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 4N-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 | |
4N-1.1 Read, write, order and compare numbers, including large numbers (millions or billions).
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4N-1.1.1 Demonstrate an understanding that the position of a digit signifies its value
4N-1.1.2 Know what each digit represents in a number up to seven digits, including the use of zero as a place holder
4N-1.1.3 Demonstrate an understanding of the symbols for greater than and less than
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Filing plans in numerical order
Reading route numbers on delivery labels
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4N-1.2 Recognize positive and negative numbers in practical contexts.
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4N-1.2.1 Demonstrate an understanding of the words positive and negative
4N-1.2.2 Demonstrate an understanding that a negative temperature is below zero
4N-1.2.3 Demonstrate an understanding that a negative amount of money represents money owed
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Reading wind-chill chart
Reading a thermometer
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4N-1.3 Read, write, order, and compare fractions and mixed numbers.
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4N-1.3.1 Know common equivalent fractions (e.g. equivalent to a half, quarters, thirds, fifths, tenths)
4N-1.3.2 Demonstrate an understanding that in unit fractions, the larger the denominator, the smaller the fraction
4N-1.3.3 Demonstrate an understanding that non-unit fractions must be ordered by their closeness to the whole
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Reading fractions used in recipes
Comparing interest rates (e.g. 1 ¼% versus 1 ½%)
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4N-1.4 Read, write, order, and compare decimals up to three decimal places.
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4N-1.4.1 Demonstrate an understanding that the position of a digit signifies its value
4N-1.4.2 Know that the decimal point separates whole numbers from decimal fractions
4N-1.4.3 Know what each digit represents, including the use of zero as a place holder
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Reading and comparing gas prices
Reading and comparing metric measurements
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4N-1.5 Recognize and use equivalencies between fractions and decimals.
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4N-1.5.1 Know any fraction is equivalent to a decimal that ends or has a repeating pattern, and vice versa
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Understanding how to read adigital scale when placing a fraction order at the deli
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4N-1.6 Can convert fractions to decimals and decimals to fractions.
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4N-1.6.1 Demonstrate an understanding that a fraction can be converted to an equivalent decimal by dividing the numerator of a fraction by the denominator
4N-1.6.2 Demonstrate an understanding that a decimal can be converted to an equivalent fraction by writing the decimal value over 10, 100, or 1,000 and reducing to simplest form
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Understanding how the scale works at the deli counter
Using an electronic calculator to make volume and area computations based on measurements made by a standard tape measure
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4N-1.7 Read, write, order, and compare simple percentages.
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4N-1.7.1 Demonstrate an understanding of percentage as the number of parts in every 100
4N-1.7.2 Know that 100% is the whole
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Finding 20% off in a sale
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4N-1.8 Demonstrate an understanding of simple percentage of increase and decrease.
Assessed by 5N-1.4
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4N-1.8.1 Demonstrate an understanding of percentage as the number of parts in every 100
4N-1.8.2 Know that 100% is the whole
4N-1.8.3 Demonstrate an understanding that a 10% pay increase is more than a 5% pay increase, but the actual increase depends on the number operated on
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Finding a price increase of 10%
Finding a cost-of-living salary increase
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4N-1.9 Recognize equivalencies between common fractions, percentages and decimals (e.g. 50% = ½, 0.25 = ¼) and use these to find part of whole-number quantities.
Assessed by 5N-1.5
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4N-1.9.1 Know common fraction equivalents (e.g. half, quarter, fifths, tenths)
4N-1.9.2 Recognize 50% off and half-price as the same
4N-1.9.3 Know ½ as 0.5 when solving a problem with a calculator
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Computing discounts efficiently and flexibly using percents or fraction equivalencies
Finding 25% discount by dividing by 4
Finding a tip using mental math
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4N-1.10 Use ratio and proportion to solve one-step percent problems.
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4N-1.10.1 Demonstrate an understanding that equal ratios are equal fractions
4N-1.10.2 Recognize the term proportion for a statement of equal ratios
4N-1.10.3 Calculate for the missing term in a proportion by a variety of methods
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Adjusting a recipe for a larger or smaller number of servings
Converting measurements from one standard to another (e.g. miles per hour to feet per second)
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4N-1.11 Recognize and use equivalent forms of common fractions (e.g. ½ = 5/10).
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4N-1.11.1 Demonstrate an understanding that equivalent fractions look different but have the same value
4N-1.11.2 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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Calculating the size of a container required to hold a variety of portions (e.g. ¼ cup of x plus ¼ cup of y plus ½ cup of z)
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Standard 4N-2. Demonstrate an understanding meanings of operations and how they relate to one another | Benchmark: At this level an adult will be expected to: | Enabling Knowledge and Skills | Examples of Where Adults Use It |
4N-2.1 Choose the correct operation for solving a multi-step narrative problem.
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4N-2.1.1 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 test
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4N-2.2 Perform multiplication operations reliably, accurately, and efficiently.
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4N-2.2.1 Demonstrate an understanding that multiplication is commutative, but that in context changing order changes meaning
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Knowing that taking two tablets four times a day is different from taking four tablets twice a day
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4N-2.3 Use ratios to describe the relationship between two sets of objects.
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4N-2.3.1 Know when something is separated into equal groups
4N-2.3.2 Demonstrate an understanding of ratio as comparison based on division
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Recognizing when a solution can be generated by the use of proportion
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4N-2.4 Read, write, and compute with exponents.
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4N-2.4.1 Be familiar with the terms square, cube, and square root
4N-2.4.2 Recognize that any value taken to the second power will form a square and that any value taken the third power will form a cube
4N-2.4.3 Recognize that exponents represent repeated multiplication
4N-2.4.4 Recognize that exponents indicate the number of times that the base is written as a factor
4N-2.4.5 Read and write expressions such as 6(6) (6) (6) (6) (6) (6) as 67
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Preparing for further study
Understanding exponential growth of bacteria or virus such as HIV |
4N-2.5 Calculate square roots of perfect squares, estimate within range of square root value, and demonstrate an understanding of how squaring and taking the square root are related.
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4N-2.5.1 Know that a number is squared by multiplying it by itself
4N-2.5.2 Know the values of perfect squares up to 152
4N-2.5.3 Know that square root is the inverse of squaring
4N-2.5.4 Know the square roots of perfect squares up to the square root of 225
4N-2.5.5 Know that the square roots of values which are not perfect squares fall between two whole numbers
| Estimating the number of 12-inch tiles needed to cover a rectangular floor. |
Standard 4N-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 |
4N-3.1 Round decimals in practical contexts and verbal problems.
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4N-3.1.1 Know how to read decimals up to four decimal places
4N-3.1.2 Recognize that rounding a decimal to a particular decimal place requires analyzing the digit in the following decimal place
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Performing estimations of mathematical problems to check work
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4N-3.2 Add, subtract, multiply, and divide decimals up to three places.
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4N-3.2.1 Know and use strategies to check answers (e.g. approximate calculations using whole numbers)
4N-3.2.2 Know how to align numbers for column addition and subtraction
4N-3.2.3 Know how to multiply decimal factors to produce decimal placement in product
4N-3.2.4 Know how to multiply divisor and dividend by the same value to determine quotient
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Working out the total amount due for an order
Working out change needed from a purchase (e.g. $20 less $14.99)
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4N-3.3 Evaluate one number as a fraction of another.
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4N-3.3.1 Demonstrate an understanding of equivalent fractions
4N-3.3.2 Demonstrate an understanding of simplest form
4N-3.3.3 Know how to bring a fraction to its simplest form (e.g. by recognizing equivalent fractions, by using factors to “cancel”)
4N-3.3.4 Recognize prime numbers (e.g. numbers that can’t be canceled)
4N-3.3.5 Demonstrate an understanding that quantities must be in the same units to evaluate one as a fraction of another
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Changing minutes to fractions of an hour to fill in a time sheet
Representing the outcome of observations as a fraction
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4N-3.4 Use fractions to add, subtract, multiply, and divide amounts or quantities.
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4N-3.4.1 Know some common addition and subtraction facts (e.g. ½ + ¼ = ¾, ¾ – ½ = ¼)
4N-3.4.2 Demonstrate an understanding of how to change fractions to equivalent fractions for the purpose of adding and subtracting
4N-3.4.3 Know some common multiplication and division facts (e.g. ½ x ½ = ¼, ¼ ½ = ½)
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Adding hours on a time sheet that includes fractions
Finding time-and-a-half pay rate when working overtime
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4N-3.5 Work out simple ratio and direct proportion.
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4N-3.5.1 Demonstrate an understanding of simple ratio as the number of parts (e.g. three parts to one part)
4N-3.5.2 Demonstrate an understanding of direct proportion as the same rate of increase or decrease (e.g. double, half)
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Diluting a liquid in a given ratio (e.g. weed killer, paint)
Changing quantities in a recipe to make twice as much
| 4N-3.6 Follow order of operations in evaluating number sentences with more than one operation.
Assessed by 3P-3.2 |
4N-3.6.1 Applies the rule for order in a horizontal notation
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Solving algebra equations containing multiple operations
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4N-3.7 Add and subtract integers.
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4N-3.7.1 Demonstrate an understanding of positive and negative numbers
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Balancing a checkbook.
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4N-3.8 Estimate answers to calculations.
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4N-3.8.1 Know how to make approximate calculations
4N-3.8.2 Demonstrate an understanding that knowledge of context enables ‘guessing’ at answers (e.g. it should be about…), or judging if answers are sensible (e.g. that’s far too big; it doesn’t make sense to have an answer less than 1, etc.)
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Estimating to check that answers are reasonable
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4N-3.9 Use a calculator to calculate efficiently using whole numbers, fractions, decimals, and percentages.
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4N-3.9.1 Know how to change a fraction to a decimal
4N-3.9.2 Know how to change a percentage to a decimal
4N-3.9.3 Know how to interpret a rounding error such as 6.9999999 as 7
4N-3.9.4 Know and use strategies to check answers obtained with a calculator
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Doing any calculations at this level
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4N-3.10 Carry out calculations using addition and subtraction with numbers of any size using efficient written methods including ways to check answers.
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4N-3.10.1 Know and use strategies to check answers (e.g. approximate calculations, estimation)
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Using mental and written methods of calculation to generate results when solving problems using whole numbers of any size
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4N-3.11 Carry out calculations using multiplication and division using efficient written methods including ways to check answers.
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4N-3.11.1 Demonstrate an understanding of the words multiple and factor and relate them to multiplication and division facts
4N-3.11.2 Demonstrate an understanding of the word prime and know prime numbers up to 20
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Using mental and written methods of calculation to generate results when solving problems using whole numbers of any size
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4N-3.12 Multiply whole numbers and decimals by 10, 100, and 1,000 to understand the impact on place value.
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4N-3.12.1 Recognize the impact on place value of zeros added to whole numbers
4N-3.12.2 Recognize the impact on place value as the position of the decimal point changes
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Simplifying large numbers to estimate products
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4N-3. 13 Divide whole numbers and decimals by 10, 100, and 1,000 to understand the impact on place value.
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4N-3.13.1 Recognize the impact on place value of zeros are cancelled in whole numbers
4N-3.13.2 Recognize the impact on place value as the position of the decimal point changes
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Simplifying large numbers to estimate quotients
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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 4P-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 |
4P-1.1 Complete number sequences (all whole numbers, simple fractions and decimals) involving two-step progressions.
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4P-1.1.1 Know multiplication tables
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Using rate tables for postage
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4P-1.2 Recognize and create repeating patterns, identify the unit being repeated, and generalize.
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4P-1.2.1 Isolate smallest unit of repetition
4P-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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4P-1.3 Given a table of amounts, generalize the relationship between the quantities.
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4P-1.3.1 Read tables
4P-1.3.2 Recognize and verbalize patterns
| Using rate tables for prices
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Standard 4P-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 |
4P-2.1 Write a simple expression or equation representing verbal situations including multiple operations, fractions, exponents, and parentheses.
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4P-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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4P-2.2 Develop and use simple formulas from tables with one or two arithmetical steps for real life contexts.
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4P-2.2.1 Discover patterns in an “in-out” table
4P-2.2.2 Verbalize a rule for finding values in an “in-out” table
4P-2.2.3 Write a general expression for finding values in an “in-out” table
4P-2.2.4 Write an equation
4P-2.2.5 Decide on the effectiveness of the developed formula by substituting known values
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Converting temperature between Celsius and Fahrenheit
Finding interest on a loan |
Standard 4P-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 |
4P-3.1 Use and interpret the +, -, x, , and = to represent combining, comparing, and equivalence.
Assessed by 4P-3.2
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4P-3.1.1 Demonstrate an understanding that + represents operations of combining
4P-3.1.2 Demonstrate an understanding that – represents operations of separation or comparison
4P-3.1.3 Demonstrate an understanding that stands for combining multiples
4P-3.1.4 Demonstrate an understanding that means separating into equal groups or discovering the number of equal groups contained within
4P-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 balance a checkbook
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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4P-3.2 Read and write number operations using algebraic notation for multiplication, division, and parentheses.
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4P-3.2.1 Read and write 5 (10) for multiplication of 5 times 10
4P-3.2.2 Read and write 10 for 10 2
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4P-3.2.3 Know that the contents of parentheses must be worked out first
4P-3.2.4 Know that exponents and roots are simplified before multiplication or division
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Following convention in notation and the order of carrying out operations
Test-taking when seeking employment
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4P-3.3 Demonstrate appropriate use of the universally accepted “order of operations”.
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4P-3.3.1 Read and write number expressions which follow the rule of order for simplifying:
Parentheses
Exponents and roots
Multiplication or division
Addition or subtraction
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Helping children with homework
Preparing for further study
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4P-3.4 Substitute the value for the variable in an addition or subtraction expression when the value is given, such as finding x + 4 and 10 – x when x has a value of 1.
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4P-3.4.1 Demonstrate an understanding that a variable represents a missing value in addition and subtraction expressions
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To prepare for further study
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4P-3.5 Substitute the value for the variable in a multiplication or division expression when the value is given (e.g. finding 2x and 8/x when x = 2 including exponents.
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4P-3.5.1 Demonstrate an understanding that a variable represents a missing value in a multiplication and division expression
4P-3.5.2 Demonstrate an understanding that when there is no operator between a number and a variable or two variables that multiplication is implied
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To prepare for further study
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4P-3.6 Evaluate expressions and make whole number substitutions in given formula to produce results.
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4P-3.6.1 Demonstrate an understanding that when there is no operator between a number and a bracket or parentheses that multiplication is implied
4P-3.6.2 Know order of operations
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Informally using d = rt to make estimates regarding speed or time of departure
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4P-3.7 Read and understand positive and negative integers.
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4P-3.7.1 Demonstrate an understanding of the words positive, negative, and zero
4P-3.7.2 Know that positive refers to values more than zero
4P-3.7.3 Know that negative refers to values below zero
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Reading thermometers
Riding an elevator below ground level
Staying “in the black” or going “into the red”
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4P-3.8 Demonstrate an understanding addition and subtraction of integers.
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4P-3.8.1 Be able to solve expressions such as: 20 – 30
-6 + 10
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Finding temperature change
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4P-3.9 Use a number line to represent values.
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4P-3.9.1 Demonstrate an understanding that a horizontal number line moves from left to right using lesser to greater values
4P-3.9.2 Demonstrate an understanding that intervals on a number line must follow a constant progression between values
4P-3.9.3 Demonstrate an understanding that numbers to the left of zero are negative and those to the right of zero are positive
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Using a “thermometer” to represent the progress of a fund raiser
Preparing for further study in algebra or higher math
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4P-3.10 Write statements of inequality for integers of any size e.g.:
2 < 10
10 > 8
99 < 100
1,000 > 999.99
-12 < - 11.
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4P-3.10.1 Demonstrate an understanding that > stands for greater than
4P-3.10.2 Demonstrate an understanding that < stands for less than
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Preparing for further study in algebra or higher math
Helping children with homework |
4P-3.11 Find the value of a variable in multi-step equations e.g.:
3x + 25 = 100
2x – 16 = 42
3y+ 3 = 42
m/5 – 25 = 200.
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4P-3.11.1 Recognize that addition and subtraction are inverse operations
4P-3.11.2 Recognize that multiplication and division are inverse operations
4P-3.11.3 Recognize that using the inverse operation can solve equations
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Preparing for further study in algebra or higher math
Helping children with homework
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Standard 4P-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 |
4P-4.1 Use graphs to analyze the nature of changes in quantities in linear relationships.
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4P-4.1.1 Know vocabulary to describe linear change (e.g. rises steadily, falls, gradually declines)
4P-4.1.2 Know mechanics of making a line graph
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Interpreting information presented in graphical form in newspapers or magazines
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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 4S-1. Collect, organize and represent data |
Benchmark: At this level an adult will be expected to:
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Enabling Knowledge and Skills
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Examples of Where Adults Use It
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4S-1.1 Pose questions about themselves and their surroundings and gather data to answer posed questions.
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4S-1.1.1 Know that answers can be found by observing and asking relevant questions and counting responses
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Conducting a survey for community planning
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4S-1.2 Group objects or responses by single or double criteria.
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4S-1.2.1 Demonstrate an understanding of the concept of categories such as shape, size, color or yes or no responses
4S-1.2.2 Know how to count each category for subtotals
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Organizing findings in a chart or table
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4S-1.3 Represent information so that it makes sense to others in any graphical form.
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4S-1.3.1 Demonstrate an understanding that information can be represented in different ways such as a list, table, or a line plot
4S-1.3.2 Demonstrate an understanding of the importance of labeling information in a list, table, or line plot
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Writing a health pamphlet
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4S-1.4 Find a total from subtotaled categories to verify inclusion of all data.
Assessed by 3S-1.4
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4S-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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Estimating the total cost of a variety of products, each of which is priced individually (e.g. corn – 6/$1.00, cucumbers - $.39 each, beans - $.99/pound)
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4S-1.5 Display categorical data in a bar graph or simple fractions of data in a circle graph.
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4S-1.5.1 Demonstrate an understanding that the one axis displays the categories
4S-1.5.2 Demonstrate an understanding that the other axis is numbered sequentially
4S-1.5.3 Demonstrate an understanding that the height (or length) of the bar is equal to the amount on the corresponding axis
4S-1.5.4 Demonstrate an understanding that fractions of data sets (1/4,1/3,1/2, 2/3,3/4) can be represented as wedges of a circle graph
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Showing various groups’ responses to school activities or programs
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4S-1.6 Convert a bar graph into a circle graph.
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4S-1.6.1 Demonstrate an understanding that all data must be included so that the circle graph represents 100% of the data
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Participating in class to understand interconnections between graphic representations
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4S-1.7 Translate data from a numerical table to a line graph and vice versa.
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4S-1.7.1 Demonstrate an understanding that a table can display the same data as a line or bar graph but in rows and columns
4S-1.7.2 Demonstrate an understanding of the importance of labeling each axis
4S-1.7.3 Demonstrate an understanding that single data points are to be connected by a line to create the line graph
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Creating a bar graph to illustrate weight gain/loss over a one-week period
Creating a line graph to illustrate temperatures over a one-week period
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Standard 4S-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 |
4S-2.1 Identify graphs and tables in available resources.
Assessed by 2S-2.1
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4S-2.1.1 Demonstrate an understanding that a graph is a visual representation
4S-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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4S-2.2 Find graphs and tables in external sources.
Assessed by 2S-2.2
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4S-2.2.1 Recognize that graphs and tables can be found in many publications
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Reading advertisements
Looking up taxes payments
Finding current interest rates
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4S-2.3 Name and sketch various types of graphs and a table.
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4S-2.3.1 Know that a bar graph uses bars of various heights to display amount
4S-2.3.2 Know that line graphs use lines to connect data points
4S-2.3.3 Know that a circle or pie graph represents the whole or 100%
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Participating in a class or working with a child on homework
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4S-2.4 Extract simple information from a list or table.
Assessed by 2S-2.3
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4S-2.4.1 Demonstrate an understanding that lists can be ordered in different ways such as alphabetically, numerically, or randomly
4S-2.4.2 Demonstrate an understanding that tables are arranged in rows and columns.
4S-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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4S-2.5 Read values on a bar, line, or circle graph.
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4S-2.5.1 Demonstrate an understanding that the height of the bar is equal to the amount on the axis across from it
4S-2.5.2 Know how to read a scale on an axis
4S-2.5.3 Demonstrate an understanding that specific data points correspond with the labels on both axes
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Using car mileage graphs
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4S-2.6 Make numerical comparisons about relative values on a bar graph or circle graph.
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4S-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 or wedge sizes
4S-2.6.2 Demonstrate an understanding of relative numerical terms such as twice or half
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Creating a circle graph illustrating how earnings are broken down and distributed by categories of expenses
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Standard 4S-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 |
4S-3.1 Identify the minimum, maximum, spread and shape of data.
Assessed by 5S-3.1
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4S-3.1.1 Be familiar with the terms minimum, maximum, and spread.
4S-3.1.2 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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4S-3.2 Use “most of” statements to describe data.
Assessed by 3S-3.2
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4S-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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Using a graph to illustrate the breakdown of household expenses while describing them orally
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4S-3.3 Find the mean.
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4S-3.3.1 Know that mean is “average” and that average in this case is about equal distribution
4S-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
4S-3.3.3 Demonstrate an understanding that what are termed “averages” are numbers supposedly “typical” of data
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Estimating one’s daily expenses
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4S-3.4 Find the median and mode.
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4S-3.4.1 Know that median is the middle value
4S-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
4S-3.4.3 Know that mode is the number or item that occurs most often in a set of data
4S-3.4.4 Know ways in which “averages” are supposed to be “typical” of data – median is the middle value and mean implies equal distribution of all data
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Explaining the median salary or median years worked in company statistics
Examining house sale prices to determine which towns are most likely to have affordable housing stock
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4S-3.5 Identify the effect of spread on mean and median.
Assessed by 5S-4.5
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4S-3.5.1 Know the minimum or maximum value can greatly affect the mean but will not affect the median
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Interpreting statistical data accurately
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Standard 4S-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 |
4S-4.1 Determine whether or not a graph/table connects to an argument/ statement using title, data labels, and percent matches.
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4S-4.1.1 Know how to locate data labels in tables and graphs to verify they match arguments/statements
4S-4.1.2 Locate and connect percent numbers in graphs and arguments/ statements
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Reading insurance documents to decide if the what they state matches what they show
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4S-4.2 Visually identify “who has more,” use numbers to compare quantities and identify obvious misstatements.
Assessed by 2S-3.4
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4S-4.2.1 Recognize bar heights and circle wedges show quantity
4S-4.2.2 Recognize where to look for numbers representing relevant quantities
4S-4.2.3 Knowing to connect numbers with statements/arguments to verify accuracy
| Reading newspaper articles and deciding if what they state accurately matches what they show |
4S-4.3 Make statements about data trends to support or reject arguments/ statements forwarded by others.
Assessed by 5S-4.4
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4S-4.3.1 Demonstrate an understanding that lines going up mean increase; lines tilting down mean decrease and that they can vary over time
4S-4.3.2 Know that a flat line means no change
4S-4.3.3 Specific vocabulary to describe trends (e.g. “sharp” increase, “plummeted,” etc.)
| Looking at reports on stock market to see if they reflect the trends represented |
4S-4.4 Know statements using “double” and “half” or fifty percent are accurate.
Assessed by 3S-4.6
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4S-4.4.1 Double and halving numbers
4S-4.4.2 Fifty percent equals one half
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Using consumer reports to make decisions
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4S-4.5 Verify that statements using three times or four times, one fourth or one tenth are accurate.
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4S-4.5.1 Know ways to estimate multiples of large numbers
4S-4.5.2 Know ways to estimate one fourth or one tenth of a number
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Using consumer reports to make decisions
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4S-4.6 Know when percent figures don’t add up to 100% and when numbers and percent figures (50%, 25%, 10%) don’t match up.
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4S-4.6.1 Demonstrate an understanding that circle graphs usually represent 100%, and all figures in them should add to 100
4S-4.6.2 Know ways to estimate or easily calculate 50%, 25% and 10% of a number
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Reading expenditure reports from local or national governments to determine if money spent is totally accounted for
Analyzing income data reports to see if the percents given reflect the amounts represented
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4S-4.7 Compare and contrast provided graphs to evaluate for contradictory or unsupported statements.
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4S-4.7.1 Recognize that statements or arguments based on data are sometimes generated by comparing or contrasting graphs
4S-4.7.2 Recognize that statements or arguments based on one graph are sometimes contradicted in another
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Analyzing accident-related data
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Standard 4S-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 |
4S-5.1 Discuss events as likely or unlikely.
Assessed by 3S-5.1
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4S-5.1.1 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.
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Deciding to avoid or use certain products
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4S-5.2 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
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4S-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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4S-5.3 State probability as a ratio fraction.
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4S-5.3.1 Know that probability is the ratio of the potential successful outcomes to total possibilities.
4S-5.3.2 Know that such ratios can be written in fraction form.
4S-5.3.3 Know that ratio fractions can be simplified
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Determining the chances of winning a prize in a drawing
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4S-5.4 Find the probability of independent events.
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4S-5.4.1 Know that probability is the ratio of the potential successful outcomes to total possibilities.
4S-5.4.2 Know that such ratios can be written in fraction form or as one value compared to another
4S-5.4.3 Know that ratio fractions can be simplified
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Designing and conducting experiments using 1, 2, 3, and 4 different colored balls to determine the likelihood of randomly selecting a specific color by chance
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4S-5.5 State the probability as a percent.
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4S-5.5.1 Know that ratio fractions can be expressed as a percent by expressing a proportion with the percent out of 100
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Converting a specific set of outcomes as likelihood of the event happening in 100 attempts
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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 4G-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 |
4G-1.1 Directly measure and compare the radius, diameter and circumference of a circle
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4G-1.1.1 Use a ruler and string to make measurements
4G-1.1.2 Demonstrate an understanding that the radius is half of the diameter
4G-1.1.3 Demonstrate an understanding that the circumference is a little more than three diameters and that the ratio is known as pi
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Measuring automobile tires
Designing circular gardens
| 4G-1.2 Directly measure different angles with a protractor.
Assessed by 5G-1.7 |
4G-1.2.1 Estimate the measure of an angle using benchmarks of 90 degrees and 180 degrees
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Cutting molding for a corner
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4G-1.3 Use informal visual methods to describe and compare shape, dimensions, perimeters, area, and angles, sides in two-dimensional (2-D) and three-dimensional (3D) objects.
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4G-1.3.1 Be able to solve practical problems using the properties of 2-D and 3-D figures
4G-1.3.2 Demonstrate an understanding that that area is conserved, but perimeter is not when 2-D objects are combined
4G-1.3.3 Build 3-D 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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4G-1.4 Identify shapes that are congruent or similar.
| 4G-1.4.1 Know that congruent shapes are exactly the same with equal sides and angles
4G-1.4.2 Know that similar shapes are the same shape, but different sizes
4G-1.4.3 Know that the corresponding angles of congruent and similar shapes are congruent
4G-1.4.4 Know that similar shapes are proportional to each other |
Assembling items bought unassembled (e.g. toys, exercise equipment, some furniture)
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4G-1.5 Identify types of angles such as right, obtuse, acute, and straight.
| 4G-1.5.1 Know that an acute angle has a measure of less than 90°
4G-1.5.2 Know that a right angle has a measure of 90°
4G-1.5.3 Know that an obtuse angle has a measure of more than 90 but less than 180°
4G-1.5.4 Know that a straight angle has a measure of 180° |
Using the basic properties of different types of triangles to prove basic theories and solve problems
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4G-1.6 Understand the relationship of angles when you have a system of parallel lines cut by a transversal.
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4G-1.6.1 Know that a line that crosses two parallel lines is called a transversal
4G-1.6.2 Know that a transversal crosses two lines that are parallel to each crosses both lines at the same angle
4G-1.6.3 Know that when a transversal crosses two parallel lines the corresponding angles are equal to each other
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Cutting molding at a correct angle so that both ends meet with no space in between
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4G-1.7 Identify different names of triangles by properties, such as isosceles, right, and equilateral.
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4G-1.7.1 Know that the sum of the angles of any triangle is 180°
4G-1.7.2 Know that equilateral triangles have three equal sides
4G-1.7.3 Know that each of the angles of an equilateral (equiangular) triangle measures 60°
4G-1.7.4 Know that any triangle with a 90° angle is a right triangle
4G-1.7.5 Know that any triangle with two equal sides is an isosceles triangle
4G-1.7.6 Know that the angles opposite the equal sides of an isosceles triangle are called the base angles, and that base angles are equal to each other
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Following plans when working on carpentry projects
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4G-1.8 Estimate the measure of an angle using benchmarks.
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4G-1.8.1 Know the range of the measure for acute, right, obtuse, and straight angles
4G-1.8.2 Demonstrate an ability to estimate the measure of an angle based on that knowledge
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Estimating where a line of symmetry would fall in a rectangular object
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Standard 4G-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 |
4G-2.1 Estimate where a line of symmetry falls in a basic shape.
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4G-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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4G-2.2 Show more than one line of symmetry in a complex shape.
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4G-2.2.1 Demonstrate an understanding of concepts of sameness or half-ness
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Creating a “snowflake” or hanging decoration using folded paper and scissors
| Standard 4G-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 |
4G-3.1 Read, interpret, and use a distance scale to find the shortest route between two locations on a map.
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4G-3.1.1 Reading a map using horizontal and vertical indices or latitude and longitude
4G-3.1.2 Reading a scale
4G-3.1.3 Use proportional reasoning
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Reading a map to plan a hiking trip
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4G-3.2 Measure common three-dimensional (3-D) shapes (e.g. a room) and represent the information on an appropriate diagram drawn to scale.
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4G-3.2.1 Demonstrate an understanding of 3-D coordinate graph
4G-3.2.2 Locate points in 3-D graphs
4G-3.2.3 Use proportional reasoning
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Creating plans for building a model
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4G-3.3 Draw two-dimensional (2-D) shapes in different orientations on a grid.
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4G-3.3.1 Use graph paper to draw 2-D shapes
4G-3.3.2 Be able to change the orientation and copy objects
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Drawing plans for a carpentry project
Creating a pattern for a sewing project
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4G-3.4 Use coordinate grid to identify and locate specific points on the x and y axes.
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4G-3.4.1 Know that the horizontal axis on a coordinate grid is labeled x
4G-3.4.2 Know that the vertical axis on a coordinate grid is labeled y
4G-3.4.3 Know that the intersection of the x and y axes is called origin
4G-3.4.4 Know that the coordinates of all points on the coordinate grid are given (x, y).
4G-3.4.5 Know that the coordinates of all points on the coordinate axes are counted from the origin point (0,0).
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Organizing and displaying data to detect patterns and departures from patterns
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Standard 4G-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 |
4G-4.1 Convert units of measure in different systems by using own informal methods.
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4G-4.1.1 Know common equivalences of measurement units
4G-4.1.2 Demonstrate an understanding of proportionality
4G-4.1.3 Know how to solve ratio and proportion problems
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Estimating number of pints of blood in the human body given the number of liters
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4G-4.2 Read, measure, and compare Fahrenheit and Celsius temperatures.
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4G-4.2.1 Reading scales
4G-4.2.2 Making one-to-one correspondence between scales
4G-4.2.3 Estimating distances between markings on a scale
4G-4.2.4 Read and compare negative numbers
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Reading a thermometer
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4G-4.3 Estimate and approximate an understanding of inter-relatedness of distance, time, and speed.
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4G-4.3.1 Investigate how a change in one variable (speed) relates to a change in a second variable (time, distance)
4G-4.3.2 Identify and describe situations with constant or varying rates of change and compare them (acceleration, slowing, down, stopping)
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Estimating the time a trip will take from point “A” to point “B” traveling at the normal speed limit
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4G-4.4 Measure with a ruler to 1/16 inch and metric ruler in cm and mm.
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4G-4.4.1 Know that a foot equals 12 inches
4G-4.4.2 Know the relationship between the fractions of an inch (16ths, 8ths, 4ths, and halves)
4G-4.4.3 Know that the metric numbers on a ruler represent centimeters (cm) and a one-foot ruler is approximately 33 cm long
4G-4.4.4 Know that the 10 divisions of a centimeter are called millimeters (mm)
4G-4.4.5 Know that a metric length is most commonly represented by a decimal. For example 4 cm 3mm would be 4.3 cm
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Completing a project demanding fairly precise measurements
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4G-4.5 Use the language (prefixes) of metric units to describe environment.
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4G-4.5.1 Know that meters measure length
4G-4.5.2 Know that grams measure mass or weight
4G-4.5.3 Know that liters measure volume
4G-4.5.4 Know the metric prefixes
milli equal to 1/1,000. centi equal to 1/100, deci equal to 1/10, deca equal to 10, hecto equal to 100, and kilo equal to 1,000
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Traveling or communicating with people outside of the United States
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4G-4.6 Make informal comparisons between grams and ounces, liters and quarts.
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4G-4.6.1 Know that an ounce is approximately equal to 28 grams and that a paper clip weighs approximately 1 gram
4G-4.6.2 Know that a kilogram is approximately 2.2 pounds
4G-4.6.3 Know that a liter is a little larger than a quart (1.1 qts.)
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Measuring medications
Replacing automotive fluids
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4G-4.7 Estimate, measure, and compare capacity using simple instruments graduated in standard units and know when to use appropriate measures.
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4G-4.7.1 Demonstrate familiarity with measures of cups, quarts, gallons, inches, feet, yards, ounces, and pounds
4G-4.7.2 Demonstrate familiarity with measures of liters, grams, kilograms, centimeters, meters, and kilometers
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Buying beverages for a large group
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4G-4.8 Work out simple volumes of cubes, cylinders, and rectangular containers.
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4G-4.8.1 Using formulas for volume of cubes, cylinders, and rectangular containers be able to solve for the total
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Filling a sand box or garden with mulch
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4G-4.9 Find perimeter/area of combination shapes using what you know about rectangles and triangles.
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4G-4.9.1 Demonstrate an ability to redefine shapes formed as combinations of rectangles and triangles and calculate the perimeter and area using these smaller parts
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Estimating amount of material required to cover a piece of furniture
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