Massachusetts Adult Basic Education
Curriculum Framework
For
Mathematics and Numeracy
Massachusetts Department of
Education
Adult and Community Learning
Services
October, 2005
TABLE OF CONTENTS
Acknowledgments. 4
Introduction.. 5
The Development of the Massachusetts ABE
Curriculum Framework 5
What is Numeracy? A Definition of Numerate
Behavior.. 7
How to use This Document (Teacher's Guide) 8
Connecting Curriculum, Instruction, and Assessment.. 10
Core Concepts. 12
Guiding Principles. 14
Habits of Mind.. 15
Content Strands and Learning Standards. 16
The Strand Number
Sense. 17
The Strand Patterns, Functions, and Algebra.. 17
The Strand Statistics and Probability.. 19
The Strand Geometry and Measurement.. 19
Outline of Learning Levels. 21
Level 1. Beginning Adult Numeracy.. 21
Strand: Number
Sense. 21
Strand: Patterns,
Functions, and Algebra. 23
Strand: Statistics
and Probability. 25
Strand: Geometry
and Measurement 26
Level 2: Beginning ABE Mathematics. 29
Strand: Number
Sense. 29
Strand: Patterns,
Functions and Algebra. 34
Strand: Statistics
and Probability. 35
Strand: Geometry
and Measurement 37
Level 3: Intermediate ABE Mathematics. 41
Strand: Number
Sense. 41
Strand: Patterns,
Functions, and Algebra. 46
Strand: Statistics
and Probability. 48
Strand: Geometry
and Measurement 53
Level 4: PreGED / ABE Standards. 56
Strand: Number
Sense. 56
Strand: Patterns,
Functions and Algebra. 61
Strand: Statistics
and Probability. 64
Strand: Geometry
and Measurement 69
Level 5: ASE / GED Standards. 74
Strand: Number
Sense. 74
Strand: Patterns,
Functions, and Algebra. 77
Strand: Statistics
and Probability. 79
Strand: Geometry
& Measurement 84
Level 6: ASE / Bridge to College Standards. 87
Strand: Number
Sense. 87
Strand: Patterns,
Functions, and Algebra. 89
Strand: Statistics
and Probability. 91
Strand: Geometry
and Measurement 97
Appendices. 99
Appendix A. Suggested Readings. 99
Appendix B. Sample Instructional Units. 100
Appendix C. Instructional Resources and
Materials. 100
Adult Numeracy
Curriculum.. 100
Number
Sense. 100
All Strands 101
ProblemSolving. 101
GED Preparation. 101
Learning
Differences and Disabilities 102
Internet Resources 102
Appendix D. Criteria for Evaluating
Instructional Materials and Programs. 103
Appendix E. Massachusetts Common Core of
Learning.. 105
Thinking and
Communicating. 105
Gaining and
Applying Knowledge. 106
Working and
Contibuting. 107
Appendix F. Equipped for the Future Role Maps
and Domain Skills 108
Parent/Family Role
Map. 108
Worker Role Map. 109
Citizen/Community
Member Role Map. 110
Lists of Skills
from the Four Domains in the EFF Standards 112
Content Framework
for EFF Standards 113
Special thanks are
due to the team who have contributed to the development of the Massachusetts
ABE Curriculum Framework for Mathematics and Numeracy over the past number of
years:
Barbara
Goodridge*
Robert
Foreman
Roberta
Froelich*
Esther
D. Leonelli*
Andrea
(Drey) Martone
Marilyn
Moses*
Jenifer
Mullen*
Mary
Jane Schmitt*
Jane
Schwerdtfeger
Ruth
Schwendeman*
Judith
Titzel
for Mathematics and Numeracy
Over
the past number of years, several initiatives have set the stage for writing
the Massachusetts ABE Curriculum Frameworks for Mathematics and Numeracy.
The First Version:
Changing the Way We Teach Math
In
1989, the National Council of Teachers of Mathematics (NCTM) published the Curriculum
and Evaluation Standards for School Mathematics, a document that served as
a template for reforming and improving K12 mathematics education across the
nation. In 1994, sixteen Massachusetts ABE/GED teachers formed a team and
studied the Massachusetts K12 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 K12 and for Adult Basic Education.
In 2000, when the Massachusetts K12 frameworks were revised, it was decided
that the adult education math framework should be rewritten and revised, and
developed as a separate document. This current version of the Massachusetts
ABE Mathematics Curriculum Frameworks is a second revision of that first
framework, but it is heavily influenced by developments in the adult education
field since then, both nationally and internationally.
National Influences: The Adult Numeracy Frameworks
and Equipped for the Future
In
March 1994, the first national Conference on Adult Mathematical Numeracy,
cosponsored 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 teacherled focus groups of learners, business, and other state policy
stakeholders in five states (including Massachusetts), and an online virtual
study group, the ANN expanded upon the “honest list” developed from the
conference. The teacher teams studied, among other documents, the
teacherdeveloped 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, ProblemSolving/Reasoning/DecisionMaking,
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 21^{st}
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 DecisionMaking Skills, it is Use Math to Solve
Problems and Communicate.
International Influences:
Looking at Adult Numeracy
In
addition to studying state and national mathematics curriculum frameworks, the
ABE Math Frameworks 2001 Development Team considered several numeracy
frameworks from other countries, including Australia, the United Kingdom, and
the Netherlands, as well as the numeracy framework developed for the Adult
Literacy and Lifeskills Survey (ALL), an international, largescale 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
schoolbased mathematics curriculum model so much as looking at the mathematics
that is used in the context of adult lives. The Massachusetts ABE Curriculum
Frameworks for Mathematics and Numeracy incorporate some of these ideas in the
current revision.
For purposes of this
framework, the following definition is incorporated for describing numeracy
and what it means to be a numerate adult:
Numerate behavior involves:
Managing a situation or
solving a problem in a real context
everyday life
work
societal
further learning
by responding
identifying or locating
acting upon
interpreting
communicating about
to information about
mathematical ideas
quantity and number
dimension and shape
pattern and relationships
data and chance
change
that is represented in a
range of ways
objects and pictures
numbers and symbols
formulae
diagrams and maps
graphs
tables
texts
and requires activation of
a range of
enabling knowledge,
behaviors, and processes.
mathematical knowledge and
understanding
mathematical
problemsolving skills
literacy skills
beliefs and attitudes.
Source:
Gal, I., van Groenestijn, M., Manly, M., Schmitt, M.J., and Tout, D. (1999). Adult
Literacy and Lifeskills Survey Numeracy Framework Working Draft. Ottawa: Statistics Canada.

The
Mathematics Frameworks presents four learning strands: Number Sense;
Patterns, Functions, and Algebra; Statistics and Probability; Geometry and
Measurement which are described beginning on page 16 (in the Section on
Content Strands and Learning Standards.) In order to present a document that
makes sense practically, as well as theoretically, the
Outline of Learning Levels on page 21 presents
each of the strands and their standards at six performance levels:
§
Level 1: Beginning Adult
Numeracy
§
Level 2: Beginning ABE
Mathematics
§
Level 3: Intermediate ABE
Mathematics
§
Level 4: PreGED/ABE
Mathematics
§
Level 5: ASE/GED
Mathematics
§
Level 6: ASE/Bridge to
College Mathematics
At each level the
strands are given in a chart, as shown below.
Level ÞLevel 1: Beginning Adult Numeracy
Strand Þ Number
Sense
Learners engage in problem solving within adult contextual
situations by communicating, reasoning, and connecting to:
Standard
Þ

Standard 2P3.
Recognize and use algebraic symbols to model mathematical and contextual
situations


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

Enabling
Knowledge and Skills

Examples
of Where Adults Use It

Benchmark
Þ
Assessment
(See
page 10)
Þ

2P3.4
Read and understand positive and negative numbers as showing direction and
change.
Assessed
by 3P3.7

2P3.4.1
Know that positive refers to values greater than zero
2P3.4.2
Know that negative refers to values less than zero

Reading thermometers
Riding
an elevator below ground level
Staying
"in the black" or going "into the red" on bill paying


2P3.5
Use a number line to represent the counting numbers.

2P3.5.1
Demonstrate an understanding that a horizontal number line moves from left to
right using lesser to greater values

Reading and interpreting scales



Ý
Enabling skill

Ý Application

Benchmark Column (e.g. At this level an adult will be
expected to:)
Benchmarks describe the set of skills learners
need to develop and achieve in order to meet the more broadly stated
standards. By providing more detailed information on the specific skills and
contexts for learners to meet the standard, benchmarks show teachers and
learners what a standard “looks like” at each of the six levels.
The strands and standards are arranged by
performance levels so that each level can build on the previous ones. At each level, the four strands and their standards are
outlined with the skills appropriate for that level. The skills defined at
each level are ones to be achieved while working through the level. The
teacher can use the frameworks as a curriculum guide. Each level builds on the
previous levels, so it is recommended that teachers familiarize themselves not
only with the level of their own class, but with the preceding levels as well.
Enabling Knowledge and Skills Column
The study of mathematics is
developmental, but many adult learners have gaps in their learning of math. At
times a learner may struggle with a skill because he or she has not grasped an
enabling skill on which it is based. To present problems and practice with a
skill, we must first lay the proper groundwork. Since not all adult education
teachers have experience teaching math at an elementary level, the skills
needed for the development of each performance skill are outlined.
Examples of Where Adults Use It Column
Teaching mathematics to adults is
different than teaching it to children. As stated in the Common Chapters for the
Massachusetts Adult Basic Education Curriculum Frameworks, “Adult learners
value education and the power it has, but they rarely see it as an end in and
of itself. Rather, education is seen as a means to other kinds of
opportunities and achievements.”
Adult learners need to know that what they are learning in the classroom is
relevant to the lives and goals outside of the classroom. For this reason, we
have included an application for each skill by giving an example of using the
skill in an adult context.
It is our expectation
that this format will be a useful tool for:
§
Lesson planning
§
Curriculum development
§
Presenting practical
applications for adult use of the math skills
§
Assessing student math
levels for placement, informal classroom instruction, and for pre and
posttest assessment
§
Connecting pre and
posttest 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 2P3.4.1, for example, the system is as follows:
 2 refers to the Proficiency Level 2
 P refers to the Strand, Patterns, Functions and Algebra (N
for Number Sense, and so on)
 3 refers to the Standard (Recognize and use algebraic
symbols to model mathematical and contextual situations)
 4 refers to the Benchmark (Read and understand positive
and negative numbers as showing direction and change)
 1 refers to the Enabling Knowledge and Skills (Know
that positive refers to values greater than zero)
How to use This Document in
The University of Massachusetts
Center for Educational Assessment, working with the Adult and Community
Learning Services of the Massachusetts Department of Education, has developed an assessment to measure adult learners’
skills as outlined in the Massachusetts ABE Curriculum Framework for Math and
Numeracy.
The
ABE Curriculum Framework for Math and Numeracy is not an end in itself but a
part of the broader goal of aligning curriculum, instruction and assessment.
To this end, Adult and Community Learning Services and ABE practitioners have
worked closely with the University of Massachusetts’ Center of Educational Assessment to develop a math and numeracy assessment that is designed to measure
the skills outlined in the Framework. This assessment will be capable of
measuring more accurately and capturing more comprehensively, the skills that
adult learners have acquired or need to acquire through the instruction
provided in adult basic education classes. Both the ABE Curriculum Framework
for Math and Numeracy and the results of the new math assessment are valuable
tools that should be used to inform classroom instruction.
The
Frameworks provide teachers with Standards, Benchmarks and Examples that
describe what it is adult learners need to know and be able to do, while the
new math assessment will help identify how well students are acquiring the
skills and knowledge as well as their ability to apply the skills and knowledge
outlined in the Frameworks. By using the Frameworks and assessment results to
inform instruction, programs and teachers can achieve the goal of aligning
curriculum, instruction and assessment.
The skill numbers in the frameworks directly
correspond with the skill numbers on the math test. The skills within each
level are assessed at that level unless otherwise noted as shown in the
example on page 8, and below.

At
this level an adult will be expected to:

Enabling
Knowledge and Skills

Examples
of Where Adults Use It

Skill
Þ
Assessment
Þ
(See
page 11)

2P3.4
Read and understand positive and negative numbers as showing direction and
change
Assessed
by 3P3.7

2P3.4.1
Know that positive refers to values greater than zero
2P3.4.2
Know that negative refers to values less than zero

Reading thermometers
Riding
an elevator below ground level
Staying
"in the black" or going "into the red" on bill paying

The math frameworks endeavor to
expose students at all levels to the four strands: NNumber Sense; PPatterns, Functions, and Algebra; SStatistics
and Probability; and GGeometry 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 3P3.7
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 wellread 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 multilevel 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, decisionmaking,
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 decisionmaking as a parent, citizen and worker.
Mathematical decisionmaking 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, workrelated or testrelated 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 workrelated settings, and
§
apply
mathematical thinking and modeling to solve problems that arise in other
disciplines, as well as in the real world and workrelated 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 doublechecking 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 textbookdriven 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 reallife
activity through the use of both handson and printed instructional materials,
group as well as individual work, and shortterm and longterm tasks.
Technology: Adult numeracy instruction offers all
learners experience with a broad range of technological tools (such as calculators,
rulers, protractors, computer programs, etc.) appropriate to a variety of
mathematical settings.
Habits
of Mind are practices that strengthen learning. In numeracy instruction,
habits of mind involve reflection, inquiry and action. They are developed by
teachers and programs that offer challenging mathematical tasks in settings
that support learners’ curiosity, respect for evidence, persistence, ownership,
and reflection about what is learned and how it is learned. These habits
flourish in instructional environments that favor uncovering mathematical
concepts and connections rather than mimicking algorithms.
The following chart
defines the habits of mind crucial to adults’ numeracy development. It also
lists questions students and teachers may share to assess their own
mathematical habits.
Habits of Mind

Habit

Learner Question

Curiosity

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

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

Do I listen
carefully for others’ use of
evidence, and do
I include evidence to support my solutions and ideas?

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

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

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

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

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

Do I notice and
analyze how and what I learn?

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

Standards
Learners will
demonstrate the ability to…

Number
Sense

N1
Represent and use numbers in a variety of equivalent
forms in contextual situations
N2
Understand meanings of operations and how they relate
to one another
N3
Compute fluently and make reasonable estimates

Patterns,
Functions and Algebra

P1
Explore, identify, analyze, and extend patterns in
mathematical and adult contextual situations
P2
Articulate and represent number and data relationships
using words, tables, graphs, rules, and equations
P3
Recognize and use algebraic symbols to model
mathematical and contextual situations
P4
Analyze change in various contexts

Statistics
and Probability

S1
Collect, organize, and represent data
S2
Read and interpret data representations
S3
Describe data using numerical descriptions, statistics, and
trend terminology
S4
Make and evaluate arguments and statements by applying
knowledge of data analysis, bias factors, graph
distortions, and context
S5
Know and apply basic probability concepts

Geometry
and Measurement

G1
Use and apply geometric properties and relationships to
describe the physical world and identify and analyze the
characteristics of geometric figures
G2
Use transformations and symmetry to analyze
mathematical situations
G3
Specify locations and describe spatial relationships using
coordinate geometry and other representational systems
G4
Understand measurable attributes of objects and the
units, systems, and processes of measurement and apply
appropriate techniques, tools, and formulas to determine
measurements

The Strand Number Sense
Number
Sense is the foundation of numeracy. Sound number sense enables us to
interpret and represent the world in which we live. It is evident in all we
do, whether in complex examples such as the Gross National Product, basic
issues such as the family budget, or as personal as a blood pressure reading.
Mathematical intuition grows with a strong basic understanding of numbers and,
with that, our ability to do mathematical problem solving.
To
be efficient workers or consumers in today's world, adults must have a strongly
developed conceptual understanding of arithmetic operations, as well as the
procedural knowledge of computation and number facts. They must be able to
perceive the idea of place value and be able to read, write, and represent numbers
and numerical relationships in a wide variety of ways. Simple paperandpencil
computation skills are not enough. Adults must be able to make decisions
regarding the best method of computation (mental math, paperandpencil, or
calculator/computer) to use for a particular situation. Knowledge of numbers,
operations and computation must include both a welldeveloped number sense and
the ability to use basic mathematicsrelated 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 timedtest situations such as
the GED. It builds on adult experience and knowledge. Good estimators use a
variety of strategies and techniques for computational estimation that can be
explored and shared by learners.
Learners engage in
problem solving within adult contextual situations by communicating,
reasoning, and connecting to:
§
Standard N1. Represent
and use numbers in a variety of equivalent forms in contextual situations,
§
Standard N2. Understand
meanings of operations and how they relate to one another, and in
§
Standard N3. Compute
fluently and make reasonable estimates.

The Strand Patterns, Functions, and Algebra
Mathematics
has been defined as the study of patterns. Learning to recognize, analyze,
describe, and represent patterns and number relationships connects math to the
world and helps us to appreciate
fully the intrinsic value of such pleasures as poetry, art, music, and
science. Math concepts formerly
taught only in basic algebra courses are increasingly part of the culture and
vocabulary of modern life. Headlines
and news reports speak of exponential growth of the national debt, a variable
rate mortgage, or a balanced budget, while medical literature uses terms like “HIVpositive,” or “RHnegative.”
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 prenumber 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 realworld 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 realworld situations that can aid adults in the home and in the
workplace.
Algebra
impacts the competency of workers, parents and citizens, and algebraic thinking skills are crucial if adults
are to compete in the global economy. Workplace skills requiring competencies
in “information,” “systems,” and “technology” stress the need for organizing,
interpreting and communicating information and employing computers as a tool
for those tasks, as well as the ability to “discover a rule or principle
underlying the relationship between two or more objects and apply it in solving
a problem.” Identifying and expressing pattern, relation and function are the
algebraic skills imbedded within these competencies.
Learners engage in
problem solving within adult contextual situations by communicating,
reasoning, and connecting to:
§
Standard P1. Explore,
identify, analyze, and extend patterns in mathematical and adult contextual
situations,
§
Standard P2. Articulate
and represent number and data relationships using words, tables, graphs,
rules, and equations,
§
Standard P3. Recognize
and use algebraic symbols to model mathematical and contextual situations,
and
§
Standard P4. Analyze
change in various contexts.

The Strand
Statistics and Probability
The
Statistics and Probability strand links numeracy and literacy learning.
Numbers, logical reasoning, and texts interweave to describe phenomena
visually, numerically and verbally in what we term data, which is the
heart of this strand.
Data
is a wideranging topic that touches on many areas of academic study and tells
us much about our world. For instance, we learn about preferences,
predilections and group characteristics when we read and interpret data. We
learn about the power of evidence as we develop the skills to make statements
and evaluate arguments based on data. We learn the power of the question and
the framer of the question when we collect and represent data, and we learn
that sometimes true, sometimes false, pictures are created when we compress
data into statistics. Data is a powerful descriptive tool.
So
powerful is data that agencies of authority often use it to generate, promote
and, sometimes, evaluate decisions. Citizens, therefore, must understand the
ways of data in order to exercise their collective and individual intelligence
by responding to the expanding presence of this dense expression of
information.
The
learning standards in the Statistics and Probability strand provide adult
learners with the tools for dealing with data.
Learners engage in
problem solving within adult contextual situations by communicating,
reasoning, and connecting to:
§
Standard S1. Collect,
organize and represent data,
§
Standard S2. Read and
interpret data representations,
§
Standard S3. Describe
data using numerical descriptions, statistics and trend terminology,
§
Standard S4. Make and
evaluate arguments or statements by applying
knowledge of data analysis, bias factors, graph distortions and context, and
§
Standard
S5. Know and apply basic probability concepts

The Strand Geometry and Measurement
Geometry
and measurement help us represent in an orderly fashion what we see in our
world. Whether we are cooking or cartooning, shopping or shipping, painting a
canvas or a wall, designing an addition for a house or a play yard for
preschool, we continually bump up against these mathematical organizers.
Lifelong learners should know and understand these interconnected and symbiotic
mathematical domains.
Adult
learners who attend basic mathematics classes at any level share a wealth of
pragmatic experience surrounding geometric and spatial concepts. They have
probably built a bookcase, laid out a garden, applied wallpaper or tiled a
floor, all the while discovering informally the rules which formally govern the
study of geometry itself
Geometry
and measurement often spark a renewed interest in mathematics for those
students who have been turned off for some reason or heretofore have felt
unsuccessful with mathematics learning. Investigating problems that involve
geometry and measurement broadens all students' mathematical understanding and
engages them as they explore mathematical ideas.
Handson,
interactive investigations using nonstandard and standard units help adult
basic education students develop an understanding of the many measurable
attributes of physical objects.
Measurement sense including length, time, temperature, capacity, weight, mass,
area, volume, and angle will benefit from this approach. This realistic
approach helps build an accessible measurement vocabulary and a meaningful
comprehension of what it means to measure.
Learners engage in
problem solving within adult contextual situations by communicating,
reasoning, and connecting to:
§
Standard G1. Use and
apply geometric properties and relationships to describe the physical world
and identify and analyze the characteristics of geometric figures,
§
Standard G2. Use
transformations and symmetry to analyze mathematical situations,
§
Standard G3. Specify
locations and describe spatial relationships using coordinate geometry and
other representational systems,
§
Standard G4. Understand
measurable attributes of objects and the units, systems, and processes of
measurement and apply appropriate techniques, tools and formulas to determine
measurements.

Outline of Learning Levels
See “How to Use This
Document (Teacher’s Guide) and (Connecting Curriculum, Instruction and
Assessment),” pages 810.
At this time, the
Massachusetts ABE Test for Math does not assess students’ knowledge at Level 1.
Strand:
Number Sense
Learners engage in
problem solving within adult contextual situations by communicating, reasoning,
and connecting to the following standards:
Standard 1N1. Represent
and use numbers in a variety of equivalent forms in contextual situations

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

Enabling Knowledge and Skills

Examples of Where Adults Use It

1N1.1
Count reliably forward and backward up to 20 items.

1N1.1.1
Demonstrate an understanding that if items are rearranged, the numbers stay
the same
1N1.1.2
Count forward and backward from ten or less
1N1.1.3 Count forward and back from 1120

Counting
children in a group to make sure no one is missing
Counting
dollar bills to pay for a purchase
Counting
items at the grocery express line
Using
the remote channel tuner for a TV
Watching
a digital timer on a microwave count down the time

1N1.2
Recognize odd and even numbers up to 100.

1N1.2.1
Demonstrate an understanding that even numbers represent amounts that can be
paired
1N1.2.2
Demonstrate an understanding that odd numbers represent amounts that when
paired have one remaining

Identifying
the number of possible couples at a dance or a dinner party
Recognizing
when house numbers go up in odd or even numbers
Finding
a room in a hospital or hotel


1N1.3.1
Explain how the position of a digit signifies its value
1N1.3.2
Demonstrate an understanding of directionality in reading numbers and
comparisons from left to right.
1N1.3.3
Explain what each digit in a twodigit number represents, including the use
of zero as a place holder
1N1.3.4
Distinguish between greater than and less than, and recognize betweenness
when comparing numbers

Telling
which address falls in a given block, knowing the first number on the block
Writing a money order for a whole dollar amount
(no change)

1N1.4
Using a 100 chart, skip count by 2’s, 5’s, and 10’s.

1N1.4.1
Know the multiples of 2, 5, and 10 to 100

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

Standard
1N2. Understand meanings of operations and how they relate to one another

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

Enabling Knowledge and Skills

Examples of Where Adults Use It

1N2.1
Demonstrate an understanding of different meanings of addition (e.g. counting
on, combining) of numbers up to 20.

1N2.1.1
Add by counting on (e.g. four objects plus three objects can be totaled by
counting on three more than four (or five, six, seven), or counting on four
more than three (or four, five, six, seven)
Demonstrate
an understanding that combining two amounts into one larger total is adding.
1N2.1.2
Use objects, pictures, or tallies to show addition
1N2.1.3
Demonstrate the ability to visualize grouping of objects

Paying
a twelve dollar amount by using a ten dollar bill and two ones
Figuring
hours of work or sleep by using fingers to count
Figuring
hours of sleep by joining the hours slept before and after midnight

1N2.2
Demonstrate an understanding of subtraction as taking away or separating from
numbers up to 20.

1N2.2.1 Subtract
by counting back (e.g. taking away four of seven objects by counting
backsix, five, four, three)

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



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

Standard 1N3. Compute
fluently and make reasonable estimates

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

Enabling Knowledge and Skills

Examples of Where Adults Use It

1N3.1
Know all pairs of numbers with a total of 10.

1N3.1.1
Combine amounts that add to 10 without having to count

Adding
using mental math

1N3.2
Add numbers with totals to 20.

1N3.2.1
Use the operation of addition and related vocabulary (e.g., add, sum of,
total, plus, etc.)

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

1N3.3
Subtract singledigit numbers from numbers up to 20.

1N3.3.1
Use the operation
of subtraction and related vocabulary (e.g. difference, take away, less
than)
1N3.3.2
Know subtraction facts for pairs of numbers with totals to 10 (e.g. 10 – 6 =
4)
1N3.3.3
Know how to
add back
to check subtraction (e.g. 10 – 6 = 4, and 6 + 4 = 10)

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



Finding the cost of tickets for an amusement ride
for two children.
Planning fare for round trip subway travel at $1 a
token

1N3.5
Finding half of whole numbers up to 20.

1N3.5.1
Know doubles of numbers to 10
1N3.5.2
Demonstrate the ability to separate amounts in two piles

Sharing
the cost of pizza between two people.

1N3.6
Use a calculator to check calculations using whole numbers.

1N3.6.1
Identify the
signs for addition, subtraction, equals
1N3.6.2
Recognize the numerals 0 – 9
1N3.6.3
Demonstrate an understanding of the order to key in numbers and operators
1N3.6.4
Demonstrate the ability to clear the display, and recognize that this should
be done before starting a new calculation

Finding
the total score for a card game
Finding
the total price of 3 items ordered from a menu
Finding
the change for a purchase

Strand:
Patterns, Functions, and Algebra
Learners engage in
problem solving within adult contextual situations by communicating, reasoning,
and connecting to the following standards:
Standard 1P1. Explore,
identify, analyze, and extend patterns in mathematical and adult contextual
situations

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

Enabling Knowledge and Skills

Examples of Where Adults Use It

1P1.1
Sort up to 20 objects or lists by color, shape, number, letter, or size.

1P1.1.1 Identify attributes of objects and
classify such as shape, size, number and/or size

Sorting
laundry
Sorting
bottles for recycling facility
Sorting
telephone numbers by area code and figuring which are long distance calls
Shelving
stock

1P1.2 Recognize and create simple repeating patterns (e.g.
color, rhythmic, shape, number, and letter) and identify the unit being
repeated.

1P1.2.1
Count forward and back by 1's from 1 to 20
1P1.2.2
Read and write whole numbers from 1 to 100
1P1.2.3
Skip count by 2’s, 5’s, and 10’s from 1 to 100
1P1.2.4
Identify odd and even

Knowing
on which side of the hall or street a room or a house is
Counting
pennies or 1 dollar bills
Counting
nickels or five dollar bills
Counting
things 2 at a time
Counting
dimes or 10 dollar bills
Counting
beats in music
Designing
a necklace and describing the assembly rule
Laying
tile on a floor

Standard 1P2. Articulate and represent number and
data relationships using words, tables, graphs, rules, and equations

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

Enabling Knowledge and Skills

Examples of Where Adults Use It

1P2.1
Explore basic number relationships (e.g., find all the ways numbers to 10 can
be written as sums).

1P2.1.1
Know all pairs of numbers with totals to 10
1P2.1.2
Decompose numbers into sums of smaller numbers 17 = 10 + 7
1P2.1.3
Demonstrate an understanding that 2 + 3 and 3 + 2 yield the same sum;
therefore, they are counted once in a list

Playing
card games
Preparing
for further study

Standard
1P3. Recognize and use algebraic symbols to model mathematical and
contextual situations

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

Enabling Knowledge and Skills

Examples of Where Adults Use It

1P3.1
Use and interpret +, , and = to represent
combining, taking away, and equivalence.

1P3.1.1
Demonstrate recognition that + represents operations of combining
1P3.1.2
Demonstrate recognition that 
represents
operations of separation
1P3.1.3
Demonstrate recognition that = represents vocabulary such as: is equal to,
is the same as, and gives you.

Using a fourfunction calculator to find the total whole dollar
amount of a grocery bill
Using a calculator to find how much change you get from a $20.00
bill
Helping
children with homework.

1P3.2
Understand simple number sentences such as: 9 + 1 = 10 and ___ + 5 = 10 and
8  3 = ___ where the ___ represents a missing amount.

1P3.2.1
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

1P3.3
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

1P3.3.1 Explain that directionality of reading
numbers and expressions moves from left to right

Helping
children with homework
Testtaking when seeking employment

Standard 1P4. Analyze change in various contexts

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

Enabling Knowledge and Skills

Examples of Where Adults Use It

1P4.1
Describe qualitative change, such as lengthening or decreasing hours of daylight,
or rising or falling of temperature over time.

1P4.1.1
Observe physical change over time
1P4.1.2
Compare changes which go up or increase with those which go down or decrease

Discussing
weather patterns
Describing seasons, daylight savings time, or
tides

Strand:
Statistics and Probability
Learners engage in
problem solving within adult contextual situations by communicating, reasoning,
and connecting to the following standards:
Standard 1S1. Collect,
organize and represent data

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

Enabling Knowledge and Skills

Examples of Where Adults Use It

1S1.1
Gather data to answer posed questions.

1S1.1.1
Demonstrate that observing and asking relevant questions and counting
gathered responses can produce answers

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


1S1.2.1
Demonstrate an understanding of the concept of categories by grouping items
by shape, size, color, or yes or no responses
1S1.2.2
Know how to count each category for subtotals up to 20

Keeping
track of who will or will not attend party
Sorting
stock by size

Standard 1S2. Read and interpret data representations

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

Enabling Knowledge and Skills

Examples of Where Adults Use It

1S2.1
Identify graphs in available resources.

1S2.1.1
Explain how graph is a visual representation

Reading
a graph in an ad or poster

1S2.2
Extract simple information from a list or twocolumn table.

1S2.2.1
Identify how lists can be ordered in different ways (e.g. alphabetically,
numerically, or randomly)
1S2.2.2
Make a 11 correspondence within a row in charts with two columns

Checking
items against a stock list

1S2.3
Read values on a bar graph up to 100.

1S2.3.1
Skipcount by 2, 5, or 10
1S2.3.2
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

1S2.4
Make comparative statements about relative values on a bar graph.

1S2.4.1
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

1S2.5
Connect simple graphs and tables to arguments or statements.

1S2.5.1
Demonstrate how to locate titles
1S2.5.2
Explain that titles indicate subject matter

Reading a chart or graph in a health pamphlet.

Standard 1S3.
Describe data using numerical descriptions, statistics, and trend terminology




Not
applicable at this level.



Standard 1S4.
Make and evaluate arguments and statements by applying knowledge of data
analysis, bias factors, graph distortions, and context




Not
applicable at this level.



Standard 1S5. Know and apply basic probability
concepts

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

Enabling Knowledge and Skills

Examples of Where Adults Use It

1S5.1
Discuss events as likely or unlikely.

1S5.1.1 Develop an understanding that while some
events are impossible, some are certain to happen, and in other events some
are more likely to occur than others

Deciding
whether or not to carry an umbrella
Making
the call when flipping a coin

Strand: Geometry and Measurement
Learners engage in
problem solving within adult contextual situations by communicating, reasoning,
and connecting to the following standards:
Standard
1G1. Use and apply geometric properties and relationships to describe the
physical world and identify and analyze the characteristics of geometric
figures

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

Enabling Knowledge and Skills

Examples of Where Adults Use It

1G1.1
Recognize, name, describe and compare common basic 2D shapes (square,
circle, rectangle, triangle) using everyday language (straight, curved,
etc.).

1G1.1.1
Identify the names of shapes
1G1.1.2
Demonstrate an understanding that shape is independent of size and
orientation
1G1.1.3
Show two triangles or two rectangles in different positions and sizes

Identifying
things (e.g. a curved road, a straight highway, a rotary)
Recognizing
the shape and meaning of a triangular yield sign and other shapes in
buildings and everyday structures


1G1.2.1
Demonstrate an understanding that the longer side is called the length.
1G1.2.2
Demonstrate an understanding that the shorter side is called the width.

Purchasing window
shades or coverings
Describing
a rectangular photo or frame; or a room size by its length and width

Standard 1G2. Use transformations and symmetry to
analyze mathematical situations

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

Enabling Knowledge and Skills

Examples of Where Adults Use It

1G2.1
Estimating where a line of symmetry falls in a basic shape.

1G2.1.1
Demonstrate an understanding concepts of sameness or halfness
1G2.1.2
Divide a figure in half

Cutting
a cake in half
Folding objects

Standard 1G3. Specify locations and
describe spatial relationships using coordinate geometry and other
representational systems

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

Enabling Knowledge and Skills

Examples of Where Adults Use It

1G3.1
Use the cardinal directions to describe where one location is relative to
another.

1G3.1.1
Know the convention that is North is the opposite direction from South
and that East and West are opposite
1G3.1.2
Explain the difference between vertical and horizontal

Reading
a road sign or route sign which uses north or south, east
or west
Making
a simple map with cardinal directions
Locating
offices, apartments that are labeled with cardinal directions


1G3.2.1
Know the meaning of terms such as left, right, bottom, top, down, up,
behind, over, through, etc.

Assembling
a piece of furniture from a diagram
Giving
oral directions for getting from one place to another

Standard
1G4. Understand measurable attributes of objects and the units, systems, and
processes of measurement and apply appropriate techniques, tools, and
formulas to determine measurements

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

Enabling Knowledge and Skills

Examples of Where Adults Use It

1G4.1
Show equivalent amounts of money using different bills and coins.

1G4.1.1
Know coin & bill names and values

Getting
out money to pay at the register
Verifying
change given at a store

1G4.2
Read, record, and use date concepts in common formats.

1G4.2.1
Know the months and corresponding numbers, days of week

Completing
forms (birth date, etc.)

1G4.3
Read, record, and understand time of the day.

1G4.3.1
Count to 60 by 5’s and 10’s

Reading
a bus schedule that uses AM and PM

1G4.4
Read analog and digital clocks.

1G4.
4.1 Demonstrate an understanding that each hour of digital time is read to 59
minutes

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

1G4.5 Compares familiar quantities, length, mass,
capacity, time, temperature, using informal comparative language and methods
(e.g. taller, heavier, smallest).

1G4.5.1
Explain how the suffixes –er, est, and how, more, less, and
too will change the quantity

Sorting
by size to organize a kitchen cabinet
Understanding a child’s growth chart

1G4.6
Read a ruler to the nearest whole inch.

1G4.6.1
Line up the edge of a ruler to measure an object

Measuring
the length and width of photo

1G4.7
Begins to develop personal reference points of measure (one’s height,
weight).

1G4.7.1
Demonstrate a general recognition of common heights and weights for women,
men and children

Give
one’s height or weight on a medical form

1G4.8
Find the perimeter of rectangles up to 20 units.

1G4.8.1
Know that the two lengths are of equal measure and the two widths are of
equal measure
1G4.8.2
Know that the perimeter of a rectangle is equal to the total of the four
sides

Buying
weather stripping
Buying
wood for a picture frame or baseboard
Finding
the length of fencing around a garden

See “How to use This
Document (Teacher’s Guide) and (Connecting Curriculum, Instruction and
Assessment),” pages 810.
Strand:
Number Sense
Learners engage in
problem solving within adult contextual situations by communicating, reasoning,
and connecting to the following standards:
Standard
2N1. Represent and use numbers in a variety of equivalent forms in
contextual situations

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

Enabling Knowledge and Skills

Examples of Where Adults Use It

2N1.1
Count, read, write, order, and compare two and threedigit numbers.

2N1.1.1
Know that the position of a digit signifies its value
2N1.1.2 Know
what each digit in a threedigit number represents, including the use of zero
as a place holder
2N1.1.3
Count on or back in 10s or 100s starting from any twodigit or threedigit
number, up to 1,000

Carrying
out a stock inventory
Finding
items for an order from bin numbers
Checking
grocery receipt against purchases

2N1.2
Distinguish between odd and even numbers up to 1,000.

2N1.2.1
Recognize that even numbers end in 0, 2, 4, 6, or 8
2N1.2.2
Recognize that odd numbers end in 1, 3, 5, 7, or 9

Telling
which side of a street a house will be on from its number
Knowing
on what days lawn watering is permitted under rationing by odd or even house
number

2N1.3
Read, write, and compare halves and quarters of quantities.

2N1.3.1
Know the words, half, fourth and the symbols 1/2, 1/4
2N1.3.2
Demonstrate an understanding that 1/2 means one group or unit separated into
2 equal parts
2N1.3.3
Demonstrate an understanding that two halves make one whole
2N1.3.4
Demonstrate an understanding that 1/4 means one group or unit separated into
4 equal parts and that four quarters make one whole
2N1.3.5
Demonstrate an understanding that two fourths and one half are equivalent

Sharing
money or brownies

2N1.4
Use 50% as equivalent for onehalf.

2N1.4.1
Understand that 100% represents the whole of something

Buying
something discounted at 50% off

2N1.5
Skip count forward or backward by 2’s, 5’s, or 10’s.

2N1.5.1 Know the multiples of 2, 5, and 10

Checking
twosided copies for missing or out of order pages
Counting
five and ten dollar bills

Standard 2N2. Understand meanings of operations and how they
relate to one another

2N2.1
Demonstrate an understanding of different meanings of addition (counting on,
combining) of two and threedigit numbers.

2N2.1.1 Know that adding can be done by counting
on by ones, tens, or hundreds
2N2.1.2
Demonstrate an understanding that when combining two amounts the total will be
the same for 2 + 4 as for 4 + 2 (commutative property)
2N2.1.3
Know that 4 + 2 + 3 gives the
same
total as 3 + 2 + 4
2N2.1.4 Demonstrate an understanding that adding
zero leaves a number unchanged

Paying
an amount in the hundreds using ten dollar bills
Checking totals by adding again in a different
order.
Figuring
how many coffees are needed for a group that includes noncoffee drinkers

2N2.2
Demonstrate an understanding of efficient and flexible strategies of
subtraction of two and three digit numbers.

2N2.2.1 Know that subtracting can be done by
counting back by ones, tens, or hundreds
2N2.2.2 Know that subtraction can be used to
answer the questions: How much more or less? (Comparing)
2N2.2.3 Demonstrate an understanding that subtracting
zero leaves a number unchanged
2N2.2.4 Demonstrate an understanding that having
4 and giving away 2 is not the same as having 2 and giving away 4.
(Subtraction is not commutative)

Figuring
out how much is left of an amount in the hundreds by counting back as ten
dollar bills are paid out
Balancing
a checkbook
Finding
the difference between two distances or amounts.

2N2.3
Demonstrate an understanding of how addition and subtraction relate to each
other for numbers up to 1,000.

2N2.3.1.1 Know how to add back to check, e.g. 10
– 6 = 4 because 6 + 4 = 10

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

2N2.4
Demonstrate an understanding of different meanings of multiplication of
numbers up to 12 (repeated addition, grouping, and arrays).

2N2.4.1
Know that multiplication is a shorter way to do repeated addition, (e.g. 3 ´ 4 = 3 + 3 + 3 + 3)
2N2.4.2
Relate skip counting to multiplication
2N2.4.3Know
how to use multiplication to find groups of items numbering 2 – 12.
2N2.4.4
Use area models to build arrays to show multiplication
2N2.4.5 Use an area model to demonstrate
distributive property by adding two rectangles (e.g. 8
´ 12 = (8 ´ 10) + (8 ´ 2)

Checking
delivery of goods in small batches
Finding
price of 2 cartons of milk or 6 bottles of soda.
Calculating
total number (e.g. three days a week for four weeks)
Generating results using mental methods of multiplication when
solving problems
In shopping, when you buy 2 different items with different
prices.

2N2.5
Demonstrate an understanding of different meanings of division (separating
into equal groups, discovering the number of equal groups contained within).

2N2.5.1
Know that division is a shorter way to do repeated subtraction (e.g.
12
¸ 4 = 3 because 12 – 4 – 4 –
4 = 0)
2N2.5.2
Know how to find how many groups of a given number of items when given the
total of items (e.g. . 6 ¸ 3
means 6 candies shared by three people or 6 candies given (or dealt) 3 to
each person
2N2.5.3
Know that division means partitioning into groups of equal size
2N2.5.4
Demonstrate an understanding of the concept that division is not commutative
(e.g.. that 12 ¸ 4 ¹ 4 ¸ 12)

Working
out how many cars are needed to transport a group of people
Finding
how many pairs of socks when given a total number of socks
Finding
how many dozens in a given amount of eggs (e.g. 24 eggs)
Knowing
that order of entry is critical when using a calculator to perform division

2N2.6
Demonstrate an understanding of how multiplication and division of one and
two digit numbers relate to each other.

2N2.6.1
Demonstrate an understanding of the relation between doubling and halving
2N2.6.2
Know how to multiply to check division (e.g., 12 ¸ 4 = 3 because 3 ´ 4 = 12)

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

Standard 2N3. Compute fluently and make reasonable estimates

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

Enabling Knowledge and Skills

Examples of Where Adults Use It

2N3.1
Add two and threedigit whole numbers flexibly, efficiently, and accurately.

2N3.1.1Know
how to align numbers in column addition
2N3.1.2
Know that regrouping occurs when the total in a column exceeds 9
2N3.1.3
Recall addition facts to 20
2N3.1.4
Compose and decompose numbers to aid addition (e.g.
97 + 23 = 90 + 20 + 7 + 3)
2N3.1.5
Demonstrate that there are different strategies for adding
2N3.1.6
Demonstrate an understanding that there are different methods of checking
answers (e.g. adding in a different order, using inverses, collecting 10's,
and using a calculator)
2N3.1.7 Estimate answers to addition

Calculating
the production shortfall from a daily target
Performing mental addition
Verifying
deposits in a checking account.

2N3.2
Estimate to the nearest 10 or 100 in numbers up to 1,000.

2N3.2.1 Know benchmark numbers of 5 and 50 are halfway in
intervals of 10 and 100 (e.g. 35 is halfway between 30 and 40 and 250 is
halfway between 200 and 300)
2N3.2.2 Tell whether a number is greater than benchmark
numbers of 5 and 50
2N3.2.3 Demonstrate an understanding of rounding to the
nearest 10 or 100 using algorithm

Estimating amount of purchase to nearest 10 dollars.
Estimating distances between cities.
Giving ballpark figures for numbers in a crowd.

2N3.3 Subtract using two and threedigit whole numbers flexibly,
efficiently, and accurately.

2N3.3.1
Know how to align numbers in column subtraction
2N3.3.2
Know that "borrowing" is regrouping
2N3.3.3
Recall subtraction facts to 20
2N3.3.4
Estimate answers
2N3.3.5
Compose and decompose numbers to aid subtraction (e.g. 107  83 = 100  80 +
7 – 3)
2N3.3.6
Demonstrate an understanding of strategies or methods for subtraction such as
borrowing or counting up

Performing mental subtraction

2N3.4
Multiply twodigit whole numbers by numbers 1,2,3,4,5,10 and 11.

2N3.4.1
Use doubling or repeated addition when multiplying by 2 or 4, e.g. To find 26
x 4, do 26 + 26, 52 + 52
2N3.4.2
Demonstrate an understanding the operation of multiplication and related
vocabulary (e.g. multiplied by, times, lots of)
2N3.4.3
Recall multiplication facts
(e.g.
multiples of 2, 3, 4, 5, 10)
2N3.4.4
Recognize two and threedigit multiples of 2, 5, or 10 and threedigit
multiples of 50 and 100
2N3.4.5
Know that multiplication can be performed in any order, so that 2(3)(4) =
4(2)(3)

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

2N3.5
Know halves of even numbers up to 100.

2N3.5.1
Double one and twodigit numbers up to 50

Separating
members into two groups

2N3.6
Divide twodigit whole numbers by singledigit whole numbers.

2N3.6.1
Demonstrate an understanding that division is the inverse of multiplication
2N3.6.2
Recall multiplication facts

Working
out the number of cars needed to transport a group of people
Finding
the number of pairs that can form in class or on a dance floor

2N3.7
Approximate by rounding to the nearest tens or hundreds in numbers up to
1,000.


Rounding
numbers to make approximate calculations

2N3.8
Use a calculator to check calculations using whole numbers.

2N3.8.1
Demonstrate an understanding of the order to enter a twodigit number
2N3.8.2
Demonstrate an understanding of the order to key in numbers and operators
2N3.8.3
Know how to clear the display and cancel a wrong entry

Performing
any calculations at this level

Strand:
Patterns, Functions and Algebra
Learners engage in
problem solving within adult contextual situations by communicating, reasoning,
and connecting to the following standards:
Standard 2P1. Explore,
identify, analyze, and extend patterns in mathematical and adult contextual
situations

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

Enabling Knowledge and Skills

Examples of Where Adults Use It

2P1.1
Complete simple repeating number patterns up to 1,000 and identify the unit
being repeated.

2P1.1.1
Skip count forward or backward by 2’s, 3's, 4's, 5’s, and 10’s

Seeing
if pages are missing or out of order in a duplicating job
Estimating
how many exits there are on the highway

2P1.2 Recognize and create repeating patterns and identify
the unit being repeated.

2P1.2.1
Isolate smallest unit of repetition

Laying
tile on a floor
Designing
a tiled floor and describing the pattern
Knitting

Standard 2P2. Articulate and represent number and
data relationships using words, tables, graphs

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

Enabling Knowledge and Skills

Examples of Where Adults Use It

2P2.1 Create
tables to show the patterns inherent in addition and multiplication of number
pairs from 0 to 12.

2P2.1.1 Know
addition and multiplication facts
2P2.1.2 Recognize and extend
patterns

Helping
children with homework
Preparing
for further study

Standard 2P3. Recognize
and use algebraic symbols to model mathematical and contextual situations

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

Enabling Knowledge and Skills

Examples of Where Adults Use It

2P3.1 Use and interpret +, , ´, ¸,
and = to represent combining, comparing, separating and equivalence.
Assessed by 2P3.6

2P3.1.1
Demonstrate an understanding that + represents operations of combining
2P3.1.2
Demonstrate an understanding that  represents operations of separation or
comparison
2P3.1.3
Demonstrate an understanding that ´
stands for combining multiples
2P3.1.4
Demonstrate an understanding that ¸
means separating into equal groups or discovering the number of equal groups
contained within
2P3.1.5
Demonstrate an understanding that = represents vocabulary such as: is
equal to, is the same as, and gives you

Using
a fourfunction calculator to find the total of a grocery bill
Using
a calculator to find how much change you get from a $20.00 bill
Using
a four function calculator to find hourly rate given weekly pay or to find
weekly pay given hourly rate
Helping
children with homework

2P3.2
Read and write simple number sentences such as n + 5 = 10,
8
 3 = €, 5 ´
= 10, 8 ¸ 2= ð
¸ 3 = 5 where the represents a missing amount or n = a
missing number

2P3.2.1
Demonstrate an understanding that n or represents a missing value in addition and
subtraction equations

Helping
children with homework.
Testtaking
when seeking employment

2P3.3
Write statements of inequality for numbers up to 1,000.

2P3.3.1
Demonstrate an understanding that > stands for greater than
2P3.3.2
Demonstrate an understanding that < stands for less than

Selecting filter for data entry

2P3.4
Read and understand positive and negative numbers as showing direction and
change.
Assessed
by 3P3.7

2P3.4.1
Know that positive refers to values greater than zero
2P3.4.2
Know that negative refers to values less than zero
2P3.4.3
Use a horizontal or vertical number line to show positive and negative values

Reading thermometers
Riding
an elevator below ground level
Staying
"in the black" or going "into the red" on bill paying

2P3.5
Use a number line to represent the counting numbers.

2P3.5.1
Demonstrate an understanding that a horizontal number line moves from left to
right using lesser to greater values
2P3.5.2
Demonstrate an understanding that intervals on a number line must follow a
consistent progression

Reading and interpreting scales

2P3.6
Write a simple expression or equation representing a verbal expression to
demonstrate an understanding of the four operations and the equal sign.

2P3.6.1Translate
simply worded problems into simple equations (e.g. Write a number sentence
for the sum of four and five is nine)

Entering
an expression in a spread sheet

Standard 2P4. Analyze
change in various contexts

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

Enabling Knowledge and Skills

Examples of Where Adults Use It

2P4.1
Describe qualitative change, such as lengthening hours of daylight or
increasing heat.

2P4.1.1
Observe steady change over time

Reporting
and planning in accordance with weather changes

2P4.2
Describe quantitative change, such as saving 3 cents a day for one month.

2P4.2.1
Record and save data
2P4.2.2
Know basic arithmetic skills

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

Strand:
Statistics and Probability
Learners engage in
problem solving within adult contextual situations by communicating, reasoning,
and connecting to the following standards:
Standard 2S1. Collect,
organize and represent data

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

Enabling Knowledge and Skills

Examples of Where Adults Use It


2S1.1.1
Know that answers can be found by observing and asking relevant questions and
counting responses

Planning
a party or meeting

2S1.2
Group objects or responses by a single criterion.

2S1.2.1
Demonstrate an understanding of categories such as shape, size, color, or yes
or no responses
2S1.2.2
Know how to count each category for subtotals

Sorting
stock by size
Keeping
track of who will or will not attend a party

2S1.3 Represent information so that it makes sense to others
(e.g. using a list, table or diagram).

2S1.3.1
Demonstrate an understanding that information can be represented in different
ways such as in a list, table, or a diagram
2S1.3.2
Demonstrate an understanding of the importance of labeling information in a
list, table, or diagram

Reporting
on responses to party or meeting
Keeping
records for a club

2S1.4
Find a total from subtotaled categories of two or threedigits to verify
inclusion of all data.

2S1.4.1
Demonstrate an understanding that when objects or responses are divided into
categories all data must be included

Checking
monthly totals against weekly totals

Standard 2S2. Read and interpret data representations

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

Enabling Knowledge and Skills

Examples of Where Adults Use It

2S2.1
Identify graphs and tables in available resources.

2S2.1.1
Demonstrate an understanding that a graph is a visual representation

Reading newspapers and magazines

2S2.2
Find graphs and tables from external sources.

2S2.2.1
Recognize that graphs can be found in many publications

Reading
advertisements.

2S2.3
Extract simple information from a list or table.

2S2.3.1
Demonstrate an understanding that lists can be ordered in different ways such
as alphabetically, numerically, or randomly
2S2.3.2
Demonstrate an understanding that tables are arranged in rows and columns
2S2.3.3
Demonstrate an understanding that titles, labels, etc. provide essential
information

Using
the yellow pages
Checking items against a stock
list

2S2.4
Read values on a bar graph up to 1,000.

2S2.4.1
Demonstrate an understanding that the height of the bar is equal to the
amount on the axis across from it

Reading newspapers and magazines

2S2.5
Make numerical comparisons about relative values on a bar graph.

2S2.5.1
Demonstrate an understanding that comparative statements such as greater
than or less than can be made based on the height of the bars
2S2.5.2
Demonstrate an understanding of relative numerical terms such as twice
or half


Standard 2S3. Make and
evaluate statements by applying knowledge of data

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

Enabling Knowledge and Skills

Examples of Where Adults Use It

2S3.1
Match graphs and tables to statements.

2S3.1.1
Know how to locate titles
2S3.1.2
Titles indicate subject matter
2S3.1.3
Know what to look for to connect data representations with statements

Reading a newsletter from the health service

2S3.2 Determine
whether or not a graph connects to an argument/ statement using title, labels
and percent matches.
Assessed
by 4S4.1

2S3.2.1
Know how to locate data labels in tables and graphs to verify they match
arguments/statements
2S3.2.2
Locate and connect percent numbers in graphs and arguments

Reading insurance documents

2S3.3
Support simple statements with data.

2S3.3.1
Know that data can be collected to verify statements such as ‘more people in
class walk than drive to class’
2S3.3.2
Know how to keep track of collected data

Taking political action to
institute changes in the community

2S3.4
Visually identify ‘who has more’ and identify obvious misstatements.

2S3.4.1
Recognize that bar heights and circle wedges show quantity
2S3.4.2
Knowing to connect bar heights and wedge sizes with statements/arguments to
verify accuracy

Reading ads with bar graphs in
newspaper article

Standard 2S4. Know and
apply basic probability concepts

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

Enabling Knowledge and Skills

Examples of Where Adults Use It

2S4.1
Discuss events as likely or unlikely.

2S4.1.1
Demonstrate an understanding that while some events are impossible, some are
certain to happen, and in other events some are more likely to occur than
others

Deciding
whether or not to carry an umbrella
Making
the call when flipping a coin

2S4.2 Give the probability of a single outcome in simple
concrete situations such as tossing a coin or rolling a die.
Assessed
by 3S5.2

2S4.2.1
Demonstrate an understanding that probability depends on the total number of
possibilities

Tossing
a coin
Rolling
dice

Strand:
Geometry and Measurement
Learners engage in
problem solving within adult contextual situations by communicating, reasoning,
and connecting to the following standards:
Standard
2G1. Use and apply geometric properties and relationships to describe the
physical world and identify and analyze the characteristics of geometric
figures

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

Enabling Knowledge and Skills

Examples of Where Adults Use It

2G1.1
Name, order, and group two dimensional shapes by properties.

2G1.1.1
Demonstrate familiarity with terms and concepts such as: Curved vs.
straight lines, equal lengths, number of sides
parallel,
square corners

Sorting
2D and 3D shapes
Matching
patterns for home decorating by design and shape

2G1.2
Investigate and explain common uses of shapes in the environment.

2G1.2.1 Identify
the names of basic 2D shapes (square, circle, rectangle, triangle) using
everyday language (straight, curved, etc.)
2G1.2.2
Demonstrate an understanding that shape is independent of size and orientation

Comparing
use of shapes in house construction or room design

Standard 2G2. Use
transformations and symmetry to analyze mathematical situations

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

Enabling Knowledge and Skills

Examples of Where Adults Use It

2G2.1
Estimate where a line of symmetry falls in a basic shape.
Assessed
by 3G2.3

2G2.1.1
Demonstrate an understanding of concepts of sameness or halfness

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

2G2.2
Show more than one line of symmetry in a basic shape.
Assessed
by 3G2.3

2G2.2.1 Demonstrate an
understanding of concepts of sameness or halfness

Creating
holiday designs for greetings cards or crafts

Standard 2G3. Specify
locations and describe spatial relationships using coordinate geometry and
other representational systems

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

Enabling Knowledge and Skills

Examples of Where Adults Use It

2G3.1 Use the compass rose on a map with
secondary (SW, NE, etc.) directions.

2G3.1.1 Know the convention that is North is the
opposite direction from South and that East and West are
opposite
2G3.1.2 Explain
the difference between vertical and horizontal
2G3.1.3
Demonstrate an understanding of diagonal direction between vertical and
horizontal
2G3.1.4
Demonstrate an understanding that secondary directions lie halfway between
the cardinal directions (e.g. northeast is the diagonal direction between
north and east

Appreciating
wind directions stated during a weather forecast
Reading
directions from a map


2G3.2.1
Explain the difference between vertical and horizontal

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

Standard
2G4. Understand measurable attributes of objects and the units, systems, and
processes of measurement and apply appropriate techniques, tools, and
formulas to determine measurements

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

Enabling Knowledge and Skills

Examples of Where Adults Use It

2G4.1
Calculate the total cost of many items and the change from a whole dollar
amount.

2G4.1.1
Use whole number addition
2G4.1.2
Know the meaning and symbols used for money

Making
everyday purchases

2G4.2
Read, record, and understand time formats of quarter and half, with a digital
and 12hour analog clock.

2G4.2.1
Familiarity with quarter and half concepts

Telling
time on various clocks

2G4.3
Estimate, measure, and compare lengths, weights, capacity using standard and
nonstandard units.

2G4.3.1
Ability to read scales such as a 12 inch ruler to ¼ inch, general knowledge
of weight and capacity vocabulary and concepts
2G4.3.2
Know that 2/4 = ½
2G4.3.3
Know that 3/4 is greater than ½

Following
a recipe

2G4.4
Use simple instruments graduated in familiar units (e.g. inches, feet, yards,
pounds, fluid ounces, and centimeters).
Assessed
by 3G4.12

2G4.4.1
Know appropriate scales for familiar measures

Reading
thermometer, scales

2G4.5
Know the relationship of familiar units (e.g. 12 inches in a foot, 3 feet in
a yard, 4 cups in a quart).

2G4.5.1
Demonstrate how to find equivalent measures with rulers, yard sticks, and cup
measures

Measuring
a baby’s length in inches
Expressing
a person’s height in feet and inches
Doubling
or halving a recipe

2G4.6
Read and compare positive temperatures in Fahrenheit.

2G4.6.1
Read scale and digital readouts
2G4.6.2
Read and compare numbers

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

2G4.7
Develop personal benchmarks for temperatures.

2G4.7.1
Read a thermometer

Knowing
that a child has a fever when reading thermometer

2G4.8
Find the perimeter of rectangles.

2G4.8.1 Know that the two lengths are of equal measure and the
two widths are of equal measure
2G4.8.2 Know that the perimeter of a rectangle is equal to the
total of the four sides

Buying
weatherstripping

2G4.9
Find the area of rectangles.
Assessed
by 3G4.11

2G4.9.1
Know that area measures the space within a figure in square units

Buying
carpeting, tiles, or wall paper

See “How to use This
Document (Teacher’s Guide) and (Connecting Curriculum, Instruction and
Assessment),” pages 810.
Strand:
Number Sense
Learners engage in
problem solving within adult contextual situations by communicating, reasoning,
and connecting to the following standards:
Standard
3N1. Represent and use numbers in a variety of equivalent forms in
contextual situations

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

Enabling Knowledge and Skills

Examples of Where Adults Use It

3N1.1
Read, write, order, and compare numbers up to 1,000,000.

3N1.1.1
Demonstrate an understanding that the position of a digit signifies its value
3N1.1.2
Know what each digit represents in a number up to six digits, including the
use of zero as a place holder
3N1.1.3
Demonstrate an understanding of the symbols for greater than, less than

Filing
plans in numerical order
Reading
route numbers on delivery labels

3N1.2
Read, write and compare common fractions (e.g. thirds, halves, and quarters).

3N1.2.1
Demonstrate an understanding that the denominator indicates the number of
equal parts in the whole
3N1.2.2
Demonstrate an understanding that the numerator identifies how many of these
equal parts are shown
3N1.2.3
Demonstrate an understanding that a unit fraction is one part of a whole
divided into equal parts (e.g. 1/4 indicates one of four equal parts is
shown)
3N1.2.4
Demonstrate an understanding that nonunit fractions are several equal parts
of a whole, indicated by the numerator (e.g. 3/4 = 1/4 + 1/4 + 1/4)
3N1.2.5
Demonstrate an understanding that the size of the fraction changes as the
numerator and denominators change

Using
a 1/4 cup measure to add 3/4 of a cup of flour to a recipe
Reading fractions used in sale
signs and special offers (e.g. 1/2 off)

3N1.3
Recognize and use equivalent forms of common fractions (e.g.1/2 = 5/10).
Assessed
by 4N1.11

3N1.3.1
Demonstrate an understanding that equivalent fractions look different but
have the same value
3N1.3.2
Demonstrate an understanding that when the top and bottom number of a
fraction are the same, the fraction is equivalent to 1

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

3N1.4
Read, write and compare decimals up to two decimal places in practical
contexts ( money in decimal notation, e.g. $10.35).

3N1.4.1
Demonstrate an understanding that the decimal point separates dollars and
parts of a dollar
3N1.4.2
Demonstrate an understanding that a dime is a tenth of a dollar
3N1.4.3
Demonstrate an understanding that a penny is a hundredth of a dollar
3N1.4.4
Demonstrate an understanding of the use of zero as a placeholder
3N1.4.5
Demonstrate an understanding of the use of a leading zero (e.g. $0.76)

Reading price tags
Understanding
prices on a menu
Counting
and recording total value of change received at a rummage sale

3N1.5
Recognize fraction, decimal, and percent equivalents for a half and one
quarter.

3N1.5.1
Know ½ = 0.5 = 50% and 1/4 = 0.25 = 25%

Ordering
a half pound at a deli that uses a digital scale
Recognizing
50% off and halfprice as the same

3N1.6 Read,
write, and compare positive and negative numbers in practical contexts.
Assessed by 4N1.2

3N1.6.1
Demonstrate an understanding of the words positive and negative
3N1.6.2
Demonstrate an understanding that a negative temperature is below zero
3N1.6.3
Demonstrate an understanding that a negative amount of money represents money
owed

Understanding
windchill information
Reading a thermometer

3N1.7
Read, write, and compute squares and cubes of whole numbers.

3N1.7.1
Read and write 4 (4) as 4^{2 }
3N1.7.2
Recognize that any value taken to the second power will form a square
3N1.7.3
Read and write 4 (4)(4) as 4^{3 }
3N1.7.4
Recognize that any value taken to the third power will form a cube

Reading
pollen count per cubic meter

3N1.8
Understand that percent represents a ratio of a part to a whole where the
whole is 100.

3N1.8.1
Know that percent means per hundred
3N1.8.2
Demonstrate an understanding of the percent ratio as a comparison based
on
division by 100
3N1.8.3
Know that 100% of one dollar is one dollar and that 50% of a dollar is 50
cents out of one dollar

Figuring
a 5% sales tax on a one dollar item

Standard
3N2. Understand meanings of operations and how they relate to one another

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

Enabling Knowledge and Skills

Examples of Where Adults Use It

3N2.1 Demonstrate an understanding that
multiplying a whole number by a unit fraction is the same as dividing the
whole number by that fraction’s denominator.


Generating
solutions using mental mathematics in situations involving common unit
fractions

3N2.2
Demonstrate an understanding of how squaring and taking the square root are
related.
Assessed
by 4N2.5

3N2.2.1
Know that to square a number one multiplies the number by itself
3N2.2.2
Know that to find the square root of an amount, one finds the number that
multiplied by itself produces that amount
3N2.2.3
Because 4 (4) = 16, Ö16 = 4

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

3N2.3
Demonstrate an understanding of how addition and subtraction relate to each
other for numbers up to 1,000,000.

3N2.3.1
Know how to add back to check, e.g. 1,000 – 250 = 750 because 250 + 750 =
1,000

Checking
the balance in a checkbook

3N2.4
Choose the correct operation for solving a onestep narrative problem.

3N2.4.1
Demonstrate an understanding that addition is combining, subtraction is
separating or comparing, multiplication is repeated addition, and division is
repeated subtraction

Taking
a standardized or employment test

3N2.5
Understand and use exponents to represent repeated multiplication.

3N2.5
Recognize that exponents indicate the number of times that the base is
written as a factor

Computing
with formulas on a standardized test

Standard 3N3. Compute
fluently and make reasonable estimates

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

Enabling Knowledge and Skills

Examples of Where Adults Use It

3N3.1
Divide by two and threedigit whole numbers and interpret remainders.
Assessed
by 3N3.11

3N3.1.1
Demonstrate an understanding of the concept of remainder, and that remainders
need to be interpreted in context when solving problems
3N3.1.2
Demonstrate an understanding of when the context requires one to round off to
a whole number
3N3.1.3
Demonstrate an understanding of when to express remainders as decimals or fractions

Finding
the average number of hotdogs per person sold at an event
Finding
how many buses are needed to transport three classes of children for a field
trip

3N3.2
Carry out calculations with threedigit whole numbers using efficient written
methods.
Assessed
by 3N3.10 and 3.11

3N3.2.1
Demonstrate an understanding that there are different strategies for carrying
out each of the four operations
3N3.2.2
Demonstrate an understanding that there are different ways to check answers

Using
written methods to generate results when solving problems with threedigit
whole numbers

3N3.3
Multiply and divide whole numbers by 10 and 100.

3N3.3.1
Demonstrate an understanding of place value for whole numbers and to
twodecimal places

Changing
dollar amounts to dimes and pennies and vice versa
Changing
meters to centimeters and vice versa

3N3.4
Carry out basic calculations with money.

3N3.4.1
Demonstrate an understanding of place value for whole numbers and to
twodecimal places

Balancing
a checkbook
Figuring
one share of a restaurant bill that is divided equally

3N3.5
Approximate by rounding numbers up to 1,000,000 to the nearest tens,
hundreds, or thousands

3N3.5.1
Demonstrate an understanding place value for units, tens, hundreds, thousands

Rounding
numbers to make approximate calculations

3N3.6
Find common parts of whole number quantities or measurements (e.g. ¾ of 12,
2/3 of 15).

3N3.6.1
Demonstrate an understanding of the relationship between unit fractions and
division when finding parts
3N3.6.2
Demonstrate an understanding that there are different strategies for finding
fractional parts

Reducing
the quantities in a recipe

3N3.7
Use equivalencies between common fractions and percentages to find part of
wholenumber quantities.

3N3.7.1
Know common fraction and percent equivalents (e.g. 50% = ½, 25% = ¼, 75% = ¾)

Estimating
savings using mental mathematics strategies at a percentage off sale

3N3.8
Find squares, square roots, and cubes of wholenumber quantities
Assessed
by 3N1.7

3N3.8.1
Know that a number is squared by multiplying it by itself
3N3.8.2
Know that a number is cubed by multiplying it by itself three times
3N3.8.3
Know that squaring and finding the square root are inverse operations
3N3.8.4
Know the calculator keys that generate squares, square roots, and cubes of
numbers

Finding
the area of a square room
Finding
the volume of a square room

3N3.9 Use a
calculator to calculate whole numbers and decimals to two places to solve
problems in context, and to check calculations.

3N3.9.1
Know how to key in and interpret money calculations (e.g. key in 85 cents as
$0.85, interpret 8.2 as $8.20)
3N3.9.2
Demonstrate an understanding that a calculator will sometimes display a
string of digits after the decimal point, and that it is only necessary (at
this level) to read the first two (e.g. 1.333333 is $1.33)
3N3.9.3
Know how to find the square and cube of a number
3N3.9.4
Know how to key in a square root calculation
3N3.9.5
Know and use strategies to check answers obtained with a calculator

Finding
the total charge on a purchase
Multiplying
the monthly cable charge by twelve to find the annual charge
Finding
the area of a square room

3N3.10
Carry out calculations using addition and subtraction with numbers up to
1,000,000 using efficient written methods, including ways to check answers.

3N3.10.1 Compose and decompose numbers to aid addition (e.g.
1240 + 2040 = 1,000 + 2000 + 100 + 40 + 40)
and estimate answers to addition
3N3.10.2 Demonstrate that there are different strategies for
adding
3N3.10.3 Demonstrate an understanding that there are different
methods of checking answers (e.g. adding in a different order, using
inverses, collecting 10's and using a calculator)
3N3.10.4 Know how to align numbers in column subtraction
3N3.10.5 Know that “borrowing” is regrouping
3N3.10.6 Can compose and decompose numbers to aid subtraction
(e.g. 1007  803 =1,000  800 + 7 – 3)
3N3.10.7 Demonstrate an understanding of strategies or methods
for subtraction such as borrowing or counting up

Calculating the production shortfall from a daily target
Performing mental addition
Checking deposits in a checking account

3N3.11 Carry out
calculations using multiplication and division with two and three digit
numbers using efficient written methods, including ways to check answers and
interpret remainders.

3N3.11.1
Demonstrate an understanding that division is the inverse of multiplication
and that the answer to a division problem can be checked by multiplication
3N3.11.2
Demonstrate the ability to determine the placement of the decimal points in
multiplication of decimal numbers of up to two places
3N3.11.3
Demonstrate an understanding of the concept of remainder, and that remainders
need to be interpreted in context when solving problems
3N3.11.4
Demonstrate an understanding of when the context requires one to round off to
a whole number
3N3.11.5
Demonstrate an understanding of when to express remainders as decimals or
fractions

Calculating
miles per gallon that a car attains
Estimating
travel time in hours based on distance and speed

3N3.12 Compute
percentages when part and whole are given using friendly numbers (e.g. 10%,
25%, 50%, and 75%).

3N3.12.1 Know
percent and fraction equivalents for benchmark numbers (e.g. 10%, 25%, 50%,
and 75%)
3N3.12.2
Demonstrate an understanding of partwhole relationship inherent in fractions
and percents

Calculating
a percent increase in pay or demographics

Strand: Patterns, Functions, and Algebra
Learners engage in
problem solving within adult contextual situations by communicating, reasoning,
and connecting to the following standards:
Standard
3P1. Explore, identify, analyze, and extend patterns in mathematical and
adult contextual situations

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

Enabling Knowledge and Skills

Examples of Where Adults Use It

3P1.1
Complete number sequences with whole numbers involving twostep progressions.

3P1.1.1
Know multiplication tables

Using
rate tables for postage

3P1.2 Recognize and create repeating patterns and identify
the unit being repeated.
Assessed by 3P1.1

3P1.2.1
Isolate smallest unit of repetition
3P1.2.2
Use a notation system to record patterns

Creating
Sales Tax tables
Using
mental math strategies

3P1.3
Given a table of amounts, generalize the relationship between the quantities
using simple patterns such as doubling.

3P1.3.1
Read tables

Using rate tables for prices

Standard
3P2. Articulate and represent number and data relationships using words,
tables, graphs

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

Enabling Knowledge and Skills

Examples of Where Adults Use It

3P2.1
Write an expression or equation representing verbal situations with one or
two operations.

3P2.1.1
Translate simple worded problems involving unknown quantities into simple
equations

Entering
an expression in a spreadsheet

3P2.2
Develop and use simple formulas from tables with one or two arithmetical
steps for real life contexts.

3P2.2.2
Verbalize a rule for finding values in an “inout” table
3P2.2.3
Write a general expression for finding values in an “inout” table
3P2.2.4
Write an equation
3P2.2.5
Decide on the effectiveness of a developed formula by substituting known
values

Converting
temperature between Celsius and Fahrenheit

Standard 3P3. Recognize
and use algebraic symbols to model mathematical and contextual situations

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

Enabling Knowledge and Skills

Examples of Where Adults Use It

3P3.1
Use and interpret +, , ´, ¸, and = to represent combining, comparing,
and equivalence.
Assessed
by 3P3.2

3P3.1.1
Demonstrate an understanding that + represents operations of combining
3P3.1.2
Demonstrate an understanding that – represents operations of separation or
comparison
3P3.1.3
Demonstrate an understanding that ´
stands for combining multiples
3P3.1.4
Demonstrate an understanding that ¸
means separating into equal groups or discovering the number of equal groups
contained within
3P3.1.5
Demonstrate an understanding that = represents vocabulary such as is equal
to, is the same as, and gives you

Using
a fourfunction calculator to find the total of a grocery bill
Using
a calculator to find how much change you get from a $20.00 bill
Using
a four function calculator to find hourly rate given weekly pay, or to find
weekly pay given hourly rate
Helping
children with homework

3P3.2
Read, write, and solve expressions using algebraic notation for addition,
subtraction, multiplication, division, and parentheses with one or two
operations.

3P3.2.1
Read and write 5 (10) for 5 ´ 10
3P3.2.2
Read and write 10 for 10 ¸
2
^{
2}
3P3.2.3
Know that the contents of parentheses must be worked out first

Following
convention in notation and order of operation
Testtaking
when seeking employment

3P3.3
Substitute the value for the variable in onestep expressions using whole
numbers when the value is given, such as finding x + 4 and
10
– x when x has a value of 1

3P3.3.1
Demonstrate an understanding that a variable represents a missing value in
addition and subtraction expressions

Preparing
for further study

3P3.4
Find the value of the variable in onestep equations with whole numbers e.g.:
x + 25 = 100
x – 16 = 42
3y
= 42
y/5
= 200.

3P3.4.1
Recognize that addition and subtraction are inverse operations
3P3.4.2
Recognize that multiplication and division are inverse operations

Preparing for further study

3P3.5
Use a number line to represent the counting numbers.
Assessed
within 4P3.9

3P3.5.1
Demonstrate an understanding that a horizontal number line moves from left to
right using lesser to greater values
3P3.5.2
Demonstrate an understanding that intervals on a number line must follow a
constant progression by values including positive numbers and common
fractions and decimals

Reading and interpreting scales

3P3.6
Write statements of inequality for numbers up to 1,000,000.

3P3.6.1
Demonstrate an ability to use the symbols > and < in number statements
with larger numbers.

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

3P3.7
Read and understand positive and negative numbers as showing direction and
change on both horizontal and vertical number lines.

3P3.7.1
Demonstrate an understanding that a horizontal number line moves from left to
right using lesser to greater values
3P3.7.2
Demonstrate an understanding that a vertical number line moves from the
bottom up using lesser to greater values.

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

Standard 3P4. Analyze
change in various contexts

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

Enabling Knowledge and Skills

Examples of Where Adults Use It

3P4.1
Investigate how a change in one variable relates to a change in a second
variable.

3P4.1.1
Record data
3P4.1.2
Represent data in graphical form

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

3P4.2
Identify and describe situations with constant or varying rates of change and
compare them.

3P4.2.1
Record data in table form
3P4.2.2
Represent data in graphical form

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

Strand:
Statistics and Probability
Learners engage in
problem solving within adult contextual situations by communicating, reasoning,
and connecting to the following standards:
Standard 3S1. Collect,
organize and represent data

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

Enabling Knowledge and Skills

Examples of Where Adults Use It


3S1.1.1
Know that answers can be found by observing and asking relevant questions and
counting responses.

Planning
a party or meeting
Conducting
a political survey

3S1.2
Group objects or responses by a single criterion.
Assessed
by 2S1.2

3S1.2.1
Demonstrate an understanding of the concept of categories, such as shape,
size, color, or yes or no responses
3S1.2.2
Know how to count each category for subtotals

Keeping
track of who will or will not attend party.
Sorting
stock by size

3S1.3 Represent information so that it makes sense to others.

3S1.3.1
Demonstrate an understanding that information can be represented in different
ways such as a list, table, or a diagram.
3S1.3.2
Demonstrate an understanding of the importance of labeling information in a
list, table, or diagram

Reporting
on responses to party or meeting
Keeping
records for a club

3S1.4
Find a total from subtotaled categories to verify inclusion of all data.

3S1.4.1
Demonstrate an understanding that when objects or responses are divided into
categories all data must be included in one and only one category; therefore,
categories must identify distinct sets

Checking
monthly totals against weekly totals

3S1.5
Represent categorical data on a line plot.

3S1.5.1
Demonstrate an understanding that each X in a line plot represents one
and only one item or response; therefore, it is verifiable that the number of
responses is equal to the number of X’s

Keeping
a visual tally of responses by category

Standard 3S2. Read and
interpret data representations

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

Enabling Knowledge and Skills

Examples of Where Adults Use It

3S2.1
Identify graphs and tables in available resources.
Assessed
by 2S2.1

3S2.1.1
Demonstrate an understanding that a graph is a visual representation
3S2.1.2
Demonstrate an understanding that a table arranges information in rows and
columns

Reading newspapers and magazines

3S2.2
Find graphs and tables in external sources.
Assessed
by 2S2.2

3S2.2.1
Recognize that graphs and tables can be found in many publications

Reading advertisements
Finding
current interest rates

3S2.3
Sort graphs and tables by type.

3S2.3.1
Know that a bar graph uses bars of various heights to display amount
3S2.3.2
Know that line graphs use lines to display changes in amount
3S2.3.3
Know that a circle or pie graph represents the whole

Participating in conversations about represented data

3S2.4
Extract simple information from a list or table.
Assessed
by 2S2.3

3S2.4.1
Demonstrate an understanding that lists can be ordered in different ways such
as alphabetically, numerically, or randomly
3S2.4.2
Demonstrate an understanding that tables are arranged in rows and columns
3S2.4.3
Demonstrate an understanding that titles, labels, etc provide essential
information

Using
the yellow pages
Checking
items against a stock list

3S2.5
Read values on a bar or line graph up to 1,000,000.

3S2.5.1
Demonstrate an understanding that the height of the bar is equal to the
amount on the axis across from it.
3S2.5.2
Know how to read a scale on an axis
3S2.5.3
Demonstrate an understanding that specific data points on a line graph
correspond with the labels on both axes.

Reading newspapers and magazines

3S2.6
Make numerical comparisons about relative values on a bar graph.

3S2.6.1
Demonstrate an understanding that comparative statements such as greater than
or less than can be made based on the height of the bars.
3S2.6.2
Demonstrate an understanding of relative numerical terms such as twice
or half.

Conversing
about information contained in newspapers and magazines

Standard 3S3. Describe data using numerical descriptions,
statistics and trend terminology

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

Enabling Knowledge and Skills

Examples of Where Adults Use It

3S3.1
Identify the minimum, maximum, spread and shape of data.
Assessed
by 5S3.1

3S3.1.1
Be familiar with termsminimum, maximum, and spread.
Recognition of gaps, holes, and clusters in the data set to
determine where data is missing and where it is heavily represented.

Reading temperature charts

3S3.2
Use “most of” statements to describe data.

3S3.2.1
Recognize that values in the data set can be repeated and some values may be
repeated more frequently than others.

Analyzing results of a survey or group consensus

3S3.3
Find the average (mean) and range for a data set.

3S3.3.1
Know that mean is “average” and that average in this case is about equal
distribution.
3S3.3.2
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.

3S3.4
Find the median.
Assessed
by 4S3.4

3S3.4.1
Know that median is the middle value.
3S3.4.2
Know that when there is an even number of values in the data set, the median
is found by calculating the mean of two middle values.

Explaining the median salary or median years worked in company statistics

Standard 3S4. Make and
evaluate arguments or statements by applying knowledge of data analysis

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

Enabling Knowledge and Skills

Examples of Where Adults Use It


3S4.1.1
Know how to locate titles
3S4.1.2 Titles
indicate subject matter
3S4.1.3
Know what to look for to connect data representations with statements

Presenting
information to children or coworkers

3S4.2
Determine whether or not a graph/table connects to a statement using title,
data labels and percent matches.
Assessed
by 4S4.1

3S4.2.1
Know how to locate data labels in tables and graphs to verify they match
statements
3S4.2.2
Locate and connect percent numbers in graphs and statements

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

3S4.3
Visually identify “who has more,” and use some numbers to compare
quantities.
Assessed
by 2S3.4

3S4.3.1
Recognize bar heights and circle wedges show quantity

Understanding graphic presentations in newspapers
and magazines

3S4.4 Support simple statements with data.

3S4.4.1
Know that data can be collected to verify statements such as “more people in
class walk than drive to class.” Know how to keep track of collected data

Taking political actions to institute changes in
the community

3S4.5
Use “most of” statements to support arguments.
Assessed
by 3S4.4

3S4.5.1
Know ways to compare numbers

Discussing numbers with peers and coworkers

3S4.6
Know statements using “double” and “half” or fifty percent are accurate.

3S4.6.1
Double and halving numbers
3S4.6.2
Fifty percent equals one half

Reading and/or responding to
consumer materials

3S4.7
Know when percent figures don’t add up to 100%.
Assessed
by 4S4.6

3S4.7.1
Awareness that circle graphs usually represent 100%, and all figures in them
should add to 100 or statements based on the graph are suspect

Reading
budget reports

3S4.8
Recognize that mean and median numbers are considered “averages,” and that
averages represent numbers typical of the data that can support an argument.
Assessed
by 4S3.4

3S4.8.1
Awareness that what are termed “averages” are numbers supposedly “typical” of
data
3S4.8.2
Know ways in which “averages” are “typical” of data – median is the middle
value and mean implies equal distribution of all data

Debating proposed rent increases

3S4.9
Recognize that bar widths can provide misleading information.

3S4.9.1
Visual messages are given by bar widths – thin relays message of “less” and
wide relays message of “more.” Visual messages can contradict or enhance
evidence

Reading advertisements
to make choices

3S4.10
See where authors of data reports can manipulate data to benefit themselves
or malign others in provided materials.
Assessed
by 5S4.7


Reading advertisements
to make choices

3S4.11
Identify obvious misstatements.

3S4.11.1
Recognize where to look for numbers representing relevant quantities

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

3S4.12
Use statements that refer to “double” and “half” or fifty percent of the
data.

3S4.12.1
Demonstrate and ability to double and find half of numbers

Calculating the cost of
items marked “onehalf” off.
Calculating the down
payment for an item requiring 50% down

Standard 3S5. Know and apply basic probability concepts

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

Enabling Knowledge and Skills

Examples of Where Adults Use It



Making
decisions about how weather may affect outdoor plans
Predicting
the outcome of a sporting event based on a team’s past performance.

3S5.2 Give the probability of a single outcome in simple
concrete situations such as tossing a coin or rolling a die.

3S5.2.1
Demonstrate an understanding that probability depends on the total number of
possibilities

Tossing
a coin
Rolling
dice

3S5.3 State probability as a ratio in multiple forms (colon,
words, and fractions) with simple scenarios.

3S5.3.1
Know that probability is the ratio of the potential successful outcomes to
total possibilities
3S5.3.2 Know that such ratios can be written in
fraction form
3S5.3.3 Know that ratio fractions can be
simplified

Determining the chances of winning a prize in a drawing

Strand:
Geometry and Measurement
Learners engage in
problem solving within adult contextual situations by communicating, reasoning,
and connecting to the following standards:
Standard 3G1. Use and
apply geometric properties and relationships to describe the physical world
and identify and analyze the characteristics of geometric figure

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

Enabling Knowledge and Skills

Examples of Where Adults Use It


3G1.1.1 Be able
to solve practical problems using the properties of 2D and 3D figures
3G1.1.2
Demonstrate an understanding that that area is conserved, but perimeter is
not when 2D objects are combined
3G1.1.3
Build 3D figures using 2D plans and blocks

Organizing
a closet
Packing
a trunk
Covering
a package with paper
Tying
string around a package

3G1.2
Identify properties, locations, and functions of right angles.

3G1.2.1
Know that a right angle is 90 degree or a quarter turn, that two right angles
make a straight line, and four right angles fill a space

Creating
tiling patterns

Standard
3G2. Use transformations and symmetry to analyze mathematical situations

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

Enabling Knowledge and Skills

Examples of Where Adults Use It



Cutting
cake in half
Folding
objects


3G2.2.1
Demonstrate an understanding of concepts of sameness or halfness

Designing
and making a quilt


3G2.3.1
Demonstrate an understanding of concepts of sameness or halfness

Recognizing
patterns and symmetry in design and architecture

Standard
3G3. Specify locations and describe spatial relationships using coordinate
geometry and other representational systems

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

Enabling Knowledge and Skills

Examples of Where Adults Use It


3G3.1.1 Use the
compass rose on a map with secondary (SW, NE, etc) directions
3G3.1.2
Demonstrate an understanding of latitude and longitude, or horizontal and
vertical indices on a map


3G3.2
Draw 2 dimensional (2D) shapes in different orientations on a grid.
Assessed
by 4G3.3

3G3.2.1
Use graph paper to draw 2D shapes
3G3.2.2
Be able to change the orientation and copy object.

Creating
a pattern for a model plane

Standard 3G4. Understand
measurable attributes of objects and the units, systems, and processes of
measurement and apply appropriate techniques, tools and formulas to determine
measurements

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

Enabling Knowledge and Skills

Examples of Where Adults Use It


3G4.1.1 Demonstrate
an understanding of place value for whole numbers and to twodecimal places
3G4.1.2
Know how to round off thousandths (mils) to the nearest hundredths (cents)

Balancing
a checkbook
Figuring
one’s share of a restaurant bill being divided equally
Finding
cost of multiples units of an item

3G4.2
Demonstrate a general understanding of interrelatedness of distance, time,
and speed.

3G4.2.1
Investigate how a change in one variable (speed) relates to a change in a
second variable (time, distance)
3G4.2.2
Identify and describe situations with constant or varying rates of change and
compare them (e.g. acceleration, slowing down, stopping)

Estimating
time of arrival with slower or faster speeds

3G4.3
Read and interpret scales with marked and unmarked labels.
Assessed
by 4G3.1

3G4.3.1
Skip counting by 5, 10, 100, 500
3G4.3.2
Making visual estimates of lengths

Inferring
distances on a road map

3G4.4
Measures with a ruler to 1/8inch and metric ruler in cm and mm.

3G4.4.1
Know that a foot equals 12 inches

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

3G4.5
Can make informal comparisons between inches and centimeters.

3G4.5.1
Demonstrate an understanding of making a onetoone correspondence between
different rulers and units.
3G4.5.2
Make visual estimates of the number of centimeters per inch.

Using
a ruler with both inches and centimeter scales
Selecting
the appropriately sized wrench when working on a Europeanmade car
Mixing
cleaning chemicals in the correct proportions by comparing metric to standard
liquid measure
Measuring
correct doses of medication.

3G4.6
Can convert units of measure in the same systems.

3G4.6.1
Know the relationship of familiar units (e.g. 12 inches in a foot, 3 feet in
a yard, 4 cups in a quart)
3G4.6.2
Know when to multiply and when to divide when converting units of measure

Substituting
the use of foot rulers for a yardstick or a one cup measure for a quart
measure
Doing
home repairs and carpentry projects

3G4.7
Use and apply concepts of weight and capacity to solve problems.

3G4.7.1 Know the
difference between weight and capacity

Correctly
loading a washing machine to maintain balance throughout the cycle
Reading
the capacity of a liquid to near exact measure

3G4.8
Use, read, and compare positive and negative Fahrenheit temperatures.

3G4.8.1
Demonstrate an understanding that temperature increases as it goes up and
decreases as it goes down
3G4.8.2
Know that the sign of the temperature changes when crossing the zero degree
point

Reading weather forecasts
Understanding
windchill factor

3G4.9
Use and interpret the 24 hour clock.

3G4.9.1
Demonstrate an understanding of standard notation for A.M and P.M.
3G4.9.2
Addition and multiplication facts to 12
3G4.9.3
Familiarity with quarter and half concepts

Matching
12 and 24 hour times

3G4.10
Calculate times using the appropriate value and converting between time
formats (including elapsed time).

3G4.10.1
Know equivalencies for hours, seconds, minutes, days, weeks, months, decades,
and centuries.
3G4.10.2
Know multiplication and division by 2digit numbers
3G4.10.3
Use mental math skills

Understanding
that 2 centuries is 200 years to appreciate past events and their place in
history

3G4.11
Directly measures perimeter in linear units and area in square units (sq.
in., sq. ft., sq. cm.).

3G4.11.1
Use a ruler to measure length and width
3G4.11.2
Compare two figures by laying them on top of each other to determine larger
area
3G4.11.3
Cover a figure with square units and count the units
3G4.11.4
Use addition and multiplication skills to aid in counting units

Planning
renovations or paint for a room
Making
a cover for a counter top
Sewing
a chair cover

3G4.12
Estimate, measure, and compare whole number weights using simple instruments,
graduated in familiar units (ounces and pounds) and know when to use
appropriate measures.

3G4.12.1
Use a scale to measure weight
3G4.12.2
Compare two figures holding them to determine which is heavier
3G4.12.3
Place two
objects on a balance scale
3G4.12.4
Use addition and multiplication skills to aid in counting units

Placing
objects of various weights on shelves or hanging them on walls
Shopping
for fresh vegetables in a market

See “How to use This
Document (Teacher’s Guide) and (Connecting Curriculum, Instruction and Assessment),”
pages 810.
Strand:
Number Sense
Learners engage in
problem solving within adult contextual situations by communicating, reasoning,
and connecting to the following standards:
Standard
4N1. Represent and use numbers in a variety of equivalent forms in
contextual situations

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

Enabling Knowledge and Skills

Examples of Where Adults Use It

4N1.1 Read,
write, order and compare numbers, including large numbers (millions or
billions).

4N1.1.1
Demonstrate an understanding that the position of a digit signifies its value
4N1.1.2
Know what each digit represents in a number up to seven digits, including the
use of zero as a place holder
4N1.1.3
Demonstrate an understanding of the symbols
for greater than and less than

Filing
plans in numerical order
Reading
route numbers on delivery labels

4N1.2
Recognize positive and negative numbers in practical contexts.

4N1.2.1
Demonstrate an understanding of the words positive and negative
4N1.2.2
Demonstrate an understanding that a negative temperature is below zero
4N1.2.3
Demonstrate an understanding that a negative amount of money represents money
owed

Reading
windchill chart
Reading a thermometer

4N1.3
Read, write, order, and compare fractions and mixed numbers.

4N1.3.1
Know common equivalent fractions (e.g. equivalent to a half, quarters,
thirds, fifths, tenths)
4N1.3.2
Demonstrate an understanding that in unit fractions, the larger the
denominator, the smaller the fraction
4N1.3.3
Demonstrate an understanding that nonunit fractions must be ordered by their
closeness to the whole

Reading fractions used in recipes
Comparing
interest rates (e.g. 1 ¼% versus 1 ½%)

4N1.4
Read, write, order, and compare decimals up to three decimal places.

4N1.4.1
Demonstrate an understanding that the position of a digit signifies its value
4N1.4.2
Know that the decimal point separates whole numbers from decimal fractions
4N1.4.3
Know what each digit represents, including the use of zero as a place holder

Reading and comparing gas prices
Reading and comparing metric
measurements

4N1.5
Recognize and use equivalencies between fractions and decimals.

4N1.5.1
Know any fraction is equivalent to a decimal that ends or has a repeating pattern,
and vice versa

Understanding
how to read adigital scale when placing a fraction order at the deli

4N1.6
Can convert fractions to decimals and decimals to fractions.

4N1.6.1
Demonstrate an understanding that a fraction can be converted to an equivalent
decimal by dividing the numerator of a fraction by the denominator
4N1.6.2
Demonstrate an understanding that a decimal can be converted to an equivalent
fraction by writing the decimal value over 10, 100, or 1,000 and reducing to
simplest form

Understanding
how the scale works at the deli counter
Using
an electronic calculator to make volume and area computations based on
measurements made by a standard tape measure

4N1.7
Read, write, order, and compare simple percentages.

4N1.7.1
Demonstrate an understanding of percentage as the number of parts in every
100
4N1.7.2
Know that 100% is the whole

Finding
20% off in a sale

4N1.8
Demonstrate an understanding of simple percentage of increase and decrease.
Assessed
by 5N1.4

4N1.8.1
Demonstrate an understanding of percentage as the number of parts in every
100
4N1.8.2
Know that 100% is the whole
4N1.8.3
Demonstrate an understanding that a 10% pay increase is more than a 5% pay
increase, but the actual increase depends on the number operated on

Finding
a price increase of 10%
Finding
a costofliving salary increase

4N1.9
Recognize equivalencies between common fractions, percentages and decimals
(e.g. 50% = ½, 0.25 = ¼) and use these to find part of wholenumber
quantities.
Assessed
by 5N1.5

4N1.9.1 Know
common fraction equivalents (e.g. half, quarter, fifths, tenths)
4N1.9.2
Recognize 50% off and halfprice as the same
4N1.9.3
Know ½ as 0.5 when solving a problem with a calculator

Computing
discounts efficiently and flexibly using percents or fraction equivalencies
Finding
25% discount by dividing by 4
Finding
a tip using mental math

4N1.10
Use ratio and proportion to solve onestep percent problems.

4N1.10.1
Demonstrate an understanding that equal ratios are equal fractions
4N1.10.2
Recognize the term proportion for a statement of equal ratios
4N1.10.3
Calculate for the missing term in a proportion by a variety of methods

Adjusting
a recipe for a larger or smaller number of servings
Converting
measurements from one standard to another (e.g. miles per hour to feet per
second)

4N1.11
Recognize and use equivalent forms of common fractions (e.g. ½ = 5/10).

4N1.11.1
Demonstrate an understanding that equivalent fractions look different but
have the same value
4N1.11.2
Demonstrate an understanding that when the top and bottom number of a
fraction are the same, the fraction is equivalent to 1

Calculating
the size of a container required to hold a variety of portions (e.g. ¼ cup of
x plus ¼ cup of y plus ½ cup of z)

Standard 4N2. Demonstrate
an understanding meanings of operations and how they relate to one another

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

Enabling Knowledge and Skills

Examples of Where Adults Use It


4N2.1.1
Demonstrate an understanding that addition is combining, subtraction is
separating or comparing, multiplication is repeated addition, and division is
repeated subtraction

Taking
a standardized test

4N2.2
Perform multiplication operations reliably, accurately, and efficiently.

4N2.2.1
Demonstrate an understanding that multiplication is commutative, but that in
context changing order changes meaning

Knowing
that taking two tablets four times a day is different from taking four
tablets twice a day

4N2.3
Use ratios to describe the relationship between two sets of objects.

4N2.3.1
Know when something is separated into equal groups
4N2.3.2
Demonstrate an understanding of ratio as comparison
based on division

Recognizing
when a solution can be generated by the use of proportion

4N2.4
Read, write, and compute with exponents.

4N2.4.1
Be familiar with the terms square, cube, and square root
4N2.4.2
Recognize that any value taken to the second power will form a square and
that any value taken the third power will form a cube
4N2.4.3
Recognize that exponents represent repeated multiplication
4N2.4.4
Recognize that exponents indicate the number of times that the base is
written as a factor
4N2.4.5
Read and write expressions such as 6(6) (6) (6) (6) (6) (6) as 6^{7}

Preparing
for further study
Understanding exponential growth of bacteria or
virus such as HIV

4N2.5
Calculate square roots of perfect squares, estimate within range of square
root value, and demonstrate an understanding of how squaring and taking the
square root are related.

4N2.5.1
Know that a number is squared by multiplying it by itself
4N2.5.2
Know the values of perfect squares up to 15^{2}
4N2.5.3
Know that square root is the inverse of squaring
4N2.5.4
Know the square roots of perfect squares up to the square root of 225
4N2.5.5
Know that the square roots of values which are not perfect squares fall
between two whole numbers

Estimating the number of 12inch tiles needed to
cover a rectangular floor.

Standard
4N3. Compute fluently and make reasonable estimates

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

Enabling Knowledge and Skills

Examples of Where Adults Use It

4N3.1
Round decimals in practical contexts and verbal problems.

4N3.1.1
Know how to read decimals up to four decimal places
4N3.1.2
Recognize that rounding a decimal to a particular decimal place requires
analyzing the digit in the following decimal place

Performing
estimations of mathematical problems to check work

4N3.2 Add, subtract, multiply, and divide decimals up to
three places.

4N3.2.1 Know and use strategies to check answers (e.g.
approximate calculations using whole numbers)
4N3.2.2 Know how to align numbers for column addition and subtraction
4N3.2.3
Know how to multiply decimal factors to produce decimal placement in product
4N3.2.4
Know how to multiply divisor and dividend by the same value to determine
quotient

Working
out the total amount due for an order
Working
out change needed from a purchase (e.g. $20 less $14.99)

4N3.3 Evaluate one number as a fraction of another.

4N3.3.1 Demonstrate an understanding of equivalent
fractions
4N3.3.2 Demonstrate an understanding of simplest form
4N3.3.3 Know how to bring a fraction to its simplest form
(e.g. by recognizing equivalent fractions, by using factors to “cancel”)
4N3.3.4 Recognize prime numbers (e.g. numbers that can’t be
canceled)
4N3.3.5 Demonstrate an understanding that quantities must
be in the same units to evaluate one as a fraction of another

Changing
minutes to fractions of an hour to fill in a time sheet
Representing
the outcome of observations as a fraction

4N3.4 Use fractions to add, subtract, multiply, and
divide amounts or quantities.

4N3.4.1 Know some common addition and subtraction facts
(e.g. ½ + ¼ = ¾, ¾ – ½ = ¼)
4N3.4.2 Demonstrate an understanding of how to change
fractions to equivalent fractions for the purpose of adding and subtracting
4N3.4.3 Know some common multiplication and division facts
(e.g. ½ x ½ = ¼, ¼ ¸ ½ = ½)

Adding
hours on a time sheet that includes fractions
Finding
timeandahalf pay rate when working overtime

4N3.5 Work out simple ratio and direct proportion.

4N3.5.1 Demonstrate an understanding of simple ratio as the
number of parts (e.g. three parts to one part)
4N3.5.2 Demonstrate an understanding of direct proportion
as the same rate of increase or decrease (e.g. double, half)

Diluting
a liquid in a given ratio (e.g. weed killer, paint)
Changing
quantities in a recipe to make twice as much

4N3.6 Follow order of operations in evaluating
number sentences with more than one operation.
Assessed by 3P3.2

4N3.6.1 Applies the rule for order in a horizontal notation

Solving
algebra equations containing multiple operations


4N3.7.1
Demonstrate an understanding of positive and negative numbers

Balancing
a checkbook.

4N3.8 Estimate
answers to calculations.

4N3.8.1
Know how to make approximate calculations
4N3.8.2
Demonstrate an understanding that knowledge of context enables ‘guessing’ at
answers (e.g. it should be about…), or judging if answers are sensible
(e.g. that’s far too big; it doesn’t make sense to have an answer less
than 1, etc.)

Estimating
to check that answers are reasonable

4N3.9
Use a calculator to calculate efficiently using whole numbers, fractions,
decimals, and percentages.

4N3.9.1
Know how to change a fraction to a decimal
4N3.9.2
Know how to change a percentage to a decimal
4N3.9.3
Know how to interpret a rounding error such as 6.9999999 as 7
4N3.9.4
Know and use strategies to check answers obtained with a calculator

Doing
any calculations at this level

4N3.10
Carry out calculations using addition and subtraction with numbers of any size
using efficient written methods including ways to check answers.

4N3.10.1 Know and use strategies to check answers (e.g.
approximate calculations, estimation)

Using
mental and written methods of calculation to generate results when solving
problems using whole numbers of any size

4N3.11
Carry out calculations using multiplication and division using efficient
written methods including ways to check answers.

4N3.11.1
Demonstrate an understanding of the words multiple and factor
and relate them to multiplication and division facts
4N3.11.2 Demonstrate an understanding of the word prime and
know prime numbers up to 20

Using
mental and written methods of calculation to generate results when solving
problems using whole numbers of any size

4N3.12
Multiply whole numbers and decimals by 10, 100, and 1,000 to understand the
impact on place value.

4N3.12.1
Recognize the impact on place value of zeros added to whole numbers
4N3.12.2
Recognize the impact on place value as the position of the decimal point
changes

Simplifying
large numbers to estimate products

4N3.
13 Divide whole numbers and decimals by 10, 100, and 1,000 to understand the
impact on place value.

4N3.13.1
Recognize the impact on place value of zeros are cancelled in whole numbers
4N3.13.2
Recognize the impact on place value as the position of the decimal point
changes

Simplifying
large numbers to estimate quotients

Strand:
Patterns, Functions and Algebra
Learners engage in
problem solving within adult contextual situations by communicating, reasoning,
and connecting to the following standards:
Standard 4P1. Explore,
identify, analyze, and extend patterns in mathematical and adult contextual
situations

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

Enabling Knowledge and Skills

Examples of Where Adults Use It



Using
rate tables for postage

4P1.2 Recognize and create repeating
patterns, identify the unit being repeated, and generalize.

4P1.2.1 Isolate smallest unit of repetition
4P1.2.2 Use a notation system to record patterns

Creating
Sales Tax tables
Using
mental math strategies

4P1.3 Given a table of amounts, generalize the
relationship between the quantities.

4P1.3.1 Read tables
4P1.3.2 Recognize and verbalize patterns

Using rate tables for prices

Standard
4P2. Articulate and represent number and data relationships using words,
tables, graphs

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

Enabling Knowledge and Skills

Examples of Where Adults Use It


4P2.1.1
Translate simple worded problems involving unknown quantities into simple
equations

Entering
an expression in a spreadsheet

4P2.2
Develop and use simple formulas from tables with one or two arithmetical
steps for real life contexts.

4P2.2.1
Discover patterns in an “inout” table
4P2.2.2
Verbalize a rule for finding values in an “inout” table
4P2.2.3
Write a general expression for finding values in an “inout” table
4P2.2.4
Write an equation
4P2.2.5
Decide on the effectiveness of the developed formula by substituting known
values

Converting
temperature between Celsius and Fahrenheit
Finding interest on a loan

Standard
4P3. Recognize and use algebraic symbols to model mathematical and
contextual situations

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

Enabling Knowledge and Skills

Examples of Where Adults Use It


4P3.1.1
Demonstrate an understanding that + represents operations of combining
4P3.1.2
Demonstrate an understanding that – represents operations of separation or
comparison
4P3.1.3
Demonstrate an understanding that ´
stands for combining multiples
4P3.1.4
Demonstrate an understanding that ¸
means separating into equal groups or discovering the number of equal groups
contained within
4P3.1.5
Demonstrate an understanding that = represents vocabulary such as is equal
to, is the same as, and gives you

Using
a fourfunction calculator to find the total of a grocery bill
Using
a calculator to balance a checkbook
Using
a fourfunction calculator to find hourly rate given weekly pay, or to find
weekly pay given hourly rate.
Helping
children with homework.

4P3.2
Read and write number operations using algebraic notation for multiplication,
division, and parentheses.

4P3.2.1
Read and write 5 (10) for multiplication of 5 times 10
4P3.2.2
Read and write 10 for 10 ¸
2
2
^{ }
^{ }4P3.2.3 Know that the
contents of parentheses must be worked out first
4P3.2.4
Know that exponents and roots are simplified before multiplication or
division

Following
convention in notation and the order of carrying out operations
Testtaking
when seeking employment

4P3.3
Demonstrate appropriate use of the universally accepted “order of
operations”.

4P3.3.1
Read and write number expressions which follow the rule of order for
simplifying:
Parentheses
Exponents
and roots
Multiplication or
division
Addition
or subtraction

Helping
children with homework
Preparing
for further study

4P3.4
Substitute the value for the variable in an addition or subtraction
expression when the value is given, such as finding x + 4 and 10 – x
when x has a value of 1.


To
prepare for further study

4P3.5
Substitute the value for the variable in a multiplication or division
expression when the value is given (e.g. finding 2x and 8/x when
x = 2 including exponents.

4P3.5.1
Demonstrate an understanding that a variable represents a missing value in a
multiplication and division expression
4P3.5.2
Demonstrate an understanding that when there is no operator between a number
and a variable or two variables that multiplication is implied

To
prepare for further study

4P3.6
Evaluate expressions and make whole number substitutions in given formula to
produce results.

4P3.6.1
Demonstrate an understanding that when there is no operator between a number
and a bracket or parentheses that multiplication is implied
4P3.6.2
Know order of operations

Informally
using d = rt to make estimates regarding speed or time of departure

4P3.7
Read and understand positive and negative integers.

4P3.7.1
Demonstrate an understanding of the words positive, negative, and zero
4P3.7.2
Know that positive refers to values more than zero
4P3.7.3
Know that negative refers to values below zero

Reading thermometers
Riding
an elevator below ground level
Staying
“in the black” or going “into the red”

4P3.8
Demonstrate an understanding addition and subtraction of integers.

4P3.8.1
Be able to solve expressions such as: 20 – 30
6
+ 10

Finding
temperature change

4P3.9
Use a number line to represent values.

4P3.9.1
Demonstrate an understanding that a horizontal number line moves from left to
right using lesser to greater values
4P3.9.2
Demonstrate an understanding that intervals on a number line must follow a
constant progression between values
4P3.9.3
Demonstrate an understanding that numbers to the left of zero are negative
and those to the right of zero are positive

Using
a “thermometer” to represent the progress of a fund raiser
Preparing
for further study in algebra or higher math

4P3.10
Write statements of inequality for integers of any size e.g.:
2
< 10
10
> 8
99
< 100
1,000
> 999.99
12
<  11.

4P3.10.1
Demonstrate an understanding that > stands for greater than
4P3.10.2
Demonstrate an understanding that < stands for less than

Preparing
for further study in algebra or higher math
Helping children with homework

4P3.11
Find the value of a variable in multistep equations e.g.:
3x + 25 = 100
2x – 16 = 42
3y+
3 = 42
m/5 – 25 = 200.

4P3.11.1
Recognize that addition and subtraction are inverse operations
4P3.11.2
Recognize that multiplication and division are inverse operations
4P3.11.3
Recognize that using the inverse operation can solve equations

Preparing
for further study in algebra or higher math
Helping
children with homework

Standard 4P4. Analyze change in various contexts

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

Enabling Knowledge and Skills

Examples of Where Adults Use It

4P4.1 Use graphs
to analyze the nature of changes in quantities in linear relationships.

4P4.1.1
Know vocabulary to describe linear change (e.g. rises steadily, falls,
gradually declines)
4P4.1.2
Know mechanics of making a line graph


Strand:
Statistics and Probability
Learners engage in
problem solving within adult contextual situations by communicating, reasoning,
and connecting to the following standards:
Standard 4S1.
Collect, organize and represent data

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

Enabling
Knowledge and Skills

Examples
of Where Adults Use It

4S1.1
Pose questions about themselves and their surroundings and gather data to
answer posed questions.


Conducting
a survey for community planning

4S1.2
Group objects or responses by single or double criteria.

4S1.2.1
Demonstrate an understanding of the concept of categories such as shape,
size, color or yes or no responses
4S1.2.2
Know how to count each category for subtotals

Organizing
findings in a chart or table

4S1.3
Represent information so that it makes sense to
others in any graphical form.

4S1.3.1
Demonstrate an understanding that information can be represented in different
ways such as a list, table, or a line plot
4S1.3.2
Demonstrate an understanding of the importance of labeling information in a
list, table, or line plot

Writing
a health pamphlet

4S1.4
Find a total from subtotaled categories to verify inclusion of all data.
Assessed
by 3S1.4

4S1.4.1
Demonstrate an understanding that when objects or responses are divided into
categories all data must be included in one and only one category; therefore,
categories must identify distinct sets

Estimating
the total cost of a variety of products, each of which is priced individually
(e.g. corn – 6/$1.00, cucumbers  $.39 each, beans  $.99/pound)

4S1.5
Display categorical data in a bar graph or simple
fractions of data in a circle graph.

4S1.5.1
Demonstrate an understanding that the one axis
displays the categories
4S1.5.2
Demonstrate an understanding that the other axis is
numbered sequentially
4S1.5.3
Demonstrate an understanding that the height (or
length) of the bar is equal to the amount on the corresponding axis
4S1.5.4
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

4S1.6
Convert a bar graph into a circle graph.

4S1.6.1
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

4S1.7
Translate data from a numerical table to a line
graph and vice versa.

4S1.7.1
Demonstrate an understanding that a table can
display the same data as a line or bar graph but in rows and columns
4S1.7.2
Demonstrate an understanding of the importance of
labeling each axis
4S1.7.3
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
oneweek period
Creating a line graph to illustrate temperatures over a oneweek
period

Standard 4S2. Read and
interpret data representations

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

Enabling Knowledge and Skills

Examples of Where Adults Use It


4S2.1.1
Demonstrate an understanding that a graph is a visual representation
4S2.1.2
Demonstrate an understanding that a table arranges information in rows and
columns



4S2.2.1
Recognize that graphs and tables can be found in many publications

Reading advertisements
Looking
up taxes payments
Finding
current interest rates

4S2.3
Name and sketch various types of graphs and a
table.

4S2.3.1
Know that a bar graph uses bars of various heights
to display amount
4S2.3.2
Know that line graphs use lines to connect data
points
4S2.3.3
Know that a circle or pie graph represents the
whole or 100%

Participating in a class or working with a child on homework

4S2.4
Extract simple information from a list or table.
Assessed by 2S2.3

4S2.4.1
Demonstrate an understanding that lists can be
ordered in different ways such as alphabetically, numerically, or randomly
4S2.4.2
Demonstrate an understanding that tables are arranged
in rows and columns.
4S2.4.3
Demonstrate an understanding that titles, labels,
etc. provide essential information

Using the yellow pages
Checking items against a stock list

4S2.5
Read values on a bar, line, or circle graph.

4S2.5.1
Demonstrate an understanding that the height of the
bar is equal to the amount on the axis across from it
4S2.5.2
Know how to read a scale on an axis
4S2.5.3
Demonstrate an understanding that specific data points correspond with the
labels on both axes

Using car mileage graphs

4S2.6
Make numerical comparisons about relative values on
a bar graph or circle graph.

4S2.6.1
Demonstrate an understanding that comparative
statements such as greater than or less than can be made based
on the height of the bars or wedge sizes
4S2.6.2
Demonstrate an understanding of relative numerical
terms such as twice or half

Creating a circle graph illustrating how earnings are broken
down and distributed by categories of expenses

Standard 4S3. Describe
data using numerical descriptions, statistics and trend terminology

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

Enabling Knowledge and Skills

Examples of Where Adults Use It


4S3.1.1 Be
familiar with the terms minimum, maximum, and spread.
4S3.1.2
Recognition of gaps, holes, and clusters in the
data set to determine where data is missing and where it is heavily
represented.

Reading temperature charts

4S3.2
Use “most of” statements to describe data.
Assessed
by 3S3.2

4S3.2.1
Recognize that values in the data set can be repeated and some values may be
repeated more frequently than others

Using a graph to illustrate the breakdown of household expenses
while describing them orally

4S3.3
Find the mean.

4S3.3.1
Know that mean is “average” and that average in this case is about equal
distribution
4S3.3.2
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
4S3.3.3
Demonstrate an understanding that what are termed
“averages” are numbers supposedly “typical” of data

Estimating one’s daily expenses

4S3.4
Find the median and mode.

4S3.4.1
Know that median is the middle value
4S3.4.2
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
4S3.4.3
Know that mode is the number or item that occurs most often in a set of data
4S3.4.4
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

4S3.5
Identify the effect of spread on mean and median.
Assessed
by 5S4.5

4S3.5.1
Know the minimum or maximum value can greatly affect the mean but will not
affect the median

Interpreting
statistical data accurately

Standard 4S4. Make and evaluate arguments or statements by
applying knowledge of data analysis

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

Enabling Knowledge and Skills

Examples of Where Adults Use It

4S4.1 Determine
whether or not a graph/table connects to an argument/ statement using title,
data labels, and percent matches.

4S4.1.1
Know how to locate data labels in tables and graphs to verify they match
arguments/statements
4S4.1.2
Locate and connect percent numbers in graphs and arguments/ statements

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

4S4.2
Visually identify “who has more,” use numbers to compare quantities and
identify obvious misstatements.
Assessed
by 2S3.4

4S4.2.1
Recognize bar heights and circle wedges show quantity
4S4.2.2
Recognize where to look for numbers representing relevant quantities
4S4.2.3
Knowing to connect numbers with statements/arguments to verify accuracy

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

4S4.3
Make statements about data trends to support or reject arguments/ statements
forwarded by others.
Assessed
by 5S4.4

4S4.3.1
Demonstrate an understanding that lines going up mean increase; lines tilting
down mean decrease and that they can vary over time
4S4.3.2
Know that a flat line means no change
4S4.3.3
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

4S4.4
Know statements using “double” and “half” or fifty percent are accurate.
Assessed
by 3S4.6

4S4.4.1
Double and halving numbers
4S4.4.2
Fifty percent equals one half

Using
consumer reports to make decisions

4S4.5
Verify that statements using three times or four times, one fourth or one
tenth are accurate.

4S4.5.1
Know ways to estimate multiples of large numbers
4S4.5.2
Know ways to estimate one fourth or one tenth of a number

Using
consumer reports to make decisions

4S4.6
Know when percent figures don’t add up to 100% and when numbers and percent
figures (50%, 25%, 10%) don’t match up.

4S4.6.1
Demonstrate an understanding that circle graphs usually represent 100%, and
all figures in them should add to 100
4S4.6.2
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

4S4.7
Compare and contrast provided graphs to evaluate for contradictory or
unsupported statements.

4S4.7.1
Recognize that statements or arguments based on data are sometimes generated
by comparing or contrasting graphs
4S4.7.2
Recognize that statements or arguments based on one graph are sometimes
contradicted in another

Analyzing
accidentrelated data

Standard 4S5. Know and apply basic probability concepts

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

Enabling Knowledge and Skills

Examples of Where Adults Use It


4S5.1.1
Demonstrate an understanding that while some events are impossible, some are
certain to happen, and in other events some are more likely to occur than others.

Deciding to avoid or use certain products

4S5.2 Give the probability of a single outcome in simple
concrete situations such as tossing a coin or rolling a die.
Assessed by 3S5.2

4S5.2.1
Demonstrate an understanding that probability depends on the total number of
possibilities

Tossing a coin
Rolling dice

4S5.3 State probability as a ratio fraction.

4S5.3.1
Know that probability is the ratio of the potential successful outcomes to
total possibilities.
4S5.3.2
Know that such ratios can be written in fraction form.
4S5.3.3 Know that ratio fractions can be simplified

Determining the chances of winning a prize in a drawing

4S5.4 Find the probability of independent events.

4S5.4.1
Know that probability is the ratio of the potential successful outcomes to
total possibilities.
4S5.4.2
Know that such ratios can be written in fraction form or as one value
compared to another
4S5.4.3
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

4S5.5 State the probability as a percent.

4S5.5.1
Know that ratio fractions can be expressed as a percent by expressing a
proportion with the percent out of 100

Converting a specific set of outcomes as likelihood of the event
happening in 100 attempts

Strand:
Geometry and Measurement
Learners engage in
problem solving within adult contextual situations by communicating, reasoning,
and connecting to the following standards:
Standard 4G1. Use and
apply geometric properties and relationships to describe the physical world
and identify and analyze the characteristics of geometric figures

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

Enabling Knowledge and Skills

Examples of Where Adults Use It


4G1.1.1
Use a ruler and string to make measurements
4G1.1.2
Demonstrate an understanding that the radius is half of the diameter
4G1.1.3
Demonstrate an understanding that the circumference is a little more than
three diameters and that the ratio is known as pi

Measuring
automobile tires
Designing
circular gardens

4G1.2 Directly measure different angles with a
protractor.
Assessed by 5G1.7

4G1.2.1
Estimate the measure of an angle using benchmarks of 90 degrees and 180
degrees

Cutting
molding for a corner


4G1.3.1 Be able
to solve practical problems using the properties of 2D and 3D figures
4G1.3.2
Demonstrate an understanding that that area is conserved, but perimeter is
not when 2D objects are combined
4G1.3.3
Build 3D figures using 2D plans and blocks

Organizing
a closet
Packing
a trunk
Covering
a package with paper
Tying
string around a package

4G1.4
Identify shapes that are congruent or similar.

4G1.4.1 Know that congruent shapes are exactly
the same with equal sides and angles
4G1.4.2 Know that similar shapes are the same
shape, but different sizes
4G1.4.3 Know that the corresponding angles of
congruent and similar shapes are congruent
4G1.4.4 Know that similar shapes are proportional
to each other

Assembling
items bought unassembled (e.g. toys, exercise equipment, some furniture)

4G1.5
Identify types of angles such as right, obtuse, acute, and straight.

4G1.5.1 Know that an acute angle has a measure of
less than 90°
4G1.5.2 Know that a right angle has a measure of
90°
4G1.5.3 Know that an obtuse angle has a measure
of more than 90 but less than 180°
4G1.5.4 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


4G1.6.1 Know
that a line that crosses two parallel lines is called a transversal
4G1.6.2 Know
that a transversal crosses two lines that are parallel to each crosses both
lines at the same angle
4G1.6.3 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


4G1.7.1 Know
that the sum of the angles of any triangle is 180°
4G1.7.2 Know
that equilateral triangles have three equal sides
4G1.7.3 Know
that each of the angles of an equilateral (equiangular) triangle measures 60°
4G1.7.4 Know
that any triangle with a 90° angle is a right triangle
4G1.7.5 Know
that any triangle with two equal sides is an isosceles triangle
4G1.7.6 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


4G1.8.1 Know the
range of the measure for acute, right, obtuse, and straight angles
4G1.8.2
Demonstrate an ability to estimate the measure of an angle based on that
knowledge

Estimating
where a line of symmetry would fall in a rectangular object

Standard 4G2. Use
transformations and symmetry to analyze mathematical situations

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

Enabling Knowledge and Skills

Examples of Where Adults Use It



Cutting
cake in half
Folding
objects



Creating
a “snowflake” or hanging decoration using folded paper and scissors

Standard
4G3. Specify locations and describe spatial relationships using coordinate
geometry and other representational systems

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

Enabling Knowledge and Skills

Examples of Where Adults Use It


4G3.1.1
Reading a map using horizontal and vertical indices or latitude and longitude
4G3.1.2
Reading a scale

Reading
a map to plan a hiking trip

4G3.2
Measure common threedimensional (3D) shapes (e.g. a room) and represent the
information on an appropriate diagram drawn to scale.

4G3.2.1
Demonstrate an understanding of 3D coordinate graph
4G3.2.2
Locate points in 3D graphs
4G3.2.3
Use proportional reasoning

Creating
plans for building a model

4G3.3
Draw twodimensional (2D) shapes in different orientations on a grid.

4G3.3.1
Use graph paper to draw 2D shapes
4G3.3.2
Be able to change the orientation and copy objects

Drawing
plans for a carpentry project
Creating
a pattern for a sewing project

4G3.4
Use coordinate grid to identify and locate specific points on the x
and y axes.

4G3.4.1
Know that the horizontal axis on a coordinate grid is labeled x
4G3.4.2
Know that the vertical axis on a coordinate grid is labeled y
4G3.4.3
Know that the intersection of the x and y axes is called origin
4G3.4.4
Know that the coordinates of all points on the coordinate grid are given (x,
y).
4G3.4.5
Know that the coordinates of all points on the coordinate axes are counted
from the origin point (0,0).


Standard 4G4. Understand
measurable attributes of objects and the units, systems, and processes of
measurement and apply appropriate techniques, tools and formulas to determine
measurements

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

Enabling Knowledge and Skills

Examples of Where Adults Use It


4G4.1.1
Know common equivalences of measurement units
4G4.1.2
Demonstrate an understanding of proportionality
4G4.1.3
Know how to solve ratio and proportion problems

Estimating
number of pints of blood in the human body given the number of liters

4G4.2
Read, measure, and compare Fahrenheit and Celsius temperatures.

4G4.2.1
Reading scales
4G4.2.2
Making onetoone correspondence between scales
4G4.2.3
Estimating distances between markings on a scale
4G4.2.4
Read and compare negative numbers

Reading a thermometer

4G4.3
Estimate and approximate an understanding of interrelatedness of distance,
time, and speed.

4G4.3.1
Investigate how a change in one variable (speed) relates to a change in a
second variable (time, distance)
4G4.3.2
Identify and describe situations with constant or varying rates of change and
compare them (acceleration, slowing, down, stopping)

Estimating
the time a trip will take from point “A” to point “B” traveling at the normal
speed limit

4G4.4
Measure with a ruler to 1/16 inch and metric ruler in cm and mm.

4G4.4.1
Know that a foot equals 12 inches
4G4.4.2
Know the relationship between the fractions of an inch (16ths, 8ths, 4ths,
and halves)
4G4.4.3
Know that the metric numbers on a ruler represent centimeters (cm) and a
onefoot ruler is approximately 33 cm long
4G4.4.4
Know that the 10 divisions of a centimeter are called millimeters (mm)
4G4.4.5
Know that a metric length is most commonly represented by a decimal. For
example 4 cm 3mm would be 4.3 cm

Completing
a project demanding fairly precise measurements

4G4.5
Use the language (prefixes) of metric units to describe environment.

4G4.5.1
Know that meters measure length
4G4.5.2
Know that grams measure mass or weight
4G4.5.3
Know that liters measure volume
4G4.5.4
Know the metric prefixes
milli equal to 1/1,000. centi
equal to 1/100, deci equal to 1/10, deca equal to 10, hecto
equal to 100, and kilo equal to 1,000

Traveling
or communicating with people outside of the United States

4G4.6
Make informal comparisons between grams and ounces, liters and quarts.

4G4.6.1
Know that an ounce is approximately equal to 28 grams and that a paper clip
weighs approximately 1 gram
4G4.6.2
Know that a kilogram is approximately 2.2 pounds
4G4.6.3
Know that a liter is a little larger than a quart (1.1 qts.)

Measuring
medications
Replacing
automotive fluids

4G4.7
Estimate, measure, and compare capacity using simple instruments graduated in
standard units and know when to use appropriate measures.

4G4.7.1
Demonstrate familiarity with measures of cups, quarts, gallons, inches, feet,
yards, ounces, and pounds
4G4.7.2
Demonstrate familiarity with measures of liters, grams, kilograms,
centimeters, meters, and kilometers

Buying
beverages for a large group

4G4.8
Work out simple volumes of cubes, cylinders, and rectangular containers.

4G4.8.1
Using formulas for volume of cubes, cylinders, and rectangular containers be
able to solve for the total

Filling
a sand box or garden with mulch

4G4.9
Find perimeter/area of combination shapes using what you know about
rectangles and triangles.

4G4.9.1
Demonstrate an ability to redefine shapes formed as combinations of
rectangles and triangles and calculate the perimeter and area using these
smaller parts

Estimating
amount of material required to cover a piece of furniture

See “How to use This
Document (Teacher’s Guide) and (Connecting Curriculum, Instruction, and
Assessment),” pages 810.
Strand:
Number Sense
Learners engage in
problem solving within adult contextual situations by communicating, reasoning,
and connecting to the following standards:
Standard 5N1. Represent
and use numbers in a variety of equivalent forms in contextual situations

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

Enabling Knowledge and Skills

Examples of Where Adults Use It

5N1.1 Read,
write, order, and compare positive and negative numbers of any size in a
practical context.

5N1.1.1
Explain that the position of a digit signifies its value
5N1.1.2
Know what each digit in a number represents, including the use of zero as a
place holder
5N1.1.3
Demonstrate an understanding of the meaning of negative numbers in a
practical context (e.g. temperature below zero, loss in trading)

Understanding
and comparing government spending figures on public services
Understanding
and comparing change in the value of stocks

5N1.2
Read, write, order, and compare fractions and mixed numbers.

5N1.2.1
Change fractions to equivalent fractions with a common denominator

Comparing
overtime rates

5N1.3
Read, write, order, and compare decimal numbers of any size.

5N1.3.1
Explain that the position of a digit signifies its value
5N1.3.2
Know that the decimal point separates whole numbers from decimal fractions
5N1.3.3
Describe what each digit represents, including the use of zero as a place
holder

Reading and comparing gas prices
Reading and comparing metric
measurements
Comparing
currency exchange rates

5N1.4
Order and compare percentages and understand percentage of increase and
decrease.

5N1.4.1
Demonstrate an understanding of percentage as the number of parts in every
100
5N1.4.2
Know that 100% is the whole
5N1.4.3
Explain how a 10% pay increase is more than a 5% pay increase, but the actual
increase depends on the number operated on

Understanding
20% off in a sale
Understanding
a price increase of 10%

5N1.5
Identify and use equivalencies between fractions, decimals and percentages.

5N1.5.1
Show that fractions, decimals, and percentages are different ways of
expressing the same thing
5N1.5.2
Know that percentages are fractions out of 100
5N1.5.3
Demonstrate how decimal fractions are expressed in tenths, hundredths,
thousandths

Writing
fractions of an hour as decimals on a time sheet, (e.g. ¾ hour as 0.75)
Recognizing
that a deli order for 1/3 pound will read about 0.33 on a digital scale

5N1.6
Read and write numbers in scientific notation.

5N1.6.1
Understand positive and negative exponent notation with ten as a base

Using
a calculator to compute with small and large numbers

5N2. Understand meanings of operations and how they relate to
one another

At
this level an adult will be expected to:

Enabling
Knowledge and Skills

Examples
of Where Adults Use It


5N2.1.1
Represent fractions using number lines and area models
5N2.1.2
Demonstrate conceptual and procedural understanding of operations with
fractions

Helping
children with homework

5N2.2
Demonstrate an understanding of the effects of each operation with integers.

5N2.2.1 Represent integers using a number line.
5N2.2.2 Use area models to demonstrate
distributive law of multiplication over addition and subtraction
5N2.2.3 Demonstrate procedural understanding of
operations with integers.

Helping
children with homework

5N2.3
Demonstrate an understanding that dividing
by the denominator of a unit fraction produces the same result as multiplying
by the decimal form of the fraction.

5N2.3.1
Demonstrate procedural knowledge of multiplication and division of fractions
and decimals

Finding
a discount

5N2.4
Recognizes equivalent fractions, decimals, and percents and can convert from
each form to the other two.

5N2.4.1
Use number lines and area models to represent fractions and decimals
5N2.4.2
Know equivalences of fractions and decimals
5N2.4.3
Know how to convert between fractions and decimal equivalences

Reading and using manufacturing
specifications

Standard 5N3. Compute fluently and
make reasonable estimates

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

Enabling
Knowledge and Skills

Examples
of Where Adults Use It

5N3.1 Add,
subtract, multiply and divide decimals of any size.

5N3.1.1
Know and use strategies to check answers (e.g. approximate calculations using
whole numbers)
5N3.1.2 Align
numbers for column addition and subtraction
5N3.1.3
Demonstrate the ability to determine the placement of decimal points in
multiplication of decimal numbers
5N3.1.4
Demonstrate the ability to determine the placement of decimal points in
division of decimal numbers

Converting
sums of money between currencies

5N3.2
Calculate ratio and direct proportion.

5N3.2.1
Explain a ratio written in the form 3:2
5N3.2.2
Know how to work out the number of parts in a given ratio, and the value of
one part

Comparing
the price of products of different weights or capacities
Mixing
household or workplace materials

5N3.3
Add, subtract, multiply, and divide using fractions and mixed numbers.

5N3.3.1
Demonstrate an understanding of how to change fractions to equivalent
fractions for the purpose of adding and subtracting
5N3.3.2
Demonstrate an understanding of how to find a fraction quotient through
multiplication

Adding
hours on a time sheet that includes fractions

5N3.4
Add, subtract, multiply, and divide using integers in practical contexts.

5N3.4.1
Understand how number direction affects the four operations

Finding
the average temperature
Figuring
the net result of banking transactions

5N3.5
Compute with percentage to solve problems in context.

5N3.5.1
Demonstrate how to use proportion to figure with percentage

Figuring
the effect on mortgage payments of a change in interest rates

5N3.6 Use a
calculator to calculate efficiently using whole numbers, integers, fractions,
decimals, and percentages.

5N3.6.1
Change the sign of a number
5N3.6.2
Change a fraction to a decimal
5N3.6.3
Change a percentage to a decimal
5N3.6.4
Interpret a rounding error such as 6.9999999 as 7
5N3.6.5
Interpret a calculator display employing scientific notation
5N3.6.6
Demonstrate an understanding of the use of memory and constant functions
5N3.6.7
Know and use strategies to check answers obtained with a calculator

Calculating
the total price on a item offered at 25 % off with 5% sales tax added

5N3.7 Determine
prime numbers up to 100.

5N3.7.1
Know that a prime number is a positive integer greater than 1 that has no
factors other than 1 and itself

Simplifying
mathematical problems by factoring out numbers from each side of an equation

Strand:
Patterns, Functions, and Algebra
Learners engage in
problem solving within adult contextual situations by communicating, reasoning,
and connecting to the following standards:
Standard 5P1. Explore,
identify, analyze, and extend patterns in mathematical and adult contextual
situations

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

Enabling
Knowledge and Skills

Examples
of Where Adults Use It

5P1.1
Extend a pattern and when applicable hypothesize reasons, and analyze how both repeating and growing patterns are
generated.

5P1.1.1
Isolate smallest unit of repetition
5P1.1.2
Use a notation system to record patterns
5P1.1.3
Make a table using pattern values
5P1.1.4
Verbalize a rule for finding values in the table
5P1.1.5
Write a general expression for finding values in the table
5P1.1.6
Decide on the effectiveness of the expression by substituting known values

Accurately
describing patterns of heating bills and explaining the patterns
Creating
a compound interest table

5P1.2
Demonstrate an understanding of graphical, tabular,
or symbolic representations for a given pattern and/or relationship.

5P1.2.1
Make a table using pattern values
5P1.2.2
Verbalize a rule for finding values in the table
5P1.2.3
Write a general expression for finding values in the table
5P1.2.4
Decide on the effectiveness of the expression by substituting known values

Reading and explaining temperature
conversion tables


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

Enabling
Knowledge and Skills

Examples
of Where Adults Use It

5P2.1
Create own equations, rules or sketch graphs from word problems or observed
situations.

5P2.1.1
Make a table using pattern values
5P2.1.2
Verbalize a rule for finding values in the table
5P2.1.3
Write a general expression for finding values in the table
5P2.1.4
Decide on the effectiveness of the expression by substituting known values

Working
out the standard elements of a household budget

5P2.2
Convert between different representations, such as tables, graphs, verbal
descriptions, and equations.

5P2.2.1
Recognize that a variety of problem situations may be modeled by the same
function or type of function

Presenting
results of data exploration

5P2.3
Develop algebraic expressions, rules, formulae, or sketch graphs to
generalize straightforward number patterns or observable relationships
between variables.

5P2.3.1
Demonstrate an understanding of the parts of a graph

Translating
graphic depictions of data into oral or written descriptions to explain
relationships

5P2.4
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.

5P2.4.1 Know graphing techniques
5P2.4.2 Understand use of a graphing calculator
or spreadsheet

Making
visual aids for depicting change patterns in business or industry

5P2.5
Identify general shapes and major characteristics of linear and simple
nonlinear graphs and interpret their real world meanings.

5P2.5.1
Recognize and use direct and indirect variation

Interpreting
graphic presentations of data to analyze events and make predictions

Standard 5P3. Recognize
and use algebraic symbols to model mathematical and contextual situations

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

Enabling
Knowledge and Skills

Examples
of Where Adults Use It

5P3.1 Find the
value of an unknown in equations that require multistep solutions e.g.:
2x
+ 4 = 6x 8
0.5y^{2}
 10 = 40.

5P3.1.1
Recognize that addition and subtraction are inverse operations
5P3.1.2
Recognize that multiplication and division are inverse operations
5P3.1.3
Recognize that using the inverse operation can solve equations

Preparing
for further study
Helping
children with homework

5P3.2 Evaluate formulas.

5P3.2.1
Know that a variable is replaced by its number value within parentheses when
a formula is evaluated
5P3.2.2
Demonstrate an understanding that when there is no operator between a number
and a bracket or parentheses that multiplication is implied
5P3.2.3
Know order of operations

Informally
using d = rt to make estimates regarding speed or time of departure
Using
a calculator

5P3.3
Solve linear and quadratic equations.

5P3.3.1
Know the quadratic formula
5P3.3.2
Know how to evaluate formulas

Helping
children with homework
Preparing
for further study

Standard 5P4. Analyze change in various contexts

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

Enabling
Knowledge and Skills

Examples
of Where Adults Use It

5P4.1
Approximate and interpret rates of change from graphical and numerical data.
Assessed by
5G4.3

5P4.1.1
Understand that slope represents rate of change
5P4.1.2
Know how to find the slope from a line graph or table of data

Looking
for trends (e.g. in the price of items, in revenue for a business)

Strand:
Statistics and Probability
Learners engage in
problem solving within adult contextual situations by communicating, reasoning,
and connecting to the following standards:
Standard 5S1.
Collect, organize and represent data

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

Enabling
Knowledge and Skills

Examples
of Where Adults Use It


5S1.1.1 Know that answers can be found by observing and asking
relevant questions and counting responses

Working on a playground committee to select equipment

5S1.2 Collect
and organize responses to questions.
Assessed
by 5S1.1

5S1.2.1 Demonstrate an understanding of the concept of
categories such as shape, size, country, ethnicity, income level or yes or no
responses

Conducting research for travel or relocation purposes

5S1.3 Choose an appropriate representation to display responses
to all types of data.

5S1.3.1 Demonstrate
an understanding that categorical data is usually displayed on bar or circle
graphs
5S1.3.2 Demonstrate
an understanding that numerical data and change over time is usually displayed
on a line graph
5S1.3.3 Know
how to choose a suitable scale to fit the data set
5S1.3.4 Calculate
percents and find percents and/or fractions of 360 degrees
5S1.3.5 Use a
protractor
5S1.3.6 Demonstrate
an understanding that a table can be more accurate than a graph when
recording precise numerical datum
5S1.3.7 Explain
the importance of labeling tables, graphs, and diagrams

Representing
findings from data gathering in a manufacturing or business setting

5S1.4 Collect
comparative data on a single given question such as responses grouped by age
group vs. responses grouped by gender.

5S1.4.1 Know
that responses grouped by different criteria must be recorded in separate
data sets

Gathering
data in the workplace and sorting it by criteria

5S1.5 Display
comparative data on a double bar or line graph.

5S1.5.1 Explain
why separate data sets must be identified by different colors or line
patterns
5S1.5.2 Demonstrate
an understanding that a key to identify each data set must be provided

Comparing
gathered workrelated data by preparation of appropriate bar or line graphs

Standard 5S2. Read and interpret data
representations

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

Enabling
Knowledge and Skills

Examples
of Where Adults Use It


5S2.1.1
Explain how a graph is a visual representation
5S2.1.2
Describe how a table arranges information in rows and columns

Reading newspapers and magazines

5S2.2
Know where graphs and tables are likely to be found.
Assessed
by 2S.2.2

5S2.2.1
Recognize that graphs and tables can be found in newspapers, magazines,
research journals, and promotional materials
5S2.2.2
Recognize that a table is an organizing tool used in manuals, tax forms,
financial statements etc.

Reading advertisements
Looking
up taxes payments
Finding
current interest rates
Reading
graphic materials in the workplace

5S2.3
Infer meaning from gaps, clusters and comparisons
of data.

5S2.3.1
Know ways to compare numbers.
5S2.3.2
Know how to connect the shape and comparisons of
data with text or background knowledge to infer causes for such phenomena

Reading exam questions
Reading corporate or government reports

5S2.4
Give a verbal description of bar, line, and circle graphs and tables.

5S2.4.1
Know that a bar graph uses bars of various heights to display amount
5S2.4.2
Know that line graphs use lines to connect data points
5S2.4.3
Know that a circle or pie graph represents the whole or 100%
5S2.4.4
Know that a table can display the same datum as a graph but in rows and
columns

Helping
with homework
Training
coworkers

5S2.5
Make numerical comparisons about relative values on graphs and tables.

5S2.5.1
Compare and contrast one set of numbers against another

Comparing
prices of vacations represented in a brochure

Standard 5S3.
Describe data using numerical descriptions, statistics and trend terminology

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

Enabling
Knowledge and Skills

Examples
of Where Adults Use It

5S3.1 Identify the minimum, maximum, spread, shape, and range
of data, mean, median, and mode to understand trends and statements.

5S3.1.1 Explain the terms minimum, maximum, and
spread
5S3.1.2 Demonstrate
an understanding that range is the difference
between the smallest and largest values in the data set
5S3.1.3 Recognize gaps, holes, and clusters in the data set to
determine where data is missing and where it is heavily represented

Reading temperature charts
Discussing with a financial planner the relative value of
different retirement investment plans offered at work

5S3.2 Identify
the effect of spread on mean and median.
Assessed
by 5S4.5

5S3.2.1 Know
the minimum or maximum value can greatly affect the mean but will not affect
the median

Determining a grade point average

Standard 5S4. Make and evaluate arguments or
statements by applying knowledge of data analysis, bias factors, and graph
distortions

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

Enabling
Knowledge and Skills

Examples
of Where Adults Use It


5S4.1.1
Distinguish between graphs by understanding the stories each tells

Working
with a group to support or oppose a change in the neighborhood

5S4.2
Support arguments with data and data representations and use number
statements to demonstrate the power of an argument.

5S4.2.1
Demonstrate the ability to collect data to support a conjecture, hypothesis
or belief
5S4.2.2
Represent collected data in a line plot, table, line or bar graph with an
accurate scale, and circle graph
5S4.2.3
Recognize that the greater the number of data supporting an argument, the
more powerful the argument
5S4.2.4
Use subtraction to compare
5S4.2.5
Use division to demonstrate how many more times data support an argument

Initiating
political actions to institute changes in the community
Creating
a survey or report to support a plea for changes in one’s community

5S4.3
Convert tables to graphs to support an argument, and convert graphs to
narratives and narratives to graphs to forward a position.

5S4.3.1
Show how to organize large sets of data in a table
5S4.3.2
Use a table as the foundation for graphic displays
5S4.3.3
Use appropriate language to describe graphic data in a way to show how the
data supports an argument
5S4.3.4
Know how to “read” the stories in graphs in order to state them as support an
argument

Preparing or reading academic research
Preparing reports favoring a political or social
position, or to negotiate salaries

5S4.4
Make statements about data trends to support or reject arguments/statements
forwarded by others.

5S4.4.1
Explain lines going up mean increase; lines tilting down mean decrease and
that they can vary over time
5S4.4.2
Explain that a flat line means no change
5S4.4.3
Use specific vocabulary to describe trends (e.g. “sharp” increase,
“plummeted,” etc.

Checking reports on stock market or discussing
smoking trends with children or peers
Understanding changes reported in one’s workplace

5S4.5
Demonstrate an understanding of the impact
of spread on mean and median, and which statistic, mean, median,
or mode, is most appropriate for data.

5S4.5.1
Finding the mean, median, and mode
5S4.5.2
Know that mean and median are compressions of data
5S4.5.3
Describe experiences with changes and spread and resulting changes or lack of
changes in mean and median
5S4.5.4
Explain why means and medians don’t always represent what is typical, and so
aren’t always best used in creating an argument
5S4.5.5
Describe some inappropriate uses of mean, median or mode
5S4.5.6
Use appropriate statistic to support an argument

Reading advertisements
or demographic reports in order to make decisions
Negotiating salary increases
Reading real estate sales reports; health and
fitness data

5S4.6
Recognize that bar widths, scale, and wedge size distortions can provide
misleading information.

5S4.6.1
Explain how visual messages are given by bar widths (e.g. thin relays message
of “less” and wide relays message of “more”)
5S4.6.2
Explain why visual messages can contradict or enhance evidence
5S4.6.3
Describe how scales are represented in regular increments
5S4.6.4
Explain why size of the increments used in scales can make changes seem more
or less significant
5S4.6.5
Explain why wedge size in circle graphs should correspond roughly to fraction
of data represented

Creating promotional materials for social change
Reading advertisements
Reading environmental and corporate reports on
pollution
Checking out population preference or conditions’
data to determine if it’s accurate

5S4.7
Explain where and how authors of data reports can manipulate data to benefit
themselves or malign others in mixed materials.

5S4.7.1
Identify who produced a data report and how their interests might affect the
report, resulting in a conflict of interest

Reading advertisements and product studies to make
consumer choices

5S4.8
Understand that different categorizations of data reveal different stories.

5S4.8.1
Know how to categorize data in a variety of ways,
including aggregate or disaggregate data
5S4.8.2
Know how to make ‘story’ statements about what is
seen in data and how these change as categories change
5S4.8.3
Know how to use different categorizations
appropriately to support an argument

Following demographic data reports or consumer
goods’ data with a critical eye

5S4.9
Demonstrate an understanding of the impacts of data compression, and when
compression helps or hinders an argument.
Not
assessed, but important to teach at this level

5S4.9.1
Explain why data representations do not necessarily show each datum;
therefore, individual variations are not visible
5S4.9.2
Explain why personal or regional (subset) variations are sometimes more
relevant to arguments/statements than aggregate data
5S4.9.3
Discern the level at which an argument is best stated

Reading
consumer preferences’ or selections’ data
Preparing
documents to advocate for school change
Gathering
data for statistical process control tasks

5S4.10
Compare and contrast provided graphs to evaluate contradictory or unsupported
statements, or to strengthen an argument.
Assessed
by 4S4.7

5S4.10.1
Explain how statements or arguments based on data are sometimes generated by
comparing or contrasting graphs
5S4.10.2
Explain how statements or arguments based on one graph are sometimes
contradicted in another
5S4.10.3
Explain how statements or arguments based on multiple graphs can be used to
support or enhance each other and one’s position

Comparing
accidentrelated data to make a point concerning safety
Comparing
workrelated progress from month to month

Standard 5S5. Know and
apply basic probability concepts

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

Enabling
Knowledge and Skills

Examples
of Where Adults Use It

5S5.1
Find the probability of both independent and
dependent events.

5S5.1.1
Explain that the probability is independent when the outcome of one event
does not influence the outcome of another
5S5.1.2
Explain that the probability is dependent when the outcome of one event
directly influences the outcome of subsequent events

Interpreting the
odds of contracting breast cancer or being in an airplane accident.

5S5.2
Find the number of possible combinations given two or more sets of data.

5S5.2.1
Know that the total number of possible combinations of items in lists can be
found by multiplying the number of items in each list times each other
5S5.2.2
Be able to find all of the possible combinations of a set of letters, digits,
or items

Determining the
number of coordinated outfits possible from a set of slacks and tops.
Determining the
possible combinations available on a menu.
Determining the
total number of combinations for a combination lock

Strand: Geometry & Measurement
Learners engage in
problem solving within adult contextual situations by communicating, reasoning,
and connecting to the following standards:
Standard 5G1. Use and apply geometric properties and
relationships to describe the physical world and identify and analyze the
characteristics of geometric figures

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

Enabling
Knowledge and Skills

Examples
of Where Adults Use It


5G1.1.1
Demonstrate an understanding of simple ratio as the number of parts (e.g. three
parts to one part)
5G1.1.2
Demonstrate an understanding of direct proportion as the same rate of
increase or decrease (e.g. double, half)


5G1.2
Use the language (prefixes) of metric units to describe environment (centi,
milli, kilo, micro, mega).
Assessed
by 4G4.5

5G1.2.1
Know definitions of measures of mass (grams), capacity (liters), and length
(meter)
5G1.2.2
Know meaning of prefixes
5G1.2.3
Develop informal benchmarks for metric units (e.g. length of thumbnail = 1
cm; 1 meter is approximately 3 feet)

Representing
measurement outcomes in the workplace

5G1.3
Use spatial visualization to describe and analyze geometric figures.
Assessed
4G1.3

5G1.3.1
Know meaning of horizontal and vertical
5G1.3.2
Develop informal benchmarks for angles
5G1.3.3
Know vocabulary for 2D shapes and orientation

Identifying
and describing objects to be measured

5G1.4
Develop and use formulae that describe relationships between variables in
familiar contexts (area and volume).

5G1.4.1
Demonstrate an understanding of area and volume of 2D and 3D figures
5G1.4.2
Use patterns to generalize

Using
a formula to determine material required to build or cover an object

5G1.5
Use properties of triangles to solve problems.

5G1.5.1
Demonstrate understanding of congruent and similar triangles
5G1.5.2
Explain the sum of the angles in a triangle in a plane equals 180 degrees
5G1.5.3
Recognize situations where properties of right triangles apply
5G1.5.4
Apply the Pythagorean theorem to right triangles

Building
and measuring objects in the manufacturing trades

5G1.6
Use properties of right triangles and Pythagorean relationship to solve
problems.

5G1.6.1
Know properties of right triangles, including angle measurement
5G1.6.2
Demonstrate an understanding of similarity in triangles
5G1.6.3
Apply proportional reasoning to find corresponding sides

Determining
the line of symmetry of a right triangle

5G1.7
Directly measure different angles with a protractor.

5G1.7.1
Know how to align a protractor with the rays of an angle

Determining
a specific angle of slope for installing housing gutters or drains


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

Enabling
Knowledge and Skills

Examples
of Where Adults Use It


5G2.1.1
Demonstrate an understanding of the coordinate graph system
5G2.1.2
Know geometric shapes

Reading scientific diagrams
Using
CAD/CAM software to design a product


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

Enabling
Knowledge and Skills

Examples
of Where Adults Use It

5G3.1 Find, use, and interpret the slope of a
line, the yintercept of a line, and the intersection of two lines.

5G3.1.1
Demonstrate an understanding of the coordinate graph system
5G3.1.2
Know how to create a table of ordered pairs which satisfy an equation
5G3.1.3
Generate a graph from a formula or equation
5G3.1.4
Generate and equation or formula from a graph
5G3.1.5
Identify coefficients with graph steepness

Using
linear modeling to determine optimal pricing

Standard 5G4. Understand
measurable attributes of objects and the units, systems, and processes of
measurement and apply appropriate techniques, tools and formulas to determine
measurements

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

Enabling
Knowledge and Skills

Examples
of Where Adults Use It


5G4.1.1
Explain the meaning of the terms perimeter, area, volume, angle, capacity,
weight and mass

Estimating
materials needs for a given job

5G4.2
Predict the impact of changes in linear dimensions on the perimeter, area,
and volume of figures.

5G4.2.1
Know the formulas for perimeter, area, and volume.
5G4.2.2
Know how to list data in a chart or table
5G4.2.3
Know how to graph data from a table
5G4.2.4
Know how to describe and analyze patterns of change in a table or graph

Deciding
whether and how suggested increases or decreases in measurement will change a
manufacturing or building project

5G4.3
Calculate and interpret rates of change from graphical and numerical data.

5G4.3.1
Demonstrate an ability to extrapolate numerical data from graphic
presentations
5G4.3.2
Demonstrate an ability to accurately calculate percentages

Determine
the rate of increase/decrease of gasoline prices based on newspaper reports

5G4.4
Solve problems of area involving inscribed figures (e.g. a circle inscribed
in square).

5G4.4.1
Demonstrate a familiarity with the formulas for area of polygons and circles.
5G4.4.2
Demonstrate an understanding of when areas in an inscribed figure are
excluded requiring subtraction

Designing
a pattern for a flower garden
Determining
an arrangement for furniture of various shapes in the home

5G4.5
Use simplified formula to convert between Fahrenheit and Celsius
temperatures.

5G4.5.1
Demonstrate an understanding of the constants and variables provided in
conversion formulas

Determining
the temperature reported in an area using either the metric or ASE system

See “How to Use This
Document (Teacher’s Guide) and (Connecting Curriculum, Instruction and
Assessment),” pages 810. At this time, the Massachusetts ABE Test for Math
does not assess students’ knowledge at this level.
Strand:
Number Sense
Learners engage in
problem solving within adult contextual situations by communicating, reasoning,
and connecting to the following standards:
Standard 6N1. Represent
and use numbers in a variety of equivalent forms in contextual situations

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

Enabling Knowledge and Skills

Examples of Where Adults Use It

6N1.1 Read,
write, order and compare positive and negative numbers of any size.

6N1.1.1 Demonstrate an understanding that the position of a
digit signifies its value
6N1.1.2 Know
what each digit in a number represents, including the use of zero as a place
holder
6N1.1.3 Demonstrate an understanding that the meaning of negative
numbers in a practical context (e.g. temperature below zero, loss in
trading)

Understanding
and comparing government spending figures on public services
Understanding
and comparing change in the value of stocks

6N1.2 Read,
write, order and compare fractions and mixed numbers.

6N1.2.1 Change
fractions to equivalent fractions with a common denominator

Comparing
overtime rates

6N1.3 Read,
write, order and compare decimal numbers.

6N1.3.1 Demonstrate an understanding that the position of a
digit signifies its value
6N1.3.2 Know
that the decimal point separates whole numbers from decimal fractions
6N1.3.3 Know
what each digit represents, including the use of zero as a place holder

Reading and comparing gas prices
Reading and comparing metric
measurements
Comparing
currency exchange rates

6N1.4 Order
and compare percentages and understand percentage increase and decrease.

6N1.4.1 Explain
percentage as the number of parts in every 100
6N1.4.2 Describe
how 100% is the whole
6N1.4.3 Demonstrate an understanding that a 10% pay increase is
more than a 5% pay increase, but the actual increase depends on the number
operated on

Understanding
20% off in a sale
Understanding
a price increase of 10%

6N1.5
Identify and use equivalencies
between fractions, decimals and percentages.

6N1.5.1 Explain
how fractions, decimals, and percentages are different ways of expressing the
same thing
6N1.5.2 Know
that percentages are fractions out of 100
6N1.5.3 Express
decimal fractions in tenths, hundredths, thousandths

Writing
fractions of an hour as decimals on a time sheet (e.g. ¾ hour as 0.75)
Recognizing
that a deli order for 1/3 pound will read about 0.33 on a digital scale

6N1.6
Read and write numbers in
exponential notation using integer exponents.

6N1.6.1 Demonstrate an understanding that a positive exponent
indicates the base is to be multiplied by itself that number of times
6N1.6.2 Demonstrate an understanding that a negative exponent
indicates the base is to be divided by itself that number of times

Using
a calculator to compute with small and large numbers
Using
exponential notation for metric conversion

Standard 6N2. Understand meanings of operations and how they
relate to one another

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

Enabling
Knowledge and Skills

Examples
of Where Adults Use It


6N2.1.1 Demonstrate conceptual and procedural
understanding of operations with decimals, fractions, and integers.
6N2.1.2 Know meaning of commutativity and
associativity and distributive properties with whole numbers


6N2.2 Demonstrate an understanding that raising a number
to a negative integer is repeated division.

6N2.2.1 Demonstrate an understanding of exponents
6N2.2.2 Use rules of exponents for multiplication
and division


Standard 6N3. Compute fluently and make reasonable estimates

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

Enabling
Knowledge and Skills

Examples
of Where Adults Use It

6N3.1 Add,
subtract, multiply and divide decimals up to three places.

6N3.1.1 Use
strategies to check answers (e.g. approximate calculations using whole
numbers)
6N3.1.2
Know how to align numbers for column addition and subtraction
6N3.1.3
Explain the placement of the decimal point in multiplying decimals
6N3.1.4
Explain the placement of the decimal point when dividing decimals

Converting
sums of money between currencies

6N3.2
Calculate ratio and direct proportion.

6N3.2.1
Demonstrate an understanding of a ratio
written in the form 3:2
6N3.2.2
Work out the number of parts in a given ratio, and the value of one part

Comparing
the price of products of different weights or capacities

6N3.3 Add,
subtract, multiply and divide using fractions.

6N3.3.1
Change fractions to equivalent fractions for the purpose of adding and
subtracting
6N3.3.2
Find a fraction quotient through multiplication

Adding
hours on a time sheet that includes fractions

6N3.4 Add,
subtract, multiply and divide using integers.

6N3.4.1
Explain how number direction affects the four operations

Finding
the average temperature
Figuring
the net result of banking transactions
Determining
profit after totaling costs

6N3.5
Compute with percentage.

6N3.5.1
Demonstrate an understanding of how to use
proportion to figure with percentage

Figuring
the effect on mortgage payments of a change in interest rates

6N3.6
Use a calculator to calculate efficiently using whole numbers, integers,
fractions, decimals, percentages.

6N3.6.1
Change the sign of a number
6N3.6.2
Change a fraction to a decimal
6N3.6.3
Change a percentage to a decimal
6N3.6.4
Interpret a calculator display employing scientific notation
6N3.6.5
Find a trigonometric function of a number (e.g. cos 90°)
6N3.6.6
Interpret a rounding error such as 6.9999999 as 7
6N3.6.7
Demonstrate an understanding of the use of
memory and constant functions
6N3.6.8
Use strategies to check answers obtained with a calculator

Any
calculations at this level

Strand: Patterns, Functions, and Algebra
Learners engage in
problem solving within adult contextual situations by communicating, reasoning,
and connecting to the following standards:
Standard 6P1. Explore,
identify, analyze, and extend patterns in mathematical and adult contextual
situations

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

Enabling
Knowledge and Skills

Examples
of Where Adults Use It

6P1.1 Describe, complete, extend, analyze, generalize, and
create a wide variety of patterns, including iterative/recursive (e.g.
Fibonnacci Numbers), linear, quadratic and exponential functions.

6P1.1.1 Create and analyze
different representations, such as tables, graphs, verbal descriptions, and
equations
6P1.1.2
Create algebraic expressions, rules, formulae, or sketch graphs to generalize
number patterns or observable relationships between variables

Creating
mathematical models

6P1.2
Explain the difference between linear and
exponential growth.

6P1.2.1
Identify general shapes and major characteristics of linear and simple
nonlinear graphs and interpret their real world meanings
6P1.2.2
Draw graphs using techniques such as plotting points; sketching from known
main features of algebraic function; or using technology like a graphing
calculator or computer package

Reading
scientific or economic charts

Standard 6P2. Articulate
and represent number and data relationships using words, tables, graphs,
rules, and equations

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

Enabling Knowledge and Skills

Examples of Where Adults Use It


6P2.1.1
Explain how a variety of problem situations may be modeled by the same
function or type of function

Connecting
visual information from a variety of sources to reach a decision about a
process, product or service

6P2.2 Develop
algebraic expressions, rules, formulae, or sketch graphs to generalize
straightforward number patterns or observable relationships between
variables.

6P2.2.1
Create own equations, rules or sketch graphs from word problems or observed
situations
6P2.2.2
Recognize and analyze patterns in number relationships and in charts and
tables

Describing
growth or change in workplace output

6P2.3
Draw graphs using techniques such as plotting points; sketching from known
main features of algebraic function; or using technology like a graphing
calculator or computer package.

6P2.3.1 Create a table of values for relations
and functions
6P2.3.2 Demonstrate an understanding of slope
6P2.3.3 Can use slopeintercept form of equations
6P2.3.4 Know spreadsheet conventions


6P2.4
Identify general shapes and major characteristics of linear and simple
nonlinear graphs and interpret their real world meanings.

6P2.4.1
Recognize and use direct and indirect variation

Applying
graphic information to the decision making process

Standard 6P3. Recognize and use algebraic symbols to model
mathematical and contextual situations

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

Enabling
Knowledge and Skills

Examples
of Where Adults Use It

6P3.1 Recognize that a variety of problem
situations may be modeled by the same function or type of function.

6P3.1.1
Describe experience using common functions

Preparing
for further study

6P3.2
Convert between different representations, such as tables, graphs, verbal
descriptions, and equations.

6P3.2.1
Graph data in table form
6P3.2.2
Form a table from data in graph form
6P3.2.3
Find the equation of a line or how to figure slope and intercept from table
data

Presenting
findings of data exploration

6P3.3
Evaluate formulas and functions.

6P3.3.1
Explain that a variable is replaced by its number value within parentheses
when a formula or function is evaluated
6P3.3.2
Demonstrate an understanding that when there is no operator between a number
and a bracket or parentheses that multiplication is implied
6P3.3.3
Demonstrate knowledge of order of operations

Informally
using d = rt to make estimates regarding speed or time of departure
Using
a scientific calculator

6P3.4
Solve equations (e.g. linear, quadratic, exponential, trigonometric) and
systems of linear equations.

6P3.4.1
Demonstrate fluency working with algebraic expressions
6P3.4.2
Demonstrate experience with a graphing calculator

Preparing
for further study
Measuring
angles in industrial settings

6P3.5
Recognize and use direct and indirect variation.

6P3.5.1
Describe experience using common functions
6P3.5.2
Describe observations of similarities between graphs of functions of the same
type


Standard 6P4. Analyze
change in various contexts

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

Enabling
Knowledge and Skills

Examples
of Where Adults Use It

6P4.1
Approximate and interpret rates of change from graphical and numerical data.

6P4.1.1
Demonstrate an understanding that slope represents rate of change
6P4.1.2
Find the slope from a line graph or table of data

Looking
for trends (e.g. in the price of items, in revenue for a business, in value
of wages)

Strand:
Statistics and Probability
Learners engage in
problem solving within adult contextual situations by communicating, reasoning,
and connecting to the following standards:
Standard 6S1. Collect,
organize and represent data

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

Enabling Knowledge and Skills

Examples
of Where Adults Use It


6S1.1.1
Demonstrate that answers can be found by observing and asking relevant
questions and counting responses

Working on a playground committee to select equipment

6S1.2
Collect and organize responses to posed questions.

6S1.2.1
Demonstrate an understanding that the concept of categories such as shape,
size, color or yes or no responses

Gathering
data for a report

6S1.3
Choose appropriate representation to display
responses to all types of data.

6S1.3.1
Demonstrate an understanding that categorical data
is usually displayed on bar or circle graphs
6S1.3.2
Demonstrate an understanding that numerical data
and change over time is usually displayed on a line graph
6S1.3.3
Know how to calculate percents and find percents and/or fractions of 360
degrees
6S1.3.4
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

6S1.4
Collect comparative data on a single given question such as responses grouped
by age group vs. responses grouped by gender.

6S1.4.1 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

6S1.5
Display comparative data on a double bar or line graph.

6S1.5.1 Explain
why separate data sets must be identified by different colors or line
patterns
6S1.5.2 Demonstrate
an understanding that a key to identify each data set must be provided

Showing
results of data collection

6S16
When computers and software are available, know how to use a spreadsheet.

6S1.6.1
Understand that the rows and columns on a spreadsheet are user defined
6S1.6.2
Understand that cells on the spreadsheet are the intersection of user defined
rows and columns
6S1.6.3
Demonstrate an ability to enter formulas for operations on cell data

Entering
information on a spreadsheet in the workplace
Creating
a spreadsheet for personal finance records

Standard 6S2. Read and interpret data representations

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

Enabling
Knowledge and Skills

Examples
of Where Adults Use It


6S2.1.1
Demonstrate an understanding that a graph is a visual representation
6S2.1.2
Understand that a table arranges information in rows and columns

Reading graphics in newspapers and magazines

6S2.2
Know where graphs and tables are likely to be found.

6S2.2.1
Explain that graphs and tables can be found in newspapers, magazines,
research journals, and promotional materials
6S2.2.2
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

6S2.3
Give a verbal description of bar, line, and circle
graphs, and tables.

6S2.3.1
Demonstrate an understanding that a bar graph uses
bars of various heights to display amount
6S2.3.2
Demonstrate an understanding that line graphs use
lines to connect data points
6S2.3.3
Demonstrate an understanding that a circle or pie
graph represents the whole or 100%

Participating in class or work discussions about data
representations

6S2.4
Make numerical comparisons about relative values on
graphs and tables.

6S2.4.1
Demonstrate and ability to use number sense skills

Following changes on sales charts for business trends

6S2.5
Infer meaning from gaps, clusters, and comparisons
of data.

6S2.5.1
Demonstrate ways to compare numbers
6S2.5.2
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

6S2.6
Infer consequences related to data outcomes.

6S2.6.1
Project possible consequences from examining data
and text and connecting these to similar situations

Reading exam questions
Reading corporate or government reports

Standard 6S3. Describe
data using numerical descriptions, statistics and trend terminology

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

Enabling
Knowledge and Skills

Examples
of Where Adults Use It

6S3.1 Identify
the minimum, maximum, spread, shape, and range of data.

6S3.1.1
Explain terms minimum, maximum, and spread
6S3.1.2
Demonstrate an understanding that range is the difference between the
smallest and largest values in the data set
6S3.1.3
Recognize gaps, holes, and clusters in the data set
to determine where data is missing and where it is heavily represented

Reading temperature charts and in discussions with a financial
planner about retirement investment plans offered at work.

6S3.2
Use 'most of' statements to describe data.

6S3.2.1
Recognize that values in the data set can be repeated and some values may be
repeated more frequently than others


6S3.3
Find the mean.

6S3.3.1
Know that mean is “average” and that average in this case is about
equal distribution
6S3.3.2
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

6S3.4
Find the median.

6S3.4.1
Know that median is the middle value
6S3.4.2
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.”

6S3.5
Identify the effect of spread on mean and median.

6S3.5.1
Recognize the minimum or maximum value can greatly
affect the mean but will not affect the median
6S3.5.2
Explain how the spread of data can affect the
“closeness” of the mean and median values

Discussing with real estate brokers the “true” value of homes in
a neighborhood

Standard 6S4.
Make and evaluate arguments or statements by applying knowledge of data
analysis, bias factors and graph distortions

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

Enabling Knowledge and Skills

Examples of Where Adults Use It

6S4.1 Make statements about data trends to support or reject
arguments/statements forwarded by others.

6S4.1.1
Demonstrate an understanding that lines going up
mean increase; lines tilting down mean decrease and that they can vary over
time
6S4.1.2
Explain that a flat line means no change
6S4.1.3
Define vocabulary to describe trends (e.g. “sharp”
increase, “plummeted,” etc.)

Analyzing reports on
stock market
Describing movement of a
product, process or service

6S4.2
Know when percents given and figures used don’t
match
Make accurate statements using percents.

6S4.2.1
Describe ways for estimating and calculating
percents of numbers
6S4.2.2
Explain what it means to have an increase of more
than 100 percent
6S4.2.3
Demonstrate an understanding of the significance of
large or small percent increases or decreases in various contexts

Analyzing social science
reports

6S4.3
Recognize that mean, median, and mode numbers are
considered “averages,” and that averages represent numbers typical of the
data that can support an argument.

6S4.3.1
Explain that what are termed “averages” are numbers
supposedly “typical” of data
6S4.3.2
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

6S4.4
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.

6S4.4.1
Use techniques for finding mean and median
6S4.4.2
Describe with spread changes and resulting changes or
lack of changes in mean and median
6S4.4.3
Explain why means and medians don’t always
represent what is typical
6S4.4.4
Describe why the choice of statistic is
inappropriate or appropriate

Reading advertisements
or demographic reports in order to make decisions
Negotiating salary
increases

6S4.5
Determine which statistic, mean or median, is appropriate for data.

6S4.5.1
Describe experience with inappropriate uses of mean and median
6S4.5.2
Use appropriate statistic to support an argument

Consuming health and fitness data to determine a
plan of action

6S4.6
Recognize that bar widths can provide misleading information, and state how
those distortions are used to affect the arguments/statements.

6S4.6.1
Demonstrate an understanding that visual messages are given by bar widths
(e.g. thin relays message of “less” and wide relays message of “more”)
6S4.6.2
Demonstrate an understanding that visual messages can contradict or enhance
evidence
6S4.6.3
Describe scale distortions and relate impacts on arguments/statements

Reading advertisements to make consumer choices

6S4.7
Recognize scale distortions in research materials, and state how those
distortions are used to affect the arguments/statements.

6S4.7.1
Explain that scales are represented in regular increments
6S4.7.2
Demonstrate an understanding that the size of the increments used in scales
can make changes seem more or less significant
6S4.7.3
Describe scale distortions and relate impacts on arguments/statements

Consuming or preparing environmental and/or
corporate reports on pollution

6S4.8
Recognize wedge size distortions, and state how those distortions are used to
affect the arguments/statements.

6S4.8.1
Wedge size in circle graphs should correspond roughly to fraction of data represented
6S4.8.2
Know how to describe wedge distortions and relate impacts on
arguments/statements

Working with population preference or condition
data; understanding advertisements

6S4.9
Note where authors of data reports can manipulate data to benefit themselves
or malign others in mixed materials and state those bias factors.

6S4.9.1
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

6S4.10
Demonstrate an understanding that different categorizations of data reveal
different stories and state how and why such effects relate to
arguments/statements.

6S4.10.1
Categorize data in a variety of ways (e.g. aggregate or disaggregate data)
6S4.10.2
Make “story” statements about what is seen in data and how that changes as
categories change
6S4.10.3
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

6S4.11
Demonstrate an understanding of the impacts of data compression and state how
and why such effects relate to arguments/statements.

6S4.11.1
Explain why data representations do not necessarily show every datum;
therefore, individual variations are not visible
6S4.11.2
Explain how personal or regional (subset) variations are sometimes more relevant
to arguments/statements than aggregate data
6S4.11.3
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

6S4.12
Compare and contrast graphs to evaluate for contradictory or unsupported
statements.

6S4.12.1
Explain that statements or arguments based on data are sometimes generated by
comparing or contrasting graphs
6S4.12.2
Explain that statements or arguments based on one graph are sometimes
contradicted in another
6S4.12.3
Where complementary data might be found

Preparing
academic research reports
Analyzing
poll data

6S4.13
Demonstrate an understanding of simple sample biases.

6S4.13.1
Explain how sample size reflects on reliability of data.
6S4.13.2
Explain how sample composition reflects on reliability of data

Preparing
academic research reports
Analyzing
corporate reports

Standard 6S5. Know and apply basic probability
concepts

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

Enabling
Knowledge and Skills

Examples
of Where Adults Use It


6S5.1.1
Demonstrate an understanding that while some events are impossible, some are
certain to happen, and in other events some are more likely to occur than
others

Deciding to avoid or use certain products

6S5.2
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

6S5.3
State probability as a ratio fraction.

6S5.3.1
Describe how probability is the ratio of the potential successful outcomes to
total possibilities
6S5.3.2
Know that such ratios can be written in fraction form
6S5.3.3
Know that ratio fractions can be simplified

Playing card games
Interpreting the odds at a sporting event
Understanding mortality rates related to certain diseases

6S5.4
State probability as a percent.

6S5.4.1
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

6S5.5
Find the probability of both independent and
dependent events.

6S5.5.1
Demonstrate an understanding that the probability is independent when the
outcome of one event does not influence the outcome of another
6S5.5.2
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.
