Strand Overview: Number
Note: Teachers should exercise their professional judgement to select and adapt the materials found in this resource to meet the needs of their students as they learn the expectations outlined in the Ontario Mathematics curriculum.
B1. Number Sense
Demonstrate an understanding of numbers and make connections to the way numbers are used in everyday life.
Learning SituationWhole Numbers
B1.1 Read and represent whole numbers up to and including 50, and describe various ways they are used in everyday life.
B1.2 Compose and decompose whole numbers up to and including 50, using a variety of tools and strategies, in various contexts.
B1.3 Compare and order whole numbers up to and including 50, in various contexts.
B1.4 Estimate the number of objects in collections of up to 50, and verify their estimates by counting.
B1.5 Count to 50 by 1s, 2s, 5s, and 10s, using a variety of tools and strategies.
B1.6 Use drawings to represent and solve fair-share problems that involve 2 and 4 sharers, respectively, and have remainders of 1 or 2.
B1.7 Recognize that one half and two fourths of the same whole are equal, in fair-sharing contexts.
B1.8 Use drawings to compare and order unit fractions representing the individual portions that result when a whole is shared by different numbers of sharers, up to a maximum of 10.
B2. Operations
B2. Use knowledge of numbers and operations to solve mathematical problems encountered in everyday life.
Learning SituationProperties and Relationships
B2.1 Use the properties of addition and subtraction, and the relationship between addition and subtraction, to solve problems and check calculations.
Math Facts
B2.2 Recall and demonstrate addition facts for numbers up to 10, and related subtraction facts.
Mental Math
B2.3 Use mental math strategies, including estimation, to add and subtract whole numbers that add up to no more than 20, and explain the strategies used.
Addition and Subtraction
B2.4 Use objects, diagrams, and equations to represent, describe, and solve situations involving addition and subtraction of whole numbers that add up to no more than 50.
Multiplication and Division
B2.5 Represent and solve equal-group problems where the total number of items is no more than 10, including problems in which each group is a half, using tools and drawings.
B1. Number Sense
Demonstrate an understanding of numbers and make connections to the way numbers are used in everyday life.
Learning Situation-
Whole Numbers
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B1.1 Read, represent, compose, and decompose whole numbers up to and including 200, using a variety of tools and strategies, and describe various ways they are used in everyday life.
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B1.2 Compare and order whole numbers up to and including 200, in various contexts.
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B1.3 Estimate the number of objects in collections of up to 200 and verify their estimates by counting.
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B1.4 Count to 200, including by 20s, 25s, and 50s, using a variety of tools and strategies.
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B1.5 Describe what makes a number even or odd.
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Fractions
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B1.6 Use drawings to represent, solve, and compare the results of fair-share problems that involve sharing up to 10 items among 2, 3, 4, and 6 sharers, including problems that result in whole numbers, mixed numbers, and fractional amounts.
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B1.7 Recognize that one third and two sixths of the same whole are equal, in fair-sharing contexts.
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B2. Operations
B2. Use knowledge of numbers and operations to solve mathematical problems encountered in everyday life.
Learning Situation-
Properties and Relationships
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B2.1 Use the properties of addition and subtraction, and the relationships between addition and multiplication and between subtraction and division, to solve problems and check calculations.
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Math Facts
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B2.2 Recall and demonstrate addition facts for numbers up to 20, and related subtraction facts.
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Mental Math
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B2.3 Use mental math strategies, including estimation, to add and subtract whole numbers that add up to no more than 50, and explain the strategies used.
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Addition and Subtraction
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B2.4 Use objects, diagrams, and equations to represent, describe, and solve situations involving addition and subtraction of whole numbers that add up to no more than 100.
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Multiplication and Division
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B2.5 Represent multiplication as repeated equal groups, including groups of one half and one fourth, and solve related problems, using various tools and drawings.
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B2.6 Represent division of up to 12 items as the equal sharing of a quantity, and solve related problems, using various tools and drawings.
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B1. Number Sense
Demonstrate an understanding of numbers and make connections to the way numbers are used in everyday life.
Learning Situation-
Whole Numbers
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B1.1 Read, represent, compose, and decompose whole numbers up to and including 1000, using a variety of tools and strategies, and describe various ways they are used in everyday life.
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B1.2 Compare and order whole numbers up to and including 1000, in various contexts.
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B1.3 Round whole numbers to the nearest ten or hundred, in various contexts.
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B1.4 Count to 1000, including by 50s, 100s, and 200s, using a variety of tools and strategies.
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B1.5 Use place value when describing and representing multi-digit numbers in a variety of ways, including with base ten materials.
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Fractions
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B1.6 Use drawings to represent, solve, and compare the results of fair-share problems that involve sharing up to 20 items among 2, 3, 4, 5, 6, 8, and 10 sharers, including problems that result in whole numbers, mixed numbers, and fractional amounts.
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B1.7 Represent and solve fair-share problems that focus on determining and using equivalent fractions, including problems that involve halves, fourths, and eighths; thirds and sixths; and fifths and tenths.
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B2. Operations
B2. Use knowledge of numbers and operations to solve mathematical problems encountered in everyday life.
Learning Situation-
Properties and Relationships
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B2.1 Use the properties of operations, and the relationships between multiplication and division, to solve problems and check calculations.
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Math Facts
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B2.2 Recall and demonstrate multiplication facts of 2, 5, and 10, and related division facts.
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Mental Math
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B2.3 Use mental math strategies, including estimation, to add and subtract whole numbers that add up to no more than 1000, and explain the strategies used.
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Addition and Subtraction
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B2.4 Demonstrate an understanding of algorithms for adding and subtracting whole numbers by making connections to and describing the way other tools and strategies are used to add and subtract.
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B2.5 Represent and solve problems involving the addition and subtraction of whole numbers that add up to no more than 1000, using various tools and algorithms.
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Multiplication and Division
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B2.6 Represent multiplication of numbers up to 10 × 10 and division up to 100 ÷ 10, using a variety of tools and drawings, including arrays.
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B2.7 Represent and solve problems involving multiplication and division, including problems that involve groups of one half, one fourth, and one third, using tools and drawings.
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B2.8 Represent the connection between the numerator of a fraction and the repeated addition of the unit fraction with the same denominator using various tools and drawings, and standard fractional notation.
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B2.9 Use the ratios of 1 to 2, 1 to 5, and 1 to 10 to scale up numbers and to solve problems.
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B1. Number Sense
Demonstrate an understanding of numbers and make connections to the way numbers are used in everyday life.
Learning Situation-
Whole Numbers
B1.1 Read, represent, compose, and decompose whole numbers up to and including 10 000, using appropriate tools and strategies, and describe various ways they are used in everyday life.
B1.2 Compare and order whole numbers up to and including 10 000, in various contexts.
B1.3 Round whole numbers to the nearest ten, hundred, or thousand, in various contexts.
Fractions and Decimals
B1.4 Represent fractions from halves to tenths using drawings, tools, and standard fractional notation, and explain the meanings of the denominator and the numerator.
B1.5 Use drawings and models to represent, compare, and order fractions representing the individual portions that result from two different fair-share scenarios involving any combination of 2, 3, 4, 5, 6, 8, and 10 sharers.
B1.6 Count to 10 by halves, thirds, fourths, fifths, sixths, eighths, and tenths, with and without the use of tools.
B1.7 Read, represent, compare, and order decimal tenths, in various contexts.
B1.8 Round decimal numbers to the nearest whole number, in various contexts.
B1.9 Describe relationships and show equivalences among fractions and decimal tenths, in various contexts.
B2. Operations
Use knowledge of numbers and operations to solve mathematical problems encountered in everyday life.
Learning Situation-
Properties and Relationships
B2.1 Use the properties of operations, and the relationships between addition, subtraction, multiplication, and division, to solve problems involving whole numbers, including those requiring more than one operation, and check calculations.
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Math Facts
B2.2 Recall and demonstrate multiplication facts for 1 × 1 to 10 × 10, and related division facts.
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Mental Math
B2.3 Use mental math strategies to multiply whole numbers by 10, 100, and 1000, divide whole numbers by 10, and add and subtract decimal tenths, and explain the strategies used.
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Addition and Subtraction
B2.4 Represent and solve problems involving the addition and subtraction of whole numbers that add up to no more than 10 000 and of decimal tenths, using appropriate tools and strategies, including algorithms.
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Multiplication and Division
B2.5 Represent and solve problems involving the multiplication of two- or three-digit whole numbers by one-digit whole numbers and by 10, 100, and 1000, using appropriate tools, including arrays.
B2.6 Represent and solve problems involving the division of two- or three-digit whole numbers by one-digit whole numbers, expressing any remainder as a fraction when appropriate, using appropriate tools, including arrays.
B2.7 Represent the relationship between the repeated addition of a unit fraction and the multiplication of that unit fraction by a whole number, using tools, drawings, and standard fractional notation.
B2.8 Show simple multiplicative relationships involving whole-number rates, using various tools and drawings.
B1. Number Sense
Demonstrate an understanding of numbers and make connections to the way numbers are used in everyday life.
Learning Situation-
Whole Numbers
B1.1 Read, represent, compose, and decompose whole numbers up to and including 100 000, using appropriate tools and strategies, and describe various ways they are used in everyday life.
B1.2 Compare and order whole numbers up to and including 100 000, in various contexts.
Fractions, Decimals, and Percents
B1.3 Represent equivalent fractions from halves to twelfths, including improper fractions and mixed numbers, using appropriate tools, in various contexts.
B1.4 Compare and order fractions from halves to twelfths, including improper fractions and mixed numbers, in various contexts.
B1.5 Read, represent, compare, and order decimal numbers up to hundredths, in various contexts.
B1.6 Round decimal numbers to the nearest tenth, in various contexts.
B1.7 Describe relationships and show equivalences among fractions, decimal numbers up to hundredths, and whole number percents, using appropriate tools and drawings, in various contexts.
B2. Operations
Use knowledge of numbers and operations to solve mathematical problems encountered in everyday life.
Learning Situation-
Properties and Relationships
B2.1 Use the properties of operations, and the relationships between operations, to solve problems involving whole numbers and decimal numbers, including those requiring more than one operation, and check calculations.
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Math Facts
B2.2 Recall and demonstrate multiplication facts from 0 × 0 to 12 × 12, and related division facts.
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Mental Math
B2.3 Use mental math strategies to multiply whole numbers by 0.1 and 0.01 and estimate sums and differences of decimal numbers up to hundredths, and explain the strategies used.
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Addition and Subtraction
B2.4 Represent and solve problems involving the addition and subtraction of whole numbers that add up to no more than 100 000, and of decimal numbers up to hundredths, using appropriate tools, strategies, and algorithms.
B2.5 Add and subtract fractions with like denominators, in various contexts.
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Multiplication and Division
B2.6 Represent and solve problems involving the multiplication of two-digit whole numbers by two-digit whole numbers using the area model and using algorithms, and make connections between the two methods.
B2.7 Represent and solve problems involving the division of three-digit whole numbers by two-digit whole numbers using the area model and using algorithms, and make connections between the two methods, while expressing any remainder appropriately.
B2.8 Multiply and divide one-digit whole numbers by unit fractions, using appropriate tools and drawings.
B2.9 Represent and create equivalent ratios and rates, using a variety of tools and models, in various contexts.
B1. Number Sense
Demonstrate an understanding of numbers and make connections to the way numbers are used in everyday life.
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Rational Numbers
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B1.1 Read and represent whole numbers up to and including one million, using appropriate tools and strategies, and describe various ways they are used in everyday life.
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B1.2 Read and represent integers, using a variety of tools and strategies, including horizontal and vertical number lines.
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B1.3 Compare and order integers, decimal numbers, and fractions, separately and in combination, in various contexts.
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Fractions, Decimals, and Percents
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B1.4 Read, represent, compare, and order decimal numbers up to thousandths, in various contexts.
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B1.5 Round decimal numbers, both terminating and repeating, to the nearest tenth, hundredth, or whole number, as applicable, in various contexts.
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B1.6 Describe relationships and show equivalences among fractions and decimal numbers up to thousandths, using appropriate tools and drawings, in various contexts.
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B2. Operations
B2. Use knowledge of numbers and operations to solve mathematical problems encountered in everyday life.
Learning Situation-
Properties and Relationships
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B2.1 Use the properties of operations, and the relationships between operations, to solve problems involving whole numbers, decimal numbers, fractions, ratios, rates, and whole number percents, including those requiring multiple steps or multiple operations.
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Math Facts
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B2.2 Understand the divisibility rules and use them to determine whether numbers are divisible by 2, 3, 4, 5, 6, 8, 9, and 10.
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Mental Math
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B2.3 Use mental math strategies to calculate percents of whole numbers, including 1%, 5%, 10%, 15%, 25%, and 50%, and explain the strategies used.
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Addition and Subtraction
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B2.4 Represent and solve problems involving the addition and subtraction of whole numbers and decimal numbers, using estimation and algorithms.
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B2.5 Add and subtract fractions with like and unlike denominators, using appropriate tools, in various contexts.
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Multiplication and Division
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B2.6 Represent composite numbers as a product of their prime factors, including through the use of factor trees.
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B2.7 Represent and solve problems involving the multiplication of three-digit whole numbers by decimal tenths, using algorithms.
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B2.8 Represent and solve problems involving the division of three-digit whole numbers by decimal tenths, using appropriate tools, strategies, and algorithms, and expressing remainders as appropriate.
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B2.9 Multiply whole numbers by proper fractions, using appropriate tools and strategies.
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B2.10 Divide whole numbers by proper fractions, using appropriate tools and strategies.
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B2.11 Represent and solve problems involving the division of decimal numbers up to thousandths by whole numbers up to 10, using appropriate tools and strategies.
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B2.12 Solve problems involving ratios, including percents and rates, using appropriate tools and strategies.
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B1. Number Sense
Demonstrate an understanding of numbers and make connections to the way numbers are used in everyday life.
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Rational Numbers
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B1.1 Represent and compare whole numbers up to and including one billion, including in expanded form using powers of ten, and describe various ways they are used in everyday life.
B1.2 Identify and represent perfect squares, and determine their square roots, in various contexts.
B1.3 Read, represent, compare, and order rational numbers, including positive and negative fractions and decimal numbers to thousandths, in various contexts.
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Fractions, Decimals, and Percents
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B1.4 Use equivalent fractions to simplify fractions, when appropriate, in various contexts.
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B1.5 Generate fractions and decimal numbers between any two quantities.
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B1.6 Round decimal numbers to the nearest tenth, hundredth, or whole number, as applicable, in various contexts.
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B1.7 Convert between fractions, decimal numbers, and percents, in various contexts.
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B2. Operations
Use knowledge of numbers and operations to solve mathematical problems encountered in everyday life.
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Properties and Relationships
B2.1 Use the properties and order of operations, and the relationships between operations, to solve problems involving whole numbers, decimal numbers, fractions, ratios, rates, and percents, including those requiring multiple steps or multiple operations.
Math Facts
B2.2 Understand and recall commonly used percents, fractions, and decimal equivalents.
Mental Math
B2.3 Use mental math strategies to increase and decrease a whole number by 1%, 5%, 10%, 25%, 50%, and 100%, and explain the strategies used.
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Addition and Subtraction
B2.4 Use objects, diagrams, and equations to represent, describe, and solve situations involving addition and subtraction of integers.
B2.5 Add and subtract fractions, including by creating equivalent fractions, in various contexts.
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Multiplication and Division
B2.6 Determine the greatest common factor for a variety of whole numbers up to 144 and the lowest common multiple for two and three whole numbers.
B2.7 Evaluate and express repeated multiplication of whole numbers using exponential notation, in various contexts.
B2.8 Multiply and divide fractions by fractions, using tools in various contexts.
B2.9 Multiply and divide decimal numbers by decimal numbers, in various contexts.
B2.10 Identify proportional and non-proportional situations and apply proportional reasoning to solve problems.
B1. Number Sense
Demonstrate an understanding of numbers and make connections to the way numbers are used in everyday life.
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Rational and Irrational Numbers
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B1.1 Represent and compare very large and very small numbers, including through the use of scientific notation, and describe various ways they are used in everyday life.
B1.2 Describe, compare, and order numbers in the real number system (rational and irrational numbers), separately and in combination, in various contexts.
B1.3 Estimate and calculate square roots, in various contexts.
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Fractions, Decimals, and Percents
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B1.4 Use fractions, decimal numbers, and percents, including percents of more than 100% or less than 1%, interchangeably and flexibly to solve a variety of problems.
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B2. Operations
Use knowledge of numbers and operations to solve mathematical problems encountered in everyday life.
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Properties and Relationships
B2.1 Use the properties and order of operations, and the relationships between operations, to solve problems involving rational numbers, ratios, rates, and percents, including those requiring multiple steps or multiple operations.
Math Facts
B2.2 Understand and recall commonly used square numbers and their square roots.
Mental Math
B2.3 Use mental math strategies to multiply and divide whole numbers and decimal numbers up to thousandths by powers of ten, and explain the strategies used.
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Addition and Subtraction
B2.4 Add and subtract integers, using appropriate strategies, in various contexts.
B2.5 Add and subtract fractions, using appropriate strategies, in various contexts.
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Multiplication and Division
B2.6 Multiply and divide fractions by fractions, as well as by whole numbers and mixed numbers, in various contexts.
B2.7 Multiply and divide integers, using appropriate strategies, in various contexts.
B2.8 Compare proportional situations and determine unknown values in proportional situations, and apply proportional reasoning to solve problems in various contexts.