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# Massachusetts Department of Education

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## Level 2: Beginning ABE Mathematics

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

### Strand: Number Sense

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

#### 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  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

#### Examples of Where Adults Use It

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

2N-3.1.1Know how to align numbers in column addition
2N-3.1.2 Know that regrouping occurs when the total in a column exceeds 9
2N-3.1.3 Recall addition facts to 20
2N-3.1.4 Compose and decompose numbers to aid addition (e.g. 97 + 23 = 90 + 20 + 7 + 3)
2N-3.1.5 Demonstrate that there are different strategies for adding

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

2N-3.1.7 Estimate answers to addition

Calculating the production shortfall from a daily target

Performing mental addition

Verifying deposits in a checking account.

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

2N-3.2.1 Know benchmark numbers of 5 and 50 are halfway in intervals of 10 and 100 (e.g. 35 is halfway between 30 and 40 and 250 is halfway between 200 and 300)
2N-3.2.2 Tell whether a number is greater than benchmark numbers of 5 and 50
2N-3.2.3 Demonstrate an understanding of rounding to the nearest 10 or 100 using algorithm

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

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

2N-3.3.1 Know how to align numbers in column subtraction
2N-3.3.2 Know that "borrowing" is regrouping
2N-3.3.3 Recall subtraction facts to 20
2N-3.3.4 Estimate answers
2N-3.3.5 Compose and decompose numbers to aid subtraction (e.g. 107 - 83 = 100 - 80 + 7 – 3)
2N-3.3.6 Demonstrate an understanding of strategies or methods for subtraction such as borrowing or counting up

Performing mental subtraction

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

2N-3.4.1 Use doubling or repeated addition when multiplying by 2 or 4, e.g. To find 26 x 4, do 26 + 26, 52 + 52
2N-3.4.2 Demonstrate an understanding the operation of multiplication and related vocabulary (e.g. multiplied by, times, lots of)
2N-3.4.3 Recall multiplication facts

(e.g. multiples of 2, 3, 4, 5, 10)

2N-3.4.4 Recognize two- and three-digit multiples of 2, 5, or 10 and three-digit multiples of 50 and 100
2N-3.4.5 Know that multiplication can be performed in any order, so that 2(3)(4) = 4(2)(3)

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

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

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

Separating members into two groups

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

2N-3.6.1 Demonstrate an understanding that division is the inverse of multiplication
2N3.6.2 Recall multiplication facts

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

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

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

Rounding numbers to make approximate calculations

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

2N-3.8.1 Demonstrate an understanding of the order to enter a two-digit number
2N-3.8.2 Demonstrate an understanding of the order to key in numbers and operators
2N-3.8.3 Know how to clear the display and cancel a wrong entry

Performing any calculations at this level

### Strand: Patterns, Functions and Algebra

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

#### 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

#### 2P-2.1.2 Recognize and extend patterns

Helping children with homework
Preparing for further study

#### 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= 

  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

#### Examples of Where Adults Use It

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

2P-4.1.1 Observe steady change over time

Reporting and planning in accordance with weather changes

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

2P-4.2.1 Record and save data
2P-4.2.2 Know basic arithmetic skills

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

### Strand: Statistics and Probability

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

#### 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

#### 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

#### 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

#### Examples of Where Adults Use It

2S-4.1 Discuss events as likely or unlikely.

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

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

2S-4.2 Give the probability of a single outcome in simple concrete situations such as tossing a coin or rolling a die.
Assessed by 3S-5.2

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

Tossing a coin
Rolling dice

### Strand: Geometry and Measurement

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

#### 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

#### 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

#### 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

#### 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

#### 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

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