Strand Overviews
Number – Junior Division
OVERALL EXPECTATION B1.
demonstrate an understanding of numbers and make connections to the way numbers are used in everyday life
| Grade 4 | Grade 5 | Grade 6 |
|---|---|---|
| Whole Numbers | title |
Rational 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 | B1.1 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 | B1.1 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 |
| B1.2 compare and order whole numbers up to and including 10 000, in various contexts | B1.2 compare and order whole numbers up to and including 100 000, in various contexts | B1.2 read and represent integers, using a variety of tools and strategies, including horizontal and vertical number lines |
| B1.3 round whole numbers to the nearest ten, hundred, or thousand, in various contexts | B1.3 compare and order integers, decimal numbers, and fractions, separately and in combination, in various contexts | |
| Fractions and Decimals | Fractions, Decimals, and Percents | title |
| 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 | B1.3 represent equivalent fractions from halves to twelfths, including improper fractions and mixed numbers, using appropriate tools, in various contexts | |
| 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 | B1.4 compare and order fractions from halves to twelfths, including improper fractions and mixed numbers, in various contexts | |
| 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 | B1.5 read, represent, compare, and order decimal numbers up to hundredths, in various contexts | B1.4 read, represent, compare, and order decimal numbers up to thousandths, in various contexts |
| B1.8 round decimal numbers to the nearest whole number, in various contexts | B1.6 round decimal numbers to the nearest tenth, 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 |
| B1.9 describe relationships and show equivalences among fractions and decimal tenths, 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 | B1.6 describe relationships and show equivalences among fractions and decimal numbers up to thousandths, using appropriate tools and drawings, in various contexts |
OVERALL EXPECTATION B2.
use knowledge of numbers and operations to solve mathematical problems encountered in everyday life
| Grade 4 | Grade 5 | Grade 6 |
|---|---|---|
| Properties and Relationships | title |
title |
| 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 | 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 | 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 |
| Math Facts | title |
title |
| B2.2 recall and demonstrate multiplication facts for 1 × 1 to 10 × 10, and related division facts | B2.2 recall and demonstrate multiplication facts from 0 × 0 to 12 × 12, and related division facts | 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 |
| Mental Math | title |
title |
| 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 | 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 | 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 |
| Addition and Subtraction | title |
title |
| 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 | 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 | B2.4 represent and solve problems involving the addition and subtraction of whole numbers and decimal numbers, using estimation and algorithms |
| B2.5 add and subtract fractions with like denominators, in various contexts | B2.5 add and subtract fractions with like and unlike denominators, using appropriate tools, 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 | ||
| B2.5 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 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 multiplication of three-digit whole numbers by decimal tenths, using algorithms |
| 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 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 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 |
| B2.7 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 multiply and divide one-digit whole numbers by unit fractions, using appropriate tools and drawings | B2.9 multiply whole numbers by proper fractions, using appropriate tools and strategies |
| B2.10 divide whole numbers by proper fractions, using appropriate tools and strategies | ||
| 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 | ||
| B2.8 show simple multiplicative relationships involving whole-number rates, using various tools and drawings | B2.9 represent and create equivalent ratios and rates, using a variety of tools and models, in various contexts | B2.12 solve problems involving ratios, including percents and rates, using appropriate tools and strategies |