Strand Overviews
Number – Intermediate Division
OVERALL EXPECTATION B1.
demonstrate an understanding of numbers and make connections to the way numbers are used in everyday life
| Grade 6 | Grade 7 | Grade 8 |
|---|---|---|
| Rational Numbers | title |
Rational and Irrational Numbers |
| 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 | 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 | B1.1 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 read and represent integers, using a variety of tools and strategies, including horizontal and vertical number lines | B1.2 identify and represent perfect squares, and determine their square roots, in various contexts | |
| B1.3 compare and order integers, decimal numbers, and fractions, separately and in combination, 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 | 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 | ||
| Fractions, Decimals, and Percents | title |
title |
| B1.4 use equivalent fractions to simplify fractions, when appropriate, in various contexts | ||
| B1.5 generate fractions and decimal numbers between any two quantities | ||
| B1.4 read, represent, compare, and order decimal numbers up to thousandths, in various contexts | ||
| B1.5 round decimal numbers, both terminating and repeating, to the nearest tenth, hundredth, or whole number, as applicable, in various contexts | B1.6 round decimal numbers to the nearest tenth, hundredth, or whole number, as applicable, in various contexts | |
| B1.6 describe relationships and show equivalences among fractions and decimal numbers up to thousandths, using appropriate tools and drawings, in various contexts | B1.7 convert between fractions, decimal numbers, and percents, in various contexts | 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 |
OVERALL EXPECTATION B2.
demonstrate an understanding of numbers and make connections to the way numbers are used in everyday life
| Grade 6 | Grade 7 | Grade 8 |
|---|---|---|
| Properties and Relationships | title |
title |
| 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 | 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 | 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 | title |
title |
| 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 | B2.2 understand and recall commonly used percents, fractions, and decimal equivalents | B2.2 understand and recall commonly used square numbers and their square roots |
| Mental Math | title |
title |
| 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 | 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 | 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 |
| Addition and Subtraction | title |
title |
| B2.4 represent and solve problems involving the addition and subtraction of whole numbers and decimal numbers, using estimation and algorithms | B2.4 use objects, diagrams, and equations to represent, describe, and solve situations involving addition and subtraction of integers | B2.4 add and subtract integers, using appropriate strategies, in various contexts |
| B2.5 add and subtract fractions with like and unlike denominators, using appropriate tools, in various contexts | B2.5 add and subtract fractions, including by creating equivalent fractions, in various contexts | B2.5 add and subtract fractions, using appropriate strategies, in various contexts |
| Multiplication and Division | title |
title |
| B2.6 represent composite numbers as a product of their prime factors, including through the use of factor trees | 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 represent and solve problems involving the multiplication of three-digit whole numbers by decimal tenths, using algorithms | B2.7 evaluate and express repeated multiplication of whole numbers using exponential notation, in various contexts | |
| 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 | ||
| B2.9 multiply whole numbers by proper fractions, using appropriate tools and strategies | B2.8 multiply and divide fractions by fractions, using tools in various contexts | B2.6 multiply and divide fractions by fractions, as well as by whole numbers and mixed numbers, in various contexts |
| B2.10 divide whole numbers by proper fractions, using appropriate tools and strategies | B2.9 multiply and divide decimal numbers by decimal numbers, in various contexts | |
| 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 | B2.7 multiply and divide integers, using appropriate strategies, in various contexts | |
| B2.12 solve problems involving ratios, including percents and rates, using appropriate tools and strategies | B2.10 identify proportional and non-proportional situations and apply proportional reasoning to solve problems | B2.8 compare proportional situations and determine unknown values in proportional situations, and apply proportional reasoning to solve problems in various contexts |