informal visual methods to describe and compare shape, dimensions, perimeters, area, and angles, sides in two-dimensional (2-D) and three-dimensional (3D) objects.
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4G-1.3.1 Be able to solve practical problems using the properties of 2-D and 3-D figures
4G-1.3.2 Demonstrate an understanding that that area is conserved, but perimeter is not when 2-D objects are combined
4G-1.3.3 Build 3-D figures using 2-D plans and blocks |
Organizing a closet
Packing a trunk
Covering a package with paper
Tying string around a package |
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4G-1.4 Identify shapes that are congruent or similar. |
4G-1.4.1 Know that congruent shapes are exactly the same with equal sides and angles
4G-1.4.2 Know that similar shapes are the same shape, but different sizes
4G-1.4.3 Know that the corresponding angles of congruent and similar shapes are congruent
4G-1.4.4 Know that similar shapes are proportional to each other |
Assembling items bought unassembled (e.g. toys, exercise equipment, some furniture) |
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4G-1.5 Identify types of angles such as right, obtuse, acute, and straight. |
4G-1.5.1 Know that an acute angle has a measure of less than 90°
4G-1.5.2 Know that a right angle has a measure of 90°
4G-1.5.3 Know that an obtuse angle has a measure of more than 90 but less than 180°
4G-1.5.4 Know that a straight angle has a measure of 180° |
Using the basic properties of different types of triangles to prove basic theories and solve problems |
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4G-1.6 Understand the relationship of angles when you have a system of parallel lines cut by a transversal. |
4G-1.6.1 Know that a line that crosses two parallel lines is called a transversal
4G-1.6.2 Know that a transversal crosses two lines that are parallel to each crosses both lines at the same angle
4G-1.6.3 Know that when a transversal crosses two parallel lines the corresponding angles are equal to each other |
Cutting molding at a correct angle so that both ends meet with no space in between |
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4G-1.7 Identify different names of triangles by properties, such as isosceles, right, and equilateral. |
4G-1.7.1 Know that the sum of the angles of any triangle is 180°
4G-1.7.2 Know that equilateral triangles have three equal sides
4G-1.7.3 Know that each of the angles of an equilateral (equiangular) triangle measures 60°
4G-1.7.4 Know that any triangle with a 90° angle is a right triangle
4G-1.7.5 Know that any triangle with two equal sides is an isosceles triangle
4G-1.7.6 Know that the angles opposite the equal sides of an isosceles triangle are called the base angles, and that base angles are equal to each other |
Following plans when working on carpentry projects |
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4G-1.8 Estimate the measure of an angle using benchmarks. |
4G-1.8.1 Know the range of the measure for acute, right, obtuse, and straight angles
4G-1.8.2 Demonstrate an ability to estimate the measure of an angle based on that knowledge |
Estimating where a line of symmetry would fall in a rectangular object |
See “How to use This Document (Teacher’s Guide) and (Connecting Curriculum, Instruction, and Assessment),” pages 8-10.
Learners engage in problem solving within adult contextual situations by communicating, reasoning, and connecting to the following standards:
Learners engage in problem solving within adult contextual situations by communicating, reasoning, and connecting to the following standards:
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Benchmark: At this level an adult will be expected to: |
Enabling Knowledge and Skills |
Examples of Where Adults Use It |
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5P-2.1 Create own equations, rules or sketch graphs from word problems or observed situations.
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5P-2.1.1 Make a table using pattern values
5P-2.1.2 Verbalize a rule for finding values in the table
5P-2.1.3 Write a general expression for finding values in the table
5P-2.1.4 Decide on the effectiveness of the expression by substituting known values |
Working out the standard elements of a household budget |
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5P-2.2 Convert between different representations, such as tables, graphs, verbal descriptions, and equations. |
5P-2.2.1 Recognize that a variety of problem situations may be modeled by the same function or type of function |
Presenting results of data exploration |
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5P-2.3 Develop algebraic expressions, rules, formulae, or sketch graphs to generalize straightforward number patterns or observable relationships between variables. |
5P-2.3.1 Demonstrate an understanding of the parts of a graph
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Translating graphic depictions of data into oral or written descriptions to explain relationships |
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5P-2.4 Draw graphs using techniques such as plotting points, sketching from known main features of algebraic function, or using technology like a graphing calculator or computer package. |
5P-2.4.1 Know graphing techniques
5P-2.4.2 Understand use of a graphing calculator or spreadsheet |
Making visual aids for depicting change patterns in business or industry |
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5P-2.5 Identify general shapes and major characteristics of linear and simple non-linear graphs and interpret their real world meanings. |
5P-2.5.1 Recognize and use direct and indirect variation
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Interpreting graphic presentations of data to analyze events and make predictions |
Learners engage in problem solving within adult contextual situations by communicating, reasoning, and connecting to the following standards:
Learners engage in problem solving within adult contextual situations by communicating, reasoning, and connecting to the following standards:
See “How to Use This Document (Teacher’s Guide) and (Connecting Curriculum, Instruction and Assessment),” pages 8-10. At this time, the Massachusetts ABE Test for Math does not assess students’ knowledge at this level.
Learners engage in problem solving within adult contextual situations by communicating, reasoning, and connecting to the following standards:
Learners engage in problem solving within adult contextual situations by communicating, reasoning, and connecting to the following standards:
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6P-1.2 Explain the difference between linear and exponential growth.
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6P-1.2.1 Identify general shapes and major characteristics of linear and simple non-linear graphs and interpret their real world meanings
6P-1.2.2 Draw graphs using techniques such as plotting points; sketching from known main features of algebraic function; or using technology like a graphing calculator or computer package |
Reading scientific or economic charts |
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6P-3.2 Convert between different representations, such as tables, graphs, verbal descriptions, and equations.
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6P-3.2.1 Graph data in table form
6P-3.2.2 Form a table from data in graph form
6P-3.2.3 Find the equation of a line or how to figure slope and intercept from table data |
Presenting findings of data exploration |
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6P-3.3 Evaluate formulas and functions.
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6P-3.3.1 Explain that a variable is replaced by its number value within parentheses when a formula or function is evaluated
6P-3.3.2 Demonstrate an understanding that when there is no operator between a number and a bracket or parentheses that multiplication is implied
6P-3.3.3 Demonstrate knowledge of order of operations |
Informally using d = rt to make estimates regarding speed or time of departure
Using a scientific calculator |
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6P-3.4 Solve equations (e.g. linear, quadratic, exponential, trigonometric) and systems of linear equations.
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6P-3.4.1 Demonstrate fluency working with algebraic expressions
6P-3.4.2 Demonstrate experience with a graphing calculator |
Preparing for further study
Measuring angles in industrial settings |
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6P-3.5 Recognize and use direct and indirect variation.
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6P-3.5.1 Describe experience using common functions
6P-3.5.2 Describe observations of similarities between graphs of functions of the same type |
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Benchmark: At this level an adult will be expected to: |
Enabling Knowledge and Skills |
Examples of Where Adults Use It |
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6P-4.1 Approximate and interpret rates of change from graphical and numerical data.
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6P-4.1.1 Demonstrate an understanding that slope represents rate of change
6P-4.1.2 Find the slope from a line graph or table of data |
Looking for trends (e.g. in the price of items, in revenue for a business, in value of wages) |
Learners engage in problem solving within adult contextual situations by communicating, reasoning, and connecting to the following standards:
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Benchmark: At this level an adult will be expected to: |
Enabling Knowledge and Skills |
Examples of Where Adults Use It |
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6S-1.1 Pose both categorical and numerical questions about himself or his environment. |
6S-1.1.1 Demonstrate that answers can be found by observing and asking relevant questions and counting responses |
Working on a playground committee to select equipment |
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6S-1.2 Collect and organize responses to posed questions. |
6S-1.2.1 Demonstrate an understanding that the concept of categories such as shape, size, color or yes or no responses |
Gathering data for a report |
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6S-1.3 Choose appropriate representation to display responses to all types of data. |
6S-1.3.1 Demonstrate an understanding that categorical data is usually displayed on bar or circle graphs
6S-1.3.2 Demonstrate an understanding that numerical data and change over time is usually displayed on a line graph
6S-1.3.3 Know how to calculate percents and find percents and/or fractions of 360 degrees
6S-1.3.4 Demonstrate an understanding that a table can be more accurate than a graph when recording precise numerical data as in decimal values. |
Analyzing data from graphs in newspapers or periodicals |
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6S-1.4 Collect comparative data on a single given question such as responses grouped by age group vs. responses grouped by gender. |
6S-1.4.1 Know that responses grouped by different criteria must be recorded in separate data sets |
Gathering information regarding taxpayer groups in a community
Gathering information regarding target audiences for products |
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6S-1.5 Display comparative data on a double bar or line graph. |
6S-1.5.1 Explain why separate data sets must be identified by different colors or line patterns
6S-1.5.2 Demonstrate an understanding that a key to identify each data set must be provided |
Showing results of data collection |
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6S-16 When computers and software are available, know how to use a spreadsheet. |
6S-1.6.1 Understand that the rows and columns on a spreadsheet are user defined
6S-1.6.2 Understand that cells on the spreadsheet are the intersection of user defined rows and columns
6S-1.6.3 Demonstrate an ability to enter formulas for operations on cell data |
Entering information on a spreadsheet in the workplace
Creating a spreadsheet for personal finance records |
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Benchmark: At this level an adult will be expected to: |
Enabling Knowledge and Skills |
Examples of Where Adults Use It |
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6S-2.1 Identify graphs and tables in available resources. |
6S-2.1.1 Demonstrate an understanding that a graph is a visual representation
6S-2.1.2 Understand that a table arranges information in rows and columns |
Reading graphics in newspapers and magazines |
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6S-2.2 Know where graphs and tables are likely to be found. |
6S-2.2.1 Explain that graphs and tables can be found in newspapers, magazines, research journals, and promotional materials
6S-2.2.2 Explain that a table is an organizing tool used in manuals, tax forms, financial statements etc. |
Reading advertisements
Looking up taxes payments
Finding current interest rates
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6S-2.3 Give a verbal description of bar, line, and circle graphs, and tables. |
6S-2.3.1 Demonstrate an understanding that a bar graph uses bars of various heights to display amount
6S-2.3.2 Demonstrate an understanding that line graphs use lines to connect data points
6S-2.3.3 Demonstrate an understanding that a circle or pie graph represents the whole or 100% |
Participating in class or work discussions about data representations |
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6S-2.4 Make numerical comparisons about relative values on graphs and tables. |
6S-2.4.1 Demonstrate and ability to use number sense skills |
Following changes on sales charts for business trends |
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6S-2.5 Infer meaning from gaps, clusters, and comparisons of data. |
6S-2.5.1 Demonstrate ways to compare numbers
6S-2.5.2 Demonstrate how to connect the shape and comparisons of data with text or background knowledge to infer causes for such phenomena |
Reading exam questions
Reading corporate or government reports |
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6S-2.6 Infer consequences related to data outcomes. |
6S-2.6.1 Project possible consequences from examining data and text and connecting these to similar situations |
Reading exam questions
Reading corporate or government reports |
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6S-3.3 Find the mean. |
6S-3.3.1 Know that mean is “average” and that average in this case is about equal distribution
6S-3.3.2 Describe how the average can be found by adding all values in the data set and dividing by the number of values in the set |
Estimating one’s daily expenses.
Determining a grade point average |
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6S-3.4 Find the median. |
6S-3.4.1 Know that median is the middle value
6S-3.4.2 Know that when there is an even number of values in the data set, the median is found by calculating the mean of two middle values |
Explaining to someone what it means to say “the median salary is $X per hour,” or that the median years worked at a company is X.” |
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6S-3.5 Identify the effect of spread on mean and median. |
6S-3.5.1 Recognize the minimum or maximum value can greatly affect the mean but will not affect the median
6S-3.5.2 Explain how the spread of data can affect the “closeness” of the mean and median values |
Discussing with real estate brokers the “true” value of homes in a neighborhood |
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6S-4.3 Recognize that mean, median, and mode numbers are considered “averages,” and that averages represent numbers typical of the data that can support an argument.
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6S-4.3.1 Explain that what are termed “averages” are numbers supposedly “typical” of data
6S-4.3.2 Describe ways in which “averages” are supposed to be “typical” of data; median is the middle value, mean implies equal distribution of all data |
Examining house sale prices to determine which towns are most likely to have affordable housing stock
Debating rent increases |
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6S-4.4 Demonstrate an understanding of the impact of spread on mean and median, and therefore, when the choice of statistic is appropriate and know that mean and medians are compressions of data. |
6S-4.4.1 Use techniques for finding mean and median
6S-4.4.2 Describe with spread changes and resulting changes or lack of changes in mean and median
6S-4.4.3 Explain why means and medians don’t always represent what is typical
6S-4.4.4 Describe why the choice of statistic is inappropriate or appropriate |
Reading advertisements or demographic reports in order to make decisions
Negotiating salary increases |
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6S-4.5 Determine which statistic, mean or median, is appropriate for data. |
6S-4.5.1 Describe experience with inappropriate uses of mean and median
6S-4.5.2 Use appropriate statistic to support an argument |
Consuming health and fitness data to determine a plan of action |
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6S-4.6 Recognize that bar widths can provide misleading information, and state how those distortions are used to affect the arguments/statements. |
6S-4.6.1 Demonstrate an understanding that visual messages are given by bar widths (e.g. thin relays message of “less” and wide relays message of “more”)
6S-4.6.2 Demonstrate an understanding that visual messages can contradict or enhance evidence
6S-4.6.3 Describe scale distortions and relate impacts on arguments/statements |
Reading advertisements to make consumer choices |
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6S-4.7 Recognize scale distortions in research materials, and state how those distortions are used to affect the arguments/statements. |
6S-4.7.1 Explain that scales are represented in regular increments
6S-4.7.2 Demonstrate an understanding that the size of the increments used in scales can make changes seem more or less significant
6S-4.7.3 Describe scale distortions and relate impacts on arguments/statements |
Consuming or preparing environmental and/or corporate reports on pollution |
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6S-4.8 Recognize wedge size distortions, and state how those distortions are used to affect the arguments/statements. |
6S-4.8.1 Wedge size in circle graphs should correspond roughly to fraction of data represented
6S-4.8.2 Know how to describe wedge distortions and relate impacts on arguments/statements |
Working with population preference or condition data; understanding advertisements |
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6S-4.9 Note where authors of data reports can manipulate data to benefit themselves or malign others in mixed materials and state those bias factors. |
6S-4.9.1 Determine who produced a data report and how their interests might affect the report (e.g. as in conflict of interest.) Know how to articulate information about conflicts of interest or bias when noted |
Reading advertisements and product reports |
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6S-4.10 Demonstrate an understanding that different categorizations of data reveal different stories and state how and why such effects relate to arguments/statements. |
6S-4.10.1 Categorize data in a variety of ways (e.g. aggregate or disaggregate data)
6S-4.10.2 Make “story” statements about what is seen in data and how that changes as categories change
6S-4.10.3 Describe possible shifts in data interpretation resulting from the choice of data categorization |
Working with demographic data reports or consumer goods’ data to refute a company’s position or to take a stand on an issue |
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6S-4.11 Demonstrate an understanding of the impacts of data compression and state how and why such effects relate to arguments/statements. |
6S-4.11.1 Explain why data representations do not necessarily show every datum; therefore, individual variations are not visible
6S-4.11.2 Explain how personal or regional (subset) variations are sometimes more relevant to arguments/statements than aggregate data
6S-4.11.3 State source and effects of data compression and relate to arguments/statements forwarded by others |
Analyzing consumer preferences’ or selections’ data to determine if it truly reflects what it purports to
Using statistical process control information in the workplace |
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6S-4.12 Compare and contrast graphs to evaluate for contradictory or unsupported statements. |
6S-4.12.1 Explain that statements or arguments based on data are sometimes generated by comparing or contrasting graphs
6S-4.12.2 Explain that statements or arguments based on one graph are sometimes contradicted in another
6S-4.12.3 Where complementary data might be found |
Preparing academic research reports
Analyzing poll data |
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6S-4.13 Demonstrate an understanding of simple sample biases. |
6S-4.13.1 Explain how sample size reflects on reliability of data.
6S-4.13.2 Explain how sample composition reflects on reliability of data |
Preparing academic research reports
Analyzing corporate reports |
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6S-5.2 Give the probability of a single outcome in simple concrete situations such as tossing a coin or rolling a die. |
Tossing a coin or Rolling dice
Explaining to children the probability of winning or losing in a competitive activity |
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6S-5.3 State probability as a ratio fraction. |
6S-5.3.1 Describe how probability is the ratio of the potential successful outcomes to total possibilities
6S-5.3.2 Know that such ratios can be written in fraction form
6S-5.3.3 Know that ratio fractions can be simplified |
Playing card games
Interpreting the odds at a sporting event
Understanding mortality rates related to certain diseases |
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6S-5.4 State probability as a percent. |
6S-5.4.1 Understand that the likelihood of an event is measured on a scale of 0% being impossible and 100% being certain |
Interpreting the odds at a sporting event
Understanding mortality rates related to certain diseases |
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6S-5.5 Find the probability of both independent and dependent events. |
6S-5.5.1 Demonstrate an understanding that the probability is independent when the outcome of one event does not influence the outcome of another
6S-5.5.2 Demonstrate an understanding that the probability is dependent when the outcome of one event directly influences the outcome of subsequent events |
Interpreting the odds of contracting breast cancer and being in an airplane accident.
Interpreting the odds of contracting lung disease from smoking and dying of lung cancer. |
Learners engage in problem solving within adult contextual situations by communicating, reasoning, and connecting to the following standards:
Curry, D., Schmitt, M.J., and Waldron, S. (1996). A Framework for Adult Numeracy Standards: The Mathematical Skills and Abilities Adults Need to be Equipped for the Future, Boston, MA: The Adult Numeracy Practitioners Network.
Clermont, Yvan; Gal, Iddo; van Groenestijn, Mieke; Manly, Myrna; Schmitt, Mary Jane; and Tout, Dave. (2000). Numeracy Conceptual Framework for the International Adult Literacy and Lifeskills (ALL) Survey, Ottawa, Canada: Statistics Canada.
Gal, I. (Ed.). (2000). Adult Numeracy Development: Theory, Research, Practice. Cresskill, NJ:
Hampton Press, Inc.
Ma, Liping. (1999). Knowing and Teaching Elementary Mathematics, Mahwah, New Jersey: Lawrence Erlbaum Associates.
Marr, Beth and Tout, Dave. (1998). Certificates in General Education for Adults. Numeracy and Mathematics Stream. Victoria, Australia: Adult, Community and Further Education Board.
Massachusetts ABE Math Team (Leonelli, E., Merson, M.W., Schmitt, M.J., and Schwendeman, R. (editors.), (1994). The Massachusetts ABE Math Standards Project. (2 Vols.). Holyoke, MA: Holyoke Community College SABES Regional Center.
Massachusetts Mathematics Educators. (Nov. 2000). Mathematics for All.
Moses, R. and Cobb, C. (2001). Radical Equations: Math Literacy and Civil Rights. Boston, MA: Beacon Press.
Mullinix, B. (1994). Exploring What Counts: Mathematics Instruction in Adult Basic Education. Boston, MA: World Education.
Principles and Standards for School Mathematics. (2000). Reston, VA: National Council of Teachers of Mathematics.
Sharma, Mahesh C. (1994). Learning Problems in Mathematics: Diagnosis and Remedial Perspectives. Framingham, MA: Center for Teaching/Learning of Mathematics.
Stein, S. (2000), Equipped for the Future Content Standards: What Adults Need to Know and Be Able to Do in the 21st Century. Washington, DC: National Institute for Literacy. ED Pubs document EX0099P.
The Basic Skills Agency. (May 2000). The Adult Basic Skills Curriculum. London, UK: Department of Education and Employment.
Massachusetts Mathematics Curriculum Framework. (Nov. 2000). Malden, MA: Massachusetts Department of Education.
Goodridge, B., Leonelli, E., Moses, M., Steinback, M., and Tierney, C. (1999). Foundation for Algebra: ABE Math Curriculum Frameworks Unit, Malden, MA: Massachusetts Department of Education.
Goodridge, B., Leonelli, E., Moses, M., Steinback, M., and Tierney, C. (1998). Number Sense: ABE Math Curriculum Frameworks Unit, Malden, MA: Massachusetts Department of Education.
Goddard, R., Marr, B, and Martin, J. (1996). Strength in Numbers: A Resource Book for Teaching Adult Numeracy. ARIS/Language Australia: Melbourne, Australia.
Holme, S. and Marr, B. (1999). Mathematics: A New Beginning. A Resource Book for Teachers of Adults Returning To Study. Language Australia: Australia.
Huntington, L., Leonelli, E., and Merson, M. (1998). ABE Priority Math Curriculum: Number Sense, Measurement, Data. Boston, MA: Adult Literacy Resource Institute.
Goodridge, B., Leonelli, E., Moses, M., Steinback, M., and Tierney, C. (1999). Foundation for Algebra: ABE Math Curriculum Frameworks Unit, Malden, MA: Massachusetts Department of Education.
Meader, Pam, and Storer, Judy. (1998). Math for All Learners. Pre-Algebra. Portland, ME. J. Weston Walch. (Reproducible activity pages come with complete teacher notes.)
Meader, Pam, and Storer, Judy. (1998). Math for All Learners. Algebra. Portland, ME. J. Weston Walch, Publisher (Reproducible activity pages come with complete teacher notes).
Baratta-Lorton, Robert. (1977). Mathematics…A Way of Thinking. Reading, MA: Addison-Wesley Publishing Company.
Goodridge, B., Leonelli, E., Moses, M., Steinback, M., and Tierney, C. (1998). Number Sense: ABE Math Curriculum Frameworks Unit, Malden, MA: Massachusetts Department of Education.
Hope, Jack A., Reys, B., and Reys, R.E. (1988). Mental Math in Junior High, Palo Alto, CA: Dale Seymour Publications.
Hope, Jack A., Reys, B., and Reys, R.E. (1987). Mental Math in the Middle Grades. Palo Alto, CA: Dale Seymour Publications.
Phillips, Jan, (1995). Smart Solutions: Whole Numbers and Money (with Teachers Manual), Syracuse, NY: New Readers Press.
Reys, R.E., Trafton, P.R., Reys, B., Zawojewski, J. (1987). Computational Estimation Grade 6. Palo Alto, CA: Dale Seymour Publications.
Burns, Marilyn, (1987). A Collection of Math Lessons From Grades 1 Through 3. White Plains , NY: Math Solutions Publications (Reprinted 1997).
Burns, Marilyn, A. (1987). Collection of Math Lessons From Grades 3 Through 6. White Plains , NY: Math Solutions Publications.
Stenmark, J. K., Thompson, V., and Cossey, R. (1986). Family Math. Berkeley, CA: Regents, University of California.
Cohen, Sandra R. (1992). Figure It Out: Thinking like a Math Problem Solver, Books 1 - 6. North Billerica, MA: Curriculum Associates, Inc.
Greenes, C., Immerzeel, G., Ockenga, E., Schulman, L., and Spungin, R. (1982). Problem-Solving Skill Sheets, Blackline Masters. Techniques of Problem Solving (TOPS). Palo Alto, CA: Dale Seymour Publications.
Greenes, C., Immerzeel, G., Ockenga, E., Schulman, L., and Spungin, R. (1982). Techniques of Problem Solving (TOPS) 200 Illustrated Problem Cards with Teacher's Commentary. Palo Alto, CA: Dale Seymour Publications.
Manly, Myrna. (1992). The GED Math Problem Solver, Reasoning Skills to Pass the Test. Lincolnwood, IL: Contemporary Books.
Bley, Nancy S. and Carol A Thornton. (1989). Teaching Mathematics to Students with Learning Disabilities (Third Edition). Austin, TX.
Burns, Marilyn . (1992). About Teaching Mathematics: A K-8 Resource. Sausalito, CA: Math Solutions Publications.
Cooper, Richard. (1992). Tic Tac Toe Math (Workbook I). Bryn Mawr, PA: Learning disAbilities Resources.
Johnson, Stanley W. (1979). Arithmetic and Learning Disabilities: Guidelines for Identification and Remediation. Boston, MA: Allyn and Bacon, Inc.
Miles, T.R. and E. Miles, editors. (1992). Dyslexia and Mathematics. New York, NY: Routledge.
Sharma, Mahesh C. (1994). Learning Problems in Mathematics: Diagnosis and Remedial Perspectives. Framingham, MA: Center for Teaching/Learning of Mathematics.
Thornton, Carol A. and Nancy.S. Bley, editors. (1994). Windows of Opportunity: Mathematics for Students with Special Needs. Reston, VA: National Council of Teachers of Mathematics.
Adult Numeracy Network
http://www.literacynet.org/ann/
National Council of Teachers of Mathematics
Science and Numeracy Special Collection, National Institute for Literacy LINCS, http://literacynet.org/sciencelincs/
or
http://www.nifl.gov/lincs/collections/collections.html
The Math Forum
The Numeracy List (electronic discussion list sponsored by the Adult Numeracy Network)
http://www.nifl.gov/lincs/discussions/numeracy/numeracy.html
Considering Your Students, Your Teaching, and Materials You Will Use
Much good teaching comes from learning to ask the right kinds of questions, and paying attention to the answers you find. On the following pages, you will find lists of questions designed to help you determine:
§ your style as a teacher, and how you might want to choose materials and strategies;
§ who your students are, and what they want to learn;
§ how to pull together materials that will help you meet your objectives.
Remember that one bad day in the classroom or one frustrated student does not make you a bad teacher.
The first thing to consider in planning instruction is your own comfort level; if you feel uncomfortable with your materials or planned activities, it doesn’t matter how theoretically sound your plan is. You cannot teach well if you don’t believe in what you’re doing. Consider the following questions.
§ How would you describe your relationship with your students?
§ What expectations do you have about your students’ readiness to learn? Are your expectations realistic?
§ Do you know your students’ study habits? Have you talked with them about the things they need to do outside of regular class sessions?
§ Have you been direct and honest with students about how long it will take them to reach their goals?
§ Do you think you have students who will never reach the goals they have set for themselves? How do you handle this?
There are no right or wrong answers to these questions, only honest and dishonest ones. These are the kinds of issues that will affect the climate of your classroom and your students’ progress; too often, we don’t consider them until we’re faced with a dilemma. Taking the time to think about your expectations before a problem arises will help you to handle difficulties more calmly and professionally. Once you’ve taken the time to figure out your own approach to teaching the language arts, you need to consider the needs, expectations, and beliefs your students bring to the classroom. Try answering the questions above as you think your students would answer them, then ask yourself these additional questions.
§ What are my students’ approaches to learning? Do they have both short-term and long-term goals?
§ How long have these students been out of school? How do they describe their past school experiences?
It’s important to remember that we all carry the images and impressions of past school experiences, positive and otherwise, when we enter a new classroom. Most students in adult education have had a number of negative experiences, and may be wary of the new educational experience, particularly if your classroom reminds them at first of others where they’ve spent time.
You should also get in the habit of helping your students to set goals. Not everyone will progress at the same pace; some students may feel as though they’re making no progress at all, a feeling that will be exacerbated if others in the class are moving much more quickly. Having goals will give them something concrete to work toward, a way of measuring progress, and a sense of control over what they’re doing.
Finally, you need to consider what you will be teaching. Much of this will be obvious, but within any given class there is an enormous range of possibilities. If you visit ten ASE classes, you will find ten different ways of proceeding, and all of the teachers will tell you they’re working toward the same basic goals. Here are three questions that will help you to select materials for your class.
§ What do you think your students need to learn?
§ What do your students think they need to learn?
§ What kinds of materials are you comfortable using?
Although your students are in your class because of their general skill level, each of them will have a different profile of strengths and weaknesses. Getting to know those profiles will help you make decisions about the skills you want to focus on in your class.
Likewise, students may have some very specific reasons for attending your class beyond the general improvement of their literacy or their desire to earn a credential. The more you can address your students’ specific goals, the more motivated and open they will be. Your attentiveness to and respect for their goals will help you establish a level of trust that will allow your students to move beyond their comfort zone, helping them to take the risks necessary for significant strides in learning.
Finally, consider what materials you are comfortable using. Do you want worksheets, or do you prefer to make up questions yourself? What kinds of readings will your students do? What language or situations, if any, would make your students uncomfortable in a classroom setting? You also need to consider what materials your program makes available to you, and how much time you have to look for additional materials. A mix of materials and teaching strategies is often helpful in teaching students with different learning styles.
These questions are a jumping off point. Planning and implementing curriculum will challenge and occasionally frustrate you, but as was noted in the previous section, when your lesson takes off and your students get more involved and excited than you ever would have hoped, you will find that the effort has been worthwhile.
The Massachusetts Common Core of Learning supports all Department of Education curriculum development efforts, including both K-12 and Adult Basic Education. To quote from the Massachusetts Department of Education website, “The Education Reform Act of 1993 called for statewide curriculum frameworks and learning standards for all students in all core academic subjects. During the first year of Education Reform (1994), the Common Core of Learning was developed to identify the broad educational goals for all students.”
By identifying “what students should know and be able to do,” the purpose of the Common Core of Learning is the first step in the process of education reform. It was followed by the development of state curriculum frameworks that contain academic content standards that establish a basis for objective measurement. The next step is the development of an assessment system to evaluate student performance and measure the success of schools and ABE programs.
The Common Core of Learning focuses on three main areas: Thinking and Communicating, Gaining and Applying Knowledge, and Working and Contributing.
All students should:
§ Read and listen critically for information, understanding, and enjoyment.
§ Write and speak clearly, factually, persuasively, and creatively in standard English.
§ Distinguish fact from opinion, identify stereotyping, and recognize bias.
§ Read, write, and converse in at least one language in addition to English.
§ Apply mathematical skills to interpret information and solve problems.
§ Use the arts to explore and express ideas, feelings, and beliefs.
§ Use computers and other technologies to obtain, organize, and communicate information and to solve problems.
Define, Analyze, and Solve Complex Problems
§ Make careful observations and ask pertinent questions.
§ Seek, select, organize, and present information from a variety of sources.
§ Analyze, interpret, and evaluate information.
§ Make reasoned inferences and construct logical arguments.
§ Develop, test, and evaluate possible solutions.
§ Develop and present conclusions through speaking, writing, artistic, and other means of expression.
All students should:
§ Read a rich variety of literary works including fiction, poetry, drama, and nonfiction from different time periods and cultures, relating them to human aspirations and life experiences.
§ Analyze implications of literary works, and communicate them through speaking, writing, artistic, and other means of expression.
§ Know and understand the development and structure of English and other languages and how learning another language fosters appreciation of peoples and cultures.
§ Know and understand major mathematical concepts such as measurement, estimation, quantity, probability, and statistics; and explore the relationship of mathematics to other areas of knowledge.
§ Recognize and use patterns, construct mathematical models, represent and reason about quantities and shapes, draw accurate conclusions from data, and solve, justify, and communicate solutions to problems.
§ Apply the fundamental principles of the life sciences, physical sciences, earth/space sciences, and the science of technology to analyze problems and relate them to human concerns and life experiences.
§ Investigate and demonstrate methods of scientific inquiry and experimentation.
§ Know and make connections among important historical events, themes, and issues; recognize the role the past has played in shaping the present; and understand the process by which individuals and groups develop and work within political, social, economic, cultural, and geographic contexts.
§ Synthesize and communicate information about important events and fundamental concepts in Massachusetts, United States and world history, including historical documents such as the Declaration of Independence, Constitution, Bill of Rights, Federalist Papers, and the Gettysburg Address.
§ Know important information regarding the physical environment and understand concepts such as location and place, critical features of a region, demographic trends and patterns, and the relationship between people and the environment.
§ Know and understand the nature of the creative process, the characteristics of visual art, music, dance, and theatre, and their importance in shaping and reflecting historical and cultural heritage.
§ Analyze and make informed judgments regarding the arts.
§ Develop skills and participate in the arts for personal growth and enjoyment.
§ Know basic concepts of human development, mental health, sexuality, parenting, physical education and fitness, nutrition and disease prevention, and understand the implications of health habits for self and society.
§ Make informed and responsible judgments regarding personal health, including avoidance of violence, tobacco, alcohol, drugs, teen pregnancy, and sexually transmitted diseases.
§ Develop skills and participate in physical activities for personal growth, fitness, and enjoyment.
§ Monitor progress and learn from both successes and mistakes.
§ Manage money, balance competing priorities and interests, and allocate time among study, work, and recreation.
§ Work both independently and in groups.
§ Work hard, persevere, and act with integrity.
§ Accept responsibility for one’s own behavior and actions.
§ Know career options and the academic and occupational requirements needed for employment and economic independence.
§ Treat others with respect and understand similarities and differences among people.
§ Learn to resolve disagreements, reduce conflict, and prevent violence.
§ Participate in meaningful community and/or school activities.
§ Understand the individual’s rights, responsibilities, and role in the community, state and nation.
§ Understand how the principles of democracy, equality, freedom, law, and justice evolve and work in society.
§ Analyze, develop, and act on informed opinions about current economic, environmental, political and social issues affecting Massachusetts, the United States, and the world.
As quoted from the National institute for Literacy’s website www.nifl.gov/lincs/collections/eff/eff_roles.html, the Equipped for the Future Role Maps “describe what adults do when they are effective in their roles as parents/family members, workers, and citizens/community members. EFF partners developed the role maps by asking adults from many different walks of life to describe what they needed to be able to do to fulfill these three roles.”
“Each role map includes the following parts: the key purpose or central aim of the role, broad areas of responsibility that are the critical functions that adults perform, and key activities through which the role is performed. We can use the role maps to identify what it is important for us to teach and learn.”
Beginning on the following page are the Role Maps for Parent/Family, Worker, and Citizen/Community Worker, and finally, a list of skills form the four domains in the EFF Standards.
Effective family members contribute to building and maintaining a strong family system that promotes growth and development.
Broad Areas of Responsibility
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Promote Family Members’ Growth and Development Family members support the growth and development of all family members, including themselves |
Meet Family Needs and Responsibilities Family members meet the needs and responsibilities of the family unit |
Strengthen the Family System Family members create and maintain a strong sense of family |
Key Activities
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§ Make and pursue plans for self-improvement § Guide and mentor other family members § Foster informal education of children § Support children’s formal education § Direct and discipline children
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§ Provide for safety and physical needs § Manage family resources § Balance priorities to meet multiple needs and responsibilities § Give and receive support outside the immediate family |
§ Create a vision for the family and work to achieve it § Promote values, ethics, and cultural heritage within the family § Form and maintain supportive family relationships § Provide opportunities for each family member to experience success § Encourage open communication among the generations |
Effective workers adapt to change and actively participate in meeting the demands of a changing workplace in a changing world.
Broad Areas of Responsibility
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Do the Work
Workers use personal and organizational resources to perform their work and adapt to changing work demands |
Work With Others
Workers interact one-on-one and participate as members of a team to meet job requirements |
Work Within the Big Picture Workers recognize that formal and informal expectations shape options in their work lives and often influence their level of success |
Plan and Direct Personal and Professional Growth Workers prepare themselves for the changing demands of the economy through personal renewal and growth
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Key Activities
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§ Organize, plan and prioritize work § Use technology, resources, ands other work tools to put ideas and work directions into action § Respond to and meet new work challenges § Take responsibility for assuring work quality, safety and results
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§ Communicate with others inside and outside the organization § Give assistance, motivation, and direction § Seek and receive assistance, motivation and direction § Value people different from yourself |
§ Work within organizational norms § Respect organizational goals, performance and structure to guide work activities § Balance individual roles and needs with those of the organization § Guide individual and organizational priorities based on industry trends, labor laws/ contracts, and competitive practices |
§ Balance and support work, career, and personal needs § Pursue work activities that provide personal satisfaction and meaning § Plan, renew, and pursue personal and career goals § Learn new skills |
Effective citizens and community members take informed action to make a positive difference in their lives, communities and the world.
Broad Areas of Responsibility
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Become and Stay Informed Citizens and community members find and use information to identify and solve problems and contribute to the community |
Form and Express Opinions and Ideas Citizens and community members develop a personal voice and use it individually and as a group |
Work Together
Citizens and community members interact with each other people to get things done toward a common purpose
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Take Action to Strengthen Communities Citizens and community members exercise their rights and responsibilities as individuals and as members of groups to improve the world around them
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Citizen/Community Member Role Map -- Key Activities
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§ Identify, monitor, and anticipate problems, community needs, strengths, and resources for yourself and others § Recognize and understand human, legal, and civic rights and responsibilities for yourself and others § Figure out how the system that affects an issue works
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§ Strengthen and express a sense of self that reflects personal history, values, beliefs, and roles in the larger community § Learn from others’ experiences and ideas § Communicate so that others understand § Reflect on and re-evaluate your own opinions and ideas |
§ Get involved in the community and get others involved § Respect others and work to eliminate discrimination and prejudice § Define common values, visions, and goals § Manage and resolve conflict § Participate in group processes and decision-making |
§ Help yourself and others § Educate others § Influence decision-makers and hold them accountable § Provide leadership within the community |
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§
Identify how to have an
impact § Find, interpret, analyze, and use diverse sources of information, including personal experience
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In order to fulfill responsibilities as parents/family members, citizens, community members, and workers, adults must be able to demonstrate these generative skills. (See also Appendix D: Content Framework for EFF Standards, where these generative skills are in context.)
Communication Skills
§ Read with Understanding
§ Convey Ideas in Writing
§ Speak So Others Can Understand
§ Listen Actively
§ Observe Critically
Decision-making Skills
§ Use Mathematics in Problem Solving and Communication
§ Solve Problems and Make Decisions
§ Plan
Interpersonal Skills
§ Cooperate with Others
§ Advocate and Influence
§ Resolve Conflict and Negotiate
§ Guide Others
Lifelong Learning Skills
§ Take Responsibility for Learning
§ Reflect and Evaluate
§ Learn through Research
§ Use Information and Communications Technology
In order to fulfill responsibilities as parents/family members, citizens/community members, and workers, adults must be able to:
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MEET THESE FOUR PURPOSES
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ACCOMPLISH THESE COMMON ACTIVITIES |
DEMONSTRATE THESE GENERATIVE SKILLS |
UNDERSTAND AND BE ABLE TO USE THESE KNOWLEDGE DOMAINS
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Access |
Gather, Analyze, and Use Information |
Communication Skills |
How We Grow and Develop |
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To information so adults can orient themselves in the world |
Manage Resources |
Read with Understanding |
How Groups and Teams Work |
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Work Within the Big Picture |
Convey Ideas in Writing |
How Systems Work |
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Work Together |
Speak So Others Can Understand |
Rights and Responsibilities |
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Voice |
Provide Leadership |
Listen Actively |
Culture, Values, and Ethics |
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To be able to express ideas and |
Guide and Support Others |
Observe Critically |
How the Past Shapes the World We Live In |
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opinions with the confidence they will be heard and taken into account |
Seek Guidance and Support from Others |
Decision-Making Skills |
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Develop and Express Sense of Self |
Use Math to Solve Problems and Communicate |
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Respect Others and Value Diversity |
Solve Problems and Make Decisions |
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Independent Action |
Exercise Rights and Responsibilities |
Plan |
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To be able to solve problems and make decisions on one’s own, acting independently, |
Create and Pursue Vision and Goals |
Interpersonal Skills |
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without having to rely on others |
Use Technology and Other Tools to Accomplish Goals |
Cooperate with Others |
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Keep Pace with Change |
Advocate and Influence |
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Resolve Conflict and Negotiate |
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Bridge to the Future |
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Guide Others |
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Learn how to learn so adults can keep up with the world as |
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Lifelong Learning Skills |
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it changes |
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Take Responsibility for Learning |
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Reflect and Evaluate |
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Learn Through Research |
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Use Information and Communications Technology
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[1] Common Chapters for the Massachusetts Adult Basic Education Curriculum Frameworks, page 10 (Who are Adult Education Students?)
[2] Adapted from the Massachusetts English Language Arts Curriculum Framework
[3] Adapted from the Massachusetts ABE English Language Arts Curriculum Framework
[4] Adapted from the Massachusetts ABE English Language Arts Curriculum Framework