
Lesson 1: Adding Integers
We begin our discussion of addition by studying how number lines can be used to show addition. In this lesson, we focus on the addition of integers, specifically how positive and negative numbers can be added using a number line.

Lesson 2: Adding Integers: Mental Arithmetic
We can add integers without using a calculator or a number line. In this lesson, we extend our previous discussion on integer addition and examine strategies for performing integer addition mentally.

Lesson 3: Equivalent Fractions
This lesson explores equivalent fractions in preparation for when we must add and subtract fractions. In the process of finding equivalent fractions, you will be given the opportunity to practise finding common multiples, using improper fractions and mixed numbers, plotting on the number line, and comparing rational numbers.

Lesson 4: Adding Rational Numbers on the Number Line
In this lesson, we build upon our understanding of addition to include rational numbers. To do this, we revisit the number line and incorporate our strategies for plotting rational numbers so that we can find their sum.

Lesson 5: Adding Rational Numbers
This lesson introduces strategies for the addition of fractions without the use of a number line. We use number lines as motivation for finding a common denominator, then we move to adding fractions without the use of visual aids.

Lesson 6: Subtracting Integers
We begin our discussion of subtraction by focusing on the integers. In this lesson, we review the operation of subtraction, show subtraction on the number line, and learn how to subtract integers both with and without a number line.

Lesson 7: Subtracting Rational Numbers
Continuing our discussion on subtraction, in this lesson we explore strategies for subtracting fractions. Our goal is to use equivalent fractions to solve subtraction problems without the use of a calculator or the number line.

Lesson 8: Multiplying Whole Numbers by Rational Numbers
This lesson explores strategies for multiplying whole numbers by fractions and decimals. We solve examples and highlight rules for performing calculations without using a calculator.

Lesson 9: Multiplication as Scaling
Multiplication is the operation that is used to scale or resize a quantity. In this lesson, we explore scale factors and discuss why we must start thinking about multiplication in terms of scaling.

Lesson 10: Dividing Whole Numbers by Rational Numbers
In this lesson, we learn how to solve calculations that involve the division of whole numbers by fractions and decimals. Through examples, we highlight rules for performing these calculations without a calculator.

Lesson 11: Order of Operations
The order of operations is reviewed and used to perform calculations involving integers, fractions, and decimals. Additionally, we explore the importance of brackets; when they are needed and when they can be removed from an expression. We conclude by using the distributive property to simplify calculations.

Lesson 12: Multiplying Integers
In this lesson, we learn how to multiply integers mentally. Specifically, we look at how the sign of each integer in a product impacts the sign of the product.

Lesson 13: Dividing Integers
Division is the opposite operation of multiplication, and so the strategies we learn for dividing integers will be similar to those we used when multiplying integers. In this lesson, we examine how the signs of the dividend and divisor impact the sign of the quotient.

Lesson 14: Multiplying Fractions
We begin this lesson by reviewing how to multiply a fraction by a whole number. We then expand our understanding to include the multiplication of any two fractions. Additionally, some focus is given to estimating the values of products.

Lesson 15: Dividing Fractions
In this lesson, we review how to divide a whole number by a fraction. We then explore how to adapt this strategy in order to divide a fraction by another fraction, without the use of a calculator.

Lesson 16: Multiplying Decimals
We begin this lesson by examining the multiplication of decimal numbers by powers of ten, including a discussion of scientific notation. We then learn how to multiply two decimal numbers, first by converting the numbers to fractions, and second by working with the decimal numbers themselves.

Lesson 17: Dividing Decimals
In this lesson, we develop strategies to evaluate division expressions that involve whole numbers and decimal numbers. We also extend these strategies to discuss division with two decimal numbers.

Lesson 18: Square Roots of Positive Integers
This lesson focuses on the relationship between squaring a number and taking the square root of a number. We discuss perfect squares and examine how to approximate the square root of a positive integer that is not a perfect square.

Lesson 19: Order of Operations with Exponents
In this lesson, we revisit the order of operations for arithmetic. We solve problems involving integers, fractions, and decimals, paying special attention to exponents.