Numerate behavior involves:

Managing a situation or solving a problem in a real context

everyday life

work

societal

further learning

by responding

identifying or locating

acting upon

interpreting

communicating about

to information about mathematical ideas

quantity and number

dimension and shape

pattern and relationships

data and chance

change

that is represented in a range of ways

objects and pictures

numbers and symbols

formulae

diagrams and maps

graphs

tables

texts

and requires activation of a range of

enabling knowledge, behaviors, and processes.

mathematical knowledge and understanding

mathematical problem-solving skills

literacy skills

beliefs and attitudes.

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

Standard     Þ

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

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

Enabling Knowledge and Skills

Examples of Where Adults Use It

Benchmark          Þ

Assessment

(See page 10)

Þ

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

Assessed by 3P-3.7

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

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

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

Reading thermometers

Riding an elevator below ground level

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

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

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

Reading and interpreting scales

Ý Enabling skill

 Ý Application

At this level an adult will be expected to:

Enabling Knowledge and Skills

Examples of Where Adults Use It

Skill           Þ

Assessment Þ

(See page 11)

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

Assessed by 3P-3.7

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

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

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

Reading thermometers

Riding an elevator below ground level

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

Habits of Mind

Habit

Learner Question

Curiosity

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

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

Respect for Evidence

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

Do I listen carefully for others’ use of

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

Persistence

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

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

Ownership

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

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

Reflection

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

Do I notice and analyze how and what I learn?

Strands

Standards  

Learners will demonstrate the ability to…

Number Sense

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

         forms in contextual situations

N-2  Understand meanings of operations and how they relate

         to one another

N-3  Compute fluently and make reasonable estimates

Patterns, Functions and Algebra

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

        mathematical and adult contextual situations

P-2  Articulate and represent number and data relationships

        using words, tables, graphs, rules, and equations

P-3  Recognize and use algebraic symbols to model

        mathematical and contextual situations

P-4  Analyze change in various contexts

Statistics and Probability

S-1  Collect, organize, and represent data

S-2  Read and interpret data representations

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

        trend terminology

S-4  Make and evaluate arguments and statements by applying

        knowledge of data analysis, bias factors, graph

       distortions, and context

S-5   Know and apply basic probability concepts

Geometry and Measurement

G-1  Use and apply geometric properties and relationships to

         describe the physical world and identify and analyze the

         characteristics of geometric figures

G-2  Use transformations and symmetry to analyze

         mathematical situations

G-3  Specify locations and describe spatial relationships using

         coordinate geometry and other representational systems

G-4  Understand measurable attributes of objects and the

         units, systems, and processes of measurement and apply

         appropriate techniques, tools, and formulas to determine

         measurements

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Enabling Knowledge and Skills

Examples of Where Adults Use It

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

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

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

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

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

Counting dollar bills to pay for a purchase

Counting items at the grocery express line

Using the remote channel tuner for a TV

Watching a digital timer on a microwave count down the time

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

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

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

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

Recognizing when house numbers go up in odd or even numbers

Finding a room in a hospital or hotel

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

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

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

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

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

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

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

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

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

Counting nickels and dimes

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

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

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

Enabling Knowledge and Skills

Examples of Where Adults Use It

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

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

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

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

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

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

Figuring hours of work or sleep by using fingers to count

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

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

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

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

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

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

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

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

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

Enabling Knowledge and Skills

Examples of Where Adults Use It

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

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

Adding using mental math

1N-3.2 Add numbers with totals to 20.

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

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

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

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

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

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

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

1N-3.4 Double whole numbers to 10.

1N-3.4.1 Know doubles of numbers to 10

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

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

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

1N-3.5.1 Know doubles of numbers to 10

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

Sharing the cost of pizza between two people.

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

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

1N-3.6.2 Recognize the numerals 0 – 9

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

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

Finding the total score for a card game

Finding the total price of 3 items ordered from a menu

Finding the change for a purchase

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

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

Enabling Knowledge and Skills

Examples of Where Adults Use It

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

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

Sorting laundry

Sorting bottles for recycling facility

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

Shelving stock

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

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

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

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

1P-1.2.4 Identify odd and even

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

Counting pennies or 1 dollar bills

Counting nickels or five dollar bills

Counting things 2 at a time

Counting dimes or 10 dollar bills

Counting beats in music

Designing a necklace and describing the assembly rule

Laying tile on a floor

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

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

Enabling Knowledge and Skills

Examples of Where Adults Use It

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

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

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

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

Playing card games

Preparing for further study

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

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

Enabling Knowledge and Skills

Examples of Where Adults Use It

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

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

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

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

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

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

Helping children with homework.

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

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

Helping children with homework.

Test taking when seeking employment

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

2 is less than 10

10 is greater than 8

99 is less than 100

6 + 5 ¹ 10

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

Helping children with homework

Test-taking when seeking employment

Standard 1P-4. Analyze change in various contexts

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

Enabling Knowledge and Skills

Examples of Where Adults Use It

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

1P-4.1.1 Observe physical change over time

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

Discussing weather patterns

Describing seasons, daylight savings time, or tides

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

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

Enabling Knowledge and Skills

Examples of Where Adults Use It

1S-1.1 Gather data to answer posed questions.

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

Planning a neighborhood party

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

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

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

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

Keeping track of who will or will not attend party

Sorting stock by size

Standard 1S-2. Read and interpret data representations

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

Enabling Knowledge and Skills

Examples of Where Adults Use It

1S-2.1 Identify graphs in available resources.

1S-2.1.1 Explain how graph is a visual representation

Reading a graph in an ad or poster

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

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

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

Checking items against a stock list

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

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

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

Reading a nutrition graph in a health poster

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

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

Conversing about information contained in newspapers and magazines

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

1S-2.5.1 Demonstrate how to locate titles

1S-2.5.2 Explain that titles indicate subject matter

Reading a chart or graph in a health pamphlet.

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

Not applicable at this level.

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

Not applicable at this level.

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

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

Enabling Knowledge and Skills

Examples of Where Adults Use It

1S-5.1 Discuss events as likely or unlikely.

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

Deciding whether or not to carry an umbrella

Making the call when flipping a coin

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

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

Enabling Knowledge and Skills

Examples of Where Adults Use It

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

1G-1.1.1 Identify the names of shapes

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

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

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

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

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

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

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

Purchasing window shades or coverings

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

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

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

Enabling Knowledge and Skills

Examples of Where Adults Use It

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

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

1G-2.1.2 Divide a figure in half

Cutting a cake in half

Folding objects

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

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

Enabling Knowledge and Skills

Examples of Where Adults Use It

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

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

1G-3.1.2 Explain the difference between vertical and horizontal

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

Making a simple map with cardinal directions

Locating offices, apartments that are labeled with cardinal directions

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

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

Assembling a piece of furniture from a diagram

Giving oral directions for getting from one place to another

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

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

Enabling Knowledge and Skills

Examples of Where Adults Use It

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

1G-4.1.1 Know coin & bill names and values

Getting out money to pay at the register

Verifying change given at a store

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

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

Completing forms (birth date, etc.)

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

1G-4.3.1 Count to 60 by 5’s and 10’s

Reading a bus schedule that uses AM and PM

1G-4.4 Read analog and digital clocks.

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

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

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

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

Sorting by size to organize a kitchen cabinet

Understanding a child’s growth chart

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

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

Measuring the length and width of photo

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

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

Give one’s height or weight on a medical form

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

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

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

Buying weather stripping

Buying wood for a picture frame or baseboard

Finding the length of fencing around a garden

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

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

Enabling Knowledge and Skills

Examples of Where Adults Use It

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

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

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

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

Carrying out a stock inventory

Finding items for an order from bin numbers

Checking grocery receipt against purchases

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

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

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

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

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

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

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

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

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

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

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

Sharing money or brownies

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

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

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

Buying something discounted at 50% off

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

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

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

Counting five and ten dollar bills

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

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

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

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

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

same total as 3 + 2 + 4

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

Paying an amount in the hundreds using ten dollar bills

Checking totals by adding again in a different order.

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

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

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

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

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

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

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

Balancing a checkbook

Finding the difference between two distances or amounts.

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

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

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

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

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

2N-2.4.2 Relate skip counting to multiplication

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

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

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

Checking delivery of goods in small batches

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

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

Generating results using mental methods of multiplication when solving problems

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Enabling Knowledge and Skills

Examples of Where Adults Use It

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

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

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

2N-3.1.3 Recall addition facts to 20

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

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

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

2N-3.1.7 Estimate answers to addition

Calculating the production shortfall from a daily target

Performing mental addition

Verifying deposits in a checking account.

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

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

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

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

Estimating amount of purchase to nearest 10 dollars.

Estimating distances between cities.

Giving ballpark figures for numbers in a crowd.

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

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

2N-3.3.2 Know that "borrowing" is regrouping

2N-3.3.3 Recall subtraction facts to 20

2N-3.3.4 Estimate answers 

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

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

Performing mental subtraction

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

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

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

2N-3.4.3 Recall multiplication facts

(e.g. multiples of  2, 3, 4, 5, 10)

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

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

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

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

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

Separating members into two groups

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

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

2N3.6.2 Recall multiplication facts

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

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

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

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

Rounding numbers to make approximate calculations

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

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

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

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

Performing any calculations at this level

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

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

Enabling Knowledge and Skills

Examples of Where Adults Use It

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

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

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

Estimating how many exits there are on the highway

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

2P-1.2.1 Isolate smallest unit of repetition

Laying tile on a floor

Designing a tiled floor and describing the pattern

Knitting

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

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

Enabling Knowledge and Skills

Examples of Where Adults Use It

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

2P-2.1.1 Know addition and multiplication facts

2P-2.1.2 Recognize and extend patterns

Helping children with homework

Preparing for further study

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

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

Enabling Knowledge and Skills

Examples of Where Adults Use It

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

Assessed by 2P-3.6

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

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

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

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

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

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

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

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

Helping children with homework

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

8 - 3 = €,  5 ´ � = 10, 8 ¸ 2= ð

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

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

Helping children with homework.

Test-taking when seeking employment

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

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

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

Selecting filter for data entry

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

Assessed by 3P-3.7

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

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

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

Reading thermometers

Riding an elevator below ground level

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

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

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

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

Reading and interpreting scales

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

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

Entering an expression in a spread sheet

Standard 2P-4. Analyze change in various contexts

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

Enabling Knowledge and Skills

Examples of Where Adults Use It

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

2P-4.1.1 Observe steady change over time

Reporting and planning in accordance with weather changes

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

2P-4.2.1 Record and save data

2P-4.2.2 Know basic arithmetic skills

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

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

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

Enabling Knowledge and Skills

Examples of Where Adults Use It

2S-1.1 Gather data to answer posed questions.

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

Planning a party or meeting

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

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

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

Sorting stock by size

Keeping track of who will or will not attend a party

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

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

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

Reporting on responses to party or meeting

Keeping records for a club

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

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

Checking monthly totals against weekly totals

Standard 2S-2. Read and interpret data representations

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

Enabling Knowledge and Skills

Examples of Where Adults Use It

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

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

Reading newspapers and magazines

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

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

Reading advertisements.

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

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

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

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

Using the yellow pages

Checking items against a stock list

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

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

Reading newspapers and magazines

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

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

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

Conversing about information contained in newspapers and magazines

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

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

Enabling Knowledge and Skills

Examples of Where Adults Use It

2S-3.1 Match graphs and tables to statements.

2S-3.1.1 Know how to locate titles

2S-3.1.2 Titles indicate subject matter

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

Reading a newsletter from the health service

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

Assessed by 4S-4.1

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

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

Reading insurance documents

2S-3.3 Support simple statements with data.

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

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

Taking political action to institute changes in the community

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

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

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

Reading ads with bar graphs in newspaper article

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

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

Enabling Knowledge and Skills

Examples of Where Adults Use It

2S-4.1 Discuss events as likely or unlikely.

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

Deciding whether or not to carry an umbrella

Making the call when flipping a coin

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

Assessed by 3S-5.2

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

Tossing a coin

Rolling dice

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

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

Enabling Knowledge and Skills

Examples of Where Adults Use It

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

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

parallel, square corners

Sorting 2D and 3D shapes

Matching patterns for home decorating by design and shape

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

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

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

Comparing use of shapes in house construction or room design

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

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

Enabling Knowledge and Skills

Examples of Where Adults Use It

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

Assessed by 3G-2.3

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

Creating designs

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

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

Assessed by 3G-2.3

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

Creating holiday designs for greetings cards or crafts

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

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

Enabling Knowledge and Skills

Examples of Where Adults Use It

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

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

2G-3.1.2 Explain the difference between vertical and horizontal

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

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

Appreciating wind directions stated during a weather forecast

Reading directions from a map

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

Assessed by 3G-3.1

2G-3.2.1 Explain the difference between vertical and horizontal

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

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

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

Enabling Knowledge and Skills

Examples of Where Adults Use It

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

2G-4.1.1 Use whole number addition

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

Making everyday purchases

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

2G-4.2.1 Familiarity with quarter and half concepts

Telling time on various clocks

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

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

2G-4.3.2 Know that 2/4 = ½

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

Following a recipe

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

Assessed by 3G-4.12

2G-4.4.1 Know appropriate scales for familiar measures

Reading thermometer, scales

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

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

Measuring a baby’s length in inches

Expressing a person’s height in feet and inches

Doubling or halving a recipe

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

2G-4.6.1 Read scale and digital read-outs

2G-4.6.2 Read and compare numbers

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

2G-4.7 Develop personal benchmarks for temperatures.

2G-4.7.1 Read a thermometer

Knowing that a child has a fever when reading thermometer

2G-4.8 Find the perimeter of rectangles.

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

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

Buying weather-stripping

2G-4.9 Find the area of rectangles.

Assessed by 3G-4.11

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

Buying carpeting, tiles, or wall paper

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

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

Enabling Knowledge and Skills

Examples of Where Adults Use It

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

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

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

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

Filing plans in numerical order

Reading route numbers on delivery labels

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

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

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

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

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

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

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

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

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

Assessed by 4N-1.11

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

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

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

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

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

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

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

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

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

Reading price tags

Understanding prices on a menu

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

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

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

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

Recognizing 50% off and half-price as the same

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

Assessed by 4N-1.2

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

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

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

Understanding wind-chill information

Reading a thermometer

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

3N-1.7.1 Read and write 4 (4) as 4² 

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

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

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

Reading pollen count per cubic meter

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

3N-1.8.1 Know that percent means per hundred

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

on division by 100

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

Figuring a 5% sales tax on a one dollar item

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

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

Enabling Knowledge and Skills

Examples of Where Adults Use It

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

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

Generating solutions using mental mathematics in situations involving common unit fractions

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

Assessed by 4N-2.5

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

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

3N-2.2.3 Because 4 (4) = 16, Ö16 = 4

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

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

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

Checking the balance in a checkbook

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

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

Taking a standardized or employment test

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

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

Computing with formulas on a standardized test

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

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

Enabling Knowledge and Skills

Examples of Where Adults Use It

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

Assessed by 3N-3.11

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

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

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

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

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

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

Assessed by 3N-3.10 and 3.11

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

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

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

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

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

Changing dollar amounts to dimes and pennies and vice versa

Changing meters to centimeters and vice versa

3N-3.4 Carry out basic calculations with money.

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

Balancing a checkbook

Figuring one share of a restaurant bill that is divided equally

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

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

Rounding numbers to make approximate calculations

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

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

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

Reducing the quantities in a recipe

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

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

Estimating savings using mental mathematics strategies at a percentage off sale

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

Assessed by 3N-1.7

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

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

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

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

Finding the area of a square room

Finding the volume of a square room

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

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

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

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

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

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

Finding the total charge on a purchase

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

Finding the area of a square room

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

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

 and estimate answers to addition

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

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

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

3N-3.10.5 Know that “borrowing” is regrouping

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

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

Calculating the production shortfall from a daily target

Performing mental addition

Checking deposits in a checking account

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

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

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

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

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

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

Calculating miles per gallon that a car attains

Estimating travel time in hours based on distance and speed

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

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

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

Calculating a percent increase in pay or demographics

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

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

Enabling Knowledge and Skills

Examples of Where Adults Use It

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

3P-1.1.1 Know multiplication tables

Using rate tables for postage

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

Assessed by 3P-1.1

3P-1.2.1 Isolate smallest unit of repetition

3P-1.2.2 Use a notation system to record patterns

Creating Sales Tax tables

Using mental math strategies

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

3P-1.3.1 Read tables

3P-1.3.2 Recognize and verbalize patterns

Using rate tables for prices

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

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

Enabling Knowledge and Skills

Examples of Where Adults Use It

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

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

Entering an expression in a spreadsheet

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

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

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

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

3P-2.2.4 Write an equation

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

Converting temperature between Celsius and Fahrenheit

Finding interest on a loan from a table

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

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

Enabling Knowledge and Skills

Examples of Where Adults Use It

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

Assessed by 3P-3.2

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

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

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

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

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

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

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

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

Helping children with homework

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

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

3P-3.2.2 Read and write 10 for 10 ¸ 2

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

Following convention in notation and order of operation

Test-taking when seeking employment

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

 10 – x when x has a value of 1

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

Preparing for further study

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

x + 25 = 100

x – 16 = 42

3y = 42

y/5 = 200.

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

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

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

Preparing for further study

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

Assessed within 4P-3.9

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

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

Reading and interpreting scales

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

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

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

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

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

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

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

Standard 3P-4. Analyze change in various contexts

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

Enabling Knowledge and Skills

Examples of Where Adults Use It

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

3P-4.1.1 Record data

3P-4.1.2 Represent data in graphical form

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

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

3P-4.2.1 Record data in table form

3P-4.2.2 Represent data in graphical form

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

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

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

Enabling Knowledge and Skills

Examples of Where Adults Use It

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

Assessed by  2S-1.1

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

Planning a party or meeting

Conducting a political survey

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

Assessed by 2S-1.2

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

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

Keeping track of who will or will not attend party.

Sorting stock by size

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

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

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

Reporting on responses to party or meeting

Keeping records for a club

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

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

Checking monthly totals against weekly totals

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

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

Keeping a visual tally of responses by category

Standard 3S-2. Read and interpret data representations

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

Enabling Knowledge and Skills

Examples of Where Adults Use It

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

Assessed by 2S-2.1

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

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

Reading newspapers and magazines

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

Assessed by 2S-2.2

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

Reading advertisements

Finding current interest rates

3S-2.3 Sort graphs and tables by type.

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

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

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

Participating in conversations about represented data

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

Assessed by 2S-2.3

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

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

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

Using the yellow pages

Checking items against a stock list

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

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

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

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

Reading newspapers and magazines

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

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

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

Conversing about information contained in newspapers and magazines

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

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

Enabling Knowledge and Skills

Examples of Where Adults Use It

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

Assessed by 5S-3.1

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

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

Reading temperature charts

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

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

Analyzing results of a survey or group consensus

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

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

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

Estimating one’s daily expenses.

3S-3.4 Find the median.

Assessed by 4S-3.4

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

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

Explaining the median salary or median years worked in company statistics

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

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

Enabling Knowledge and Skills

Examples of Where Adults Use It

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

Assessed by 2S-3.1

3S-4.1.1 Know how to locate titles

3S-4.1.2 Titles indicate subject matter

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

Presenting information to children or co-workers

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

Assessed by 4S-4.1

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

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

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

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

Assessed by 2S-3.4

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

Understanding graphic presentations in newspapers and magazines

3S-4.4 Support simple statements with data.

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

Taking political actions to institute changes in the community

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

Assessed by 3S-4.4

3S-4.5.1 Know ways to compare numbers

Discussing numbers with peers and co-workers

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

3S-4.6.1 Double and halving numbers

3S-4.6.2 Fifty percent equals one half

Reading and/or responding to consumer materials

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

Assessed by 4S-4.6

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

Reading budget reports

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

Assessed by 4S-3.4

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

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

Debating proposed rent increases

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

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

Reading advertisements to make choices

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

Assessed by 5S-4.7

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

Reading advertisements to make choices

3S-4.11 Identify obvious misstatements.

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

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

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

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

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

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

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

Calculating the down payment for an item requiring 50% down

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