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:
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: | | Examples of Where Adults Use It |
3N-1.1 Read, write, order, and compare numbers up to 1,000,000.
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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
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Filing plans in numerical order
Reading route numbers on delivery labels
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3N-1.2 Read, write and compare common fractions (e.g. thirds, halves, and quarters).
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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
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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)
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3N-1.3 Recognize and use equivalent forms of common fractions (e.g.1/2 = 5/10).
Assessed by 4N-1.11
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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
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In the context of measures, recognizing relationships (e.g. that 2/8 inch = 1/4 inch)
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3N-1.4 Read, write and compare decimals up to two decimal places in practical contexts ( money in decimal notation, e.g. $10.35).
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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)
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Reading price tags
Understanding prices on a menu
Counting and recording total value of change received at a rummage sale
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3N-1.5 Recognize fraction, decimal, and percent equivalents for a half and one quarter.
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3N-1.5.1 Know ½ = 0.5 = 50% and 1/4 = 0.25 = 25%
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Ordering a half pound at a deli that uses a digital scale
Recognizing 50% off and half-price as the same
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3N-1.6 Read, write, and compare positive and negative numbers in practical contexts.
Assessed by 4N-1.2
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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
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Understanding wind-chill information
Reading a thermometer
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3N-1.7 Read, write, and compute squares and cubes of whole numbers.
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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
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Reading pollen count per cubic meter
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3N-1.8 Understand that percent represents a ratio of a part to a whole where the whole is 100.
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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
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Figuring a 5% sales tax on a one dollar item
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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.
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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)
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Generating solutions using mental mathematics in situations involving common unit fractions
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3N-2.2 Demonstrate an understanding of how squaring and taking the square root are related.
Assessed by 4N-2.5
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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, 16 = 4
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Finding the area of a square room from the length of a side or to find the length of a side from the area
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3N-2.3 Demonstrate an understanding of how addition and subtraction relate to each other for numbers up to 1,000,000.
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3N-2.3.1 Know how to add back to check, e.g. 1,000 – 250 = 750 because 250 + 750 = 1,000
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Checking the balance in a checkbook
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3N-2.4 Choose the correct operation for solving a one-step narrative problem.
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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
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Taking a standardized or employment test
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3N-2.5 Understand and use exponents to represent repeated multiplication.
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3N-2.5 Recognize that exponents indicate the number of times that the base is written as a factor
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Computing with formulas on a standardized test
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| | 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
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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
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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
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3N-3.2 Carry out calculations with three-digit whole numbers using efficient written methods.
Assessed by 3N-3.10 and 3.11
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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
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Using written methods to generate results when solving problems with three-digit whole numbers
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3N-3.3 Multiply and divide whole numbers by 10 and 100.
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3N-3.3.1 Demonstrate an understanding of place value for whole numbers and to two-decimal places
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Changing dollar amounts to dimes and pennies and vice versa
Changing meters to centimeters and vice versa
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3N-3.4 Carry out basic calculations with money.
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3N-3.4.1 Demonstrate an understanding of place value for whole numbers and to two-decimal places
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Balancing a checkbook
Figuring one share of a restaurant bill that is divided equally
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3N-3.5 Approximate by rounding numbers up to 1,000,000 to the nearest tens, hundreds, or thousands
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3N-3.5.1 Demonstrate an understanding place value for units, tens, hundreds, thousands
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Rounding numbers to make approximate calculations
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3N-3.6 Find common parts of whole number quantities or measurements (e.g. ¾ of 12, 2/3 of 15).
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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
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Reducing the quantities in a recipe
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3N-3.7 Use equivalencies between common fractions and percentages to find part of whole-number quantities.
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3N-3.7.1 Know common fraction and percent equivalents (e.g. 50% = ½, 25% = ¼, 75% = ¾)
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Estimating savings using mental mathematics strategies at a percentage off sale
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3N-3.8 Find squares, square roots, and cubes of whole-number quantities
Assessed by 3N-1.7
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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
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Finding the area of a square room
Finding the volume of a square room
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3N-3.9 Use a calculator to calculate whole numbers and decimals to two places to solve problems in context, and to check calculations.
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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
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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
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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.
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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
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Calculating the production shortfall from a daily target
Performing mental addition
Checking deposits in a checking account
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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.
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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
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Calculating miles per gallon that a car attains
Estimating travel time in hours based on distance and speed
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3N-3.12 Compute percentages when part and whole are given using friendly numbers (e.g. 10%, 25%, 50%, and 75%).
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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
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Calculating a percent increase in pay or demographics
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Strand: Patterns, Functions, and Algebra
Learners engage in problem solving within adult contextual situations by communicating, reasoning, and connecting to the following standards:
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.
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3P-1.1.1 Know multiplication tables
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Using rate tables for postage
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3P-1.2 Recognize and create repeating patterns and identify the unit being repeated.
Assessed by 3P-1.1
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3P-1.2.1 Isolate smallest unit of repetition
3P-1.2.2 Use a notation system to record patterns
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Creating Sales Tax tables
Using mental math strategies
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3P-1.3 Given a table of amounts, generalize the relationship between the quantities using simple patterns such as doubling.
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3P-1.3.1 Read tables
3P-1.3.2 Recognize and verbalize patterns
| Using rate tables for prices
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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.
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3P-2.1.1 Translate simple worded problems involving unknown quantities into simple equations
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Entering an expression in a spreadsheet
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3P-2.2 Develop and use simple formulas from tables with one or two arithmetical steps for real life contexts.
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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
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Converting temperature between Celsius and Fahrenheit
Finding interest on a loan from a table
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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
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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
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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
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3P-3.2 Read, write, and solve expressions using algebraic notation for addition, subtraction, multiplication, division, and parentheses with one or two operations.
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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
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Following convention in notation and order of operation
Test-taking when seeking employment
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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
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3P-3.3.1 Demonstrate an understanding that a variable represents a missing value in addition and subtraction expressions
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Preparing for further study
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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.
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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
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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
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Reading and interpreting scales
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3P-3.6 Write statements of inequality for numbers up to 1,000,000.
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3P-3.6.1 Demonstrate an ability to use the symbols > and < in number statements with larger numbers.
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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.
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3P-3.7 Read and understand positive and negative numbers as showing direction and change on both horizontal and vertical number lines.
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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.
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Viewing an automotive electrical gauge to determine if the battery is charging or discharging.
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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.
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3P-4.1.1 Record data
3P-4.1.2 Represent data in graphical form
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Tracking wages when paid an hourly rate on a variable work schedule
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3P-4.2 Identify and describe situations with constant or varying rates of change and compare them.
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3P-4.2.1 Record data in table form
3P-4.2.2 Represent data in graphical form
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Following monthly bills (e.g. rent, heating and telephone, in order to budget)
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Strand: Statistics and Probability
Learners engage in problem solving within adult contextual situations by communicating, reasoning, and connecting to the following standards:
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
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3S-1.1.1 Know that answers can be found by observing and asking relevant questions and counting responses.
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Planning a party or meeting
Conducting a political survey
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3S-1.2 Group objects or responses by a single criterion.
Assessed by 2S-1.2
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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
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Keeping track of who will or will not attend party.
Sorting stock by size
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3S-1.3 Represent information so that it makes sense to others.
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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
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Reporting on responses to party or meeting
Keeping records for a club
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3S-1.4 Find a total from subtotaled categories to verify inclusion of all data.
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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
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Checking monthly totals against weekly totals
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3S-1.5 Represent categorical data on a line plot.
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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
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Keeping a visual tally of responses by category
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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
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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
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Reading newspapers and magazines
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3S-2.2 Find graphs and tables in external sources.
Assessed by 2S-2.2
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3S-2.2.1 Recognize that graphs and tables can be found in many publications
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Reading advertisements
Finding current interest rates
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3S-2.3 Sort graphs and tables by type.
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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
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Participating in conversations about represented data
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3S-2.4 Extract simple information from a list or table.
Assessed by 2S-2.3
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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
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Using the yellow pages
Checking items against a stock list
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3S-2.5 Read values on a bar or line graph up to 1,000,000.
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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.
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Reading newspapers and magazines
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3S-2.6 Make numerical comparisons about relative values on a bar graph.
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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.
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Conversing about information contained in newspapers and magazines
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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
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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.
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Reading temperature charts
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3S-3.2 Use “most of” statements to describe data.
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3S-3.2.1 Recognize that values in the data set can be repeated and some values may be repeated more frequently than others.
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Analyzing results of a survey or group consensus
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3S-3.3 Find the average (mean) and range for a data set.
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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.
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Estimating one’s daily expenses.
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3S-3.4 Find the median.
Assessed by 4S-3.4
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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.
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Explaining the median salary or median years worked in company statistics
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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
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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
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Presenting information to children or co-workers
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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
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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
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Reading insurance documents to decide if the what they state matches what they show
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3S-4.3 Visually identify “who has more,” and use some numbers to compare quantities.
Assessed by 2S-3.4
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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
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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.
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3S-4.6.1 Double and halving numbers
3S-4.6.2 Fifty percent equals one half
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Reading and/or responding to consumer materials
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3S-4.7 Know when percent figures don’t add up to 100%.
Assessed by 4S-4.6
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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
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Reading budget reports
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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
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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.
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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
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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.
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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.
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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 | Benchmark: At this level an adult will be expected to: | Enabling Knowledge and Skills | Examples of Where Adults Use It |
3S-5.1 Discuss events as likely or unlikely using benchmarks.
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3S-5.1.1 Demonstrate an understanding that while some events are impossible, some are certain to happen and some are more likely to occur than others.
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Making decisions about how weather may affect outdoor plans
Predicting the outcome of a sporting event based on a team’s past performance.
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3S-5.2 Give the probability of a single outcome in simple concrete situations such as tossing a coin or rolling a die.
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3S-5.2.1 Demonstrate an understanding that probability depends on the total number of possibilities
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Tossing a coin
Rolling dice
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3S-5.3 State probability as a ratio in multiple forms (colon, words, and fractions) with simple scenarios.
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3S-5.3.1 Know that probability is the ratio of the potential successful outcomes to total possibilities
3S-5.3.2 Know that such ratios can be written in fraction form
3S-5.3.3 Know that ratio fractions can be simplified |
Determining the chances of winning a prize in a drawing
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Strand: Geometry and Measurement
Learners engage in problem solving within adult contextual situations by communicating, reasoning, and connecting to the following standards:
Standard 3G-1. Use and apply geometric properties and relationships to describe the physical world and identify and analyze the characteristics of geometric figure | Benchmark: At this level an adult will be expected to: | Enabling Knowledge and Skills | Examples of Where Adults Use It |
3G-1.1 Use informal visual methods to describe and compare shape, dimension, perimeter, area, angles and sides in two dimensional and 3-D objects.
3D objects – Assessed by 4G-1.3
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3G-1.1.1 Be able to solve practical problems using the properties of 2D and 3D figures
3G-1.1.2 Demonstrate an understanding that that area is conserved, but perimeter is not when 2-D objects are combined
3G-1.1.3 Build 3D figures using 2-D plans and blocks
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Organizing a closet
Packing a trunk
Covering a package with paper
Tying string around a package
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3G-1.2 Identify properties, locations, and functions of right angles.
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3G-1.2.1 Know that a right angle is 90 degree or a quarter turn, that two right angles make a straight line, and four right angles fill a space
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Creating tiling patterns
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Standard 3G-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 |
3G-2.1 Estimate where a line of symmetry falls in a basic shape.
Assessed by 3G-2.3
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3G-2.1.1 Demonstrate an understanding of concepts of sameness or half-ness
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Cutting cake in half
Folding objects
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3G-2.2 Show more than one line of symmetry in a basic shape.
Assessed by 3G-2.3
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3G-2.2.1 Demonstrate an understanding of concepts of sameness or half-ness
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Designing and making a quilt
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3G-2.3 Identify where a line of symmetry falls in a basic shape.
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3G-2.3.1 Demonstrate an understanding of concepts of sameness or half-ness
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Recognizing patterns and symmetry in design and architecture
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Standard 3G-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 |
3G-3.1 Use direction, distance, coordinates, simple scales, labels, symbols, and keys to read and use maps and plans.
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3G-3.1.1 Use the compass rose on a map with secondary (SW, NE, etc) directions
3G-3.1.2 Demonstrate an understanding of latitude and longitude, or horizontal and vertical indices on a map
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Planning an automobile trip
Finding a city on a globe
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3G-3.2 Draw 2 dimensional (2-D) shapes in different orientations on a grid.
Assessed by 4G-3.3
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3G-3.2.1 Use graph paper to draw 2-D shapes
3G-3.2.2 Be able to change the orientation and copy object.
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Creating a pattern for a model plane
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Standard 3G-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 |
3G-4.1 Add, subtract, multiply and divide sums of money including decimal notation.
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3G-4.1.1 Demonstrate an understanding of place value for whole numbers and to two-decimal places
3G-4.1.2 Know how to round off thousandths (mils) to the nearest hundredths (cents)
3G-4.1.3 Know how to use a calculator
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Balancing a checkbook
Figuring one’s share of a restaurant bill being divided equally
Finding cost of multiples units of an item
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3G-4.2 Demonstrate a general understanding of inter-relatedness of distance, time, and speed.
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3G-4.2.1 Investigate how a change in one variable (speed) relates to a change in a second variable (time, distance)
3G-4.2.2 Identify and describe situations with constant or varying rates of change and compare them (e.g. acceleration, slowing down, stopping)
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Estimating time of arrival with slower or faster speeds
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3G-4.3 Read and interpret scales with marked and unmarked labels.
Assessed by 4G-3.1
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3G-4.3.1 Skip counting by 5, 10, 100, 500
3G-4.3.2 Making visual estimates of lengths
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Inferring distances on a road map
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3G-4.4 Measures with a ruler to 1/8inch and metric ruler in cm and mm.
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3G-4.4.1 Know that a foot equals 12 inches
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Knowing when more exact measure is needed (e.g. woodworking project)
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3G-4.5 Can make informal comparisons between inches and centimeters.
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3G-4.5.1 Demonstrate an understanding of making a one-to-one correspondence between different rulers and units.
3G-4.5.2 Make visual estimates of the number of centimeters per inch.
3G-4.5.3 Create physical (bodily) benchmarks for units (e.g. fingernail = 1 cm; thumb joint = 1 inch.)
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Using a ruler with both inches and centimeter scales
Selecting the appropriately sized wrench when working on a European-made car
Mixing cleaning chemicals in the correct proportions by comparing metric to standard liquid measure
Measuring correct doses of medication.
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3G-4.6 Can convert units of measure in the same systems.
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3G-4.6.1 Know the relationship of familiar units (e.g. 12 inches in a foot, 3 feet in a yard, 4 cups in a quart)
3G-4.6.2 Know when to multiply and when to divide when converting units of measure
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Substituting the use of foot rulers for a yardstick or a one cup measure for a quart measure
Doing home repairs and carpentry projects
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3G-4.7 Use and apply concepts of weight and capacity to solve problems.
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3G-4.7.1 Know the difference between weight and capacity
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Correctly loading a washing machine to maintain balance throughout the cycle
Reading the capacity of a liquid to near exact measure
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3G-4.8 Use, read, and compare positive and negative Fahrenheit temperatures.
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3G-4.8.1 Demonstrate an understanding that temperature increases as it goes up and decreases as it goes down
3G-4.8.2 Know that the sign of the temperature changes when crossing the zero degree point
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Reading weather forecasts
Understanding wind-chill factor
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3G-4.9 Use and interpret the 24 hour clock.
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3G-4.9.1 Demonstrate an understanding of standard notation for A.M and P.M.
3G-4.9.2 Addition and multiplication facts to 12
3G-4.9.3 Familiarity with quarter and half concepts
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Matching 12 and 24 hour times
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3G-4.10 Calculate times using the appropriate value and converting between time formats (including elapsed time).
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3G-4.10.1 Know equivalencies for hours, seconds, minutes, days, weeks, months, decades, and centuries.
3G-4.10.2 Know multiplication and division by 2-digit numbers
3G-4.10.3 Use mental math skills
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Understanding that 2 centuries is 200 years to appreciate past events and their place in history
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3G-4.11 Directly measures perimeter in linear units and area in square units (sq. in., sq. ft., sq. cm.).
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3G-4.11.1 Use a ruler to measure length and width
3G-4.11.2 Compare two figures by laying them on top of each other to determine larger area
3G-4.11.3 Cover a figure with square units and count the units
3G-4.11.4 Use addition and multiplication skills to aid in counting units
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Planning renovations or paint for a room
Making a cover for a counter top
Sewing a chair cover
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3G-4.12 Estimate, measure, and compare whole number weights using simple instruments, graduated in familiar units (ounces and pounds) and know when to use appropriate measures.
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3G-4.12.1 Use a scale to measure weight
3G-4.12.2 Compare two figures holding them to determine which is heavier
3G-4.12.3 Place two objects on a balance scale
3G-4.12.4 Use addition and multiplication skills to aid in counting units
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Placing objects of various weights on shelves or hanging them on walls
Shopping for fresh vegetables in a market
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