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

Standard G1. Use and apply geometric properties and relationships to describe the physical world and identify and analyze the characteristics of geometric figures,

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

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

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

Outline of Learning Levels
Level 1. Beginning Adult Numeracy
See “How to Use This Document (Teacher’s Guide) and (Connecting Curriculum, Instruction and Assessment),” pages 810.
At this time, the Massachusetts ABE Test for Math does not assess students’ knowledge at Level 1.
Strand: Number Sense
Learners engage in problem solving within adult contextual situations by communicating, reasoning, and connecting to the following standards:
Standard 1N1. Represent and use numbers in a variety of equivalent forms in contextual situations  Benchmark: At this level an adult will be expected to:   Examples of Where Adults Use It 
1N1.1 Count reliably forward and backward up to 20 items.

1N1.1.1 Demonstrate an understanding that if items are rearranged, the numbers stay the same
1N1.1.2 Count forward and backward from ten or less
1N1.1.3 Count forward and back from 1120 
Counting children in a group to make sure no one is missing
Counting dollar bills to pay for a purchase
Counting items at the grocery express line
Using the remote channel tuner for a TV
Watching a digital timer on a microwave count down the time

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

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

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

1N1.3 Read, write, and compare numbers from 0 up to 100.

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

Telling which address falls in a given block, knowing the first number on the block
Writing a money order for a whole dollar amount (no change) 
1N1.4 Using a 100 chart, skip count by 2’s, 5’s, and 10’s.

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

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

 Benchmark: At this level an adult will be expected to:  Enabling Knowledge and Skills  Examples of Where Adults Use It 
1N2.1 Demonstrate an understanding of different meanings of addition (e.g. counting on, combining) of numbers up to 20.

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

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

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

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

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

1N2.3 Demonstrate an understanding of how addition and subtraction relate to each other.

1N2.3.1 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)

 Benchmark: At this level an adult will be expected to:  Enabling Knowledge and Skills  Examples of Where Adults Use It 
1N3.1 Know all pairs of numbers with a total of 10.

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

Adding using mental math

1N3.2 Add numbers with totals to 20.

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

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

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

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

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

1N3.4 Double whole numbers to 10.

1N3.4.1 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 
1N3.5 Finding half of whole numbers up to 20.

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

Sharing the cost of pizza between two people.

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

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

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

Strand: Patterns, Functions, and Algebra
Learners engage in problem solving within adult contextual situations by communicating, reasoning, and connecting to the following standards:
Standard 1P1. Explore, identify, analyze, and extend patterns in mathematical and adult contextual situations  Benchmark: At this level an adult will be expected to:  Enabling Knowledge and Skills  Examples of Where Adults Use It 
1P1.1 Sort up to 20 objects or lists by color, shape, number, letter, or size.
 1P1.1.1 Identify attributes of objects and classify such as shape, size, number and/or size 
Sorting laundry
Sorting bottles for recycling facility
Sorting telephone numbers by area code and figuring which are long distance calls
Shelving stock

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

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

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

Standard 1P2. Articulate and represent number and data relationships using words, tables, graphs, rules, and equations  Benchmark: At this level an adult will be expected to:  Enabling Knowledge and Skills  Examples of Where Adults Use It 
1P2.1 Explore basic number relationships (e.g., find all the ways numbers to 10 can be written as sums).

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

Playing card games
Preparing for further study

Standard 1P3. Recognize and use algebraic symbols to model mathematical and contextual situations  Benchmark: At this level an adult will be expected to:  Enabling Knowledge and Skills  Examples of Where Adults Use It 
1P3.1 Use and interpret +, , and = to represent combining, taking away, and equivalence.

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

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

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

1P3.2.1 Demonstrate an understanding that an underlined blank space represents a missing value in addition and subtraction equations

Helping children with homework.
Test taking when seeking employment 
1P3.3 Make statements of inequality e.g.:
2 is less than 10
10 is greater than 8
99 is less than 100
6 + 5 10
 1P3.3.1 Explain that directionality of reading numbers and expressions moves from left to right 
Helping children with homework
Testtaking when seeking employment 
Standard 1P4. Analyze change in various contexts  Benchmark: At this level an adult will be expected to:  Enabling Knowledge and Skills  Examples of Where Adults Use It 
1P4.1 Describe qualitative change, such as lengthening or decreasing hours of daylight, or rising or falling of temperature over time.

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

Discussing weather patterns
Describing seasons, daylight savings time, or tides 
Strand: Statistics and Probability
Learners engage in problem solving within adult contextual situations by communicating, reasoning, and connecting to the following standards:
Standard 1S1. Collect, organize and represent data  Benchmark: At this level an adult will be expected to:  Enabling Knowledge and Skills  Examples of Where Adults Use It 
1S1.1 Gather data to answer posed questions.

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

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

1S1.2 Group objects or responses by a single criterion.

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

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

Standard 1S2. Read and interpret data representations  Benchmark: At this level an adult will be expected to:  Enabling Knowledge and Skills  Examples of Where Adults Use It 
1S2.1 Identify graphs in available resources.

1S2.1.1 Explain how graph is a visual representation

Reading a graph in an ad or poster

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

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

Checking items against a stock list

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

1S2.3.1 Skipcount by 2, 5, or 10
1S2.3.2 Demonstrate an understanding and that the height of the bar is equal to the amount on the axis across from it

Reading a nutrition graph in a health poster

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

1S2.4.1 Explain how comparative statements such as greater than or less than can be made based on the height of the bars

Conversing about information contained in newspapers and magazines

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

1S2.5.1 Demonstrate how to locate titles
1S2.5.2 Explain that titles indicate subject matter
 Reading a chart or graph in a health pamphlet. 
Standard 1S3. Describe data using numerical descriptions, statistics, and trend terminology    
Not applicable at this level.


 Standard 1S4. Make and evaluate arguments and statements by applying knowledge of data analysis, bias factors, graph distortions, and context    
Not applicable at this level.



Standard 1S5. Know and apply basic probability concepts  Benchmark: At this level an adult will be expected to:  Enabling Knowledge and Skills  Examples of Where Adults Use It 
1S5.1 Discuss events as likely or unlikely.
 1S5.1.1 Develop an understanding that while some events are impossible, some are certain to happen, and in other events some are more likely to occur than others 
Deciding whether or not to carry an umbrella
Making the call when flipping a coin

Strand: Geometry and Measurement
Learners engage in problem solving within adult contextual situations by communicating, reasoning, and connecting to the following standards:
Standard 1G1. Use and apply geometric properties and relationships to describe the physical world and identify and analyze the characteristics of geometric figures  Benchmark: At this level an adult will be expected to:  Enabling Knowledge and Skills  Examples of Where Adults Use It 
1G1.1 Recognize, name, describe and compare common basic 2D shapes (square, circle, rectangle, triangle) using everyday language (straight, curved, etc.).

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

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

1G1.2 Understand the conventions for naming a rectangle by its length and width.

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

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

Standard 1G2. Use transformations and symmetry to analyze mathematical situations  Benchmark: At this level an adult will be expected to:  Enabling Knowledge and Skills  Examples of Where Adults Use It 
1G2.1 Estimating where a line of symmetry falls in a basic shape.

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

Cutting a cake in half
Folding objects 
Standard 1G3. Specify locations and describe spatial relationships using coordinate geometry and other representational systems  Benchmark: At this level an adult will be expected to:  Enabling Knowledge and Skills  Examples of Where Adults Use It 
1G3.1 Use the cardinal directions to describe where one location is relative to another.

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

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

1G3.2 Understand and use location prepositions and everyday language of position appropriately.

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

Assembling a piece of furniture from a diagram
Giving oral directions for getting from one place to another
 Standard 1G4. Understand measurable attributes of objects and the units, systems, and processes of measurement and apply appropriate techniques, tools, and formulas to determine measurements  Benchmark: At this level an adult will be expected to:  Enabling Knowledge and Skills  Examples of Where Adults Use It 
1G4.1 Show equivalent amounts of money using different bills and coins.

1G4.1.1 Know coin & bill names and values

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

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

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

Completing forms (birth date, etc.)

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

1G4.3.1 Count to 60 by 5’s and 10’s

Reading a bus schedule that uses AM and PM

1G4.4 Read analog and digital clocks.

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

Looking at clock outside a bank and know if one is on time
 1G4.5 Compares familiar quantities, length, mass, capacity, time, temperature, using informal comparative language and methods (e.g. taller, heavier, smallest). 
1G4.5.1 Explain how the suffixes –er, est, and how, more, less, and too will change the quantity

Sorting by size to organize a kitchen cabinet
Understanding a child’s growth chart 
1G4.6 Read a ruler to the nearest whole inch.

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

Measuring the length and width of photo

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

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

Give one’s height or weight on a medical form

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

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

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

