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Grades 7 & 8 Mathematics
This course covers the topics typically taught in Canadian Grade 7 and 8 Mathematics curricula and, in some instances, extends ideas beyond grade level. Letters are included beside the unit names to help group the units into similar themes.
For more information about the structure and general use of this courseware, see the Course Information unit.
Units
Representing and Comparing Numbers (N)
Part A (Lessons 1–7)
Topics include representing and comparing positive rational numbers (integers, fractions, and decimals), finding multiples and factors of positive integers, and determining the least common multiple (LCM) and the greatest common factor (GCF) of a pair of positive integers.
Part B (Lessons 8–12)
Topics include representing negative fractions and negative decimals, comparing the values of any two rational numbers, exponential notation, and using factor trees and prime factorizations to find the LCM or the GCF of a pair of positive integers.
Operations (N)
Part A (Lessons 1–11)
Topics include adding and subtracting rational numbers, multiplying and dividing a whole number by a positive rational number, and evaluating expressions using the order of operations.
Part B (Lessons 12–19)
Topics include multiplying, and dividing integers, fractions and decimal numbers, approximating square roots of positive integers, and evaluating expressions that include exponents using the order of operations.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
In this lesson, we revisit the order of operations for arithmetic. We solve problems involving integers, fractions, and decimals, paying special attention to exponents.
Ratios, Rates, and Proportions (N)
Part A (Lessons 1–6)
Topics include writing and interpreting ratios; finding equivalent ratios; converting between fractions, decimals, and percents; increasing and decreasing by a percentage; converting between units of measurement; and solving problems involving unit rates.
Part B (Lessons 7–11)
Topics include recognizing proportional situations in word problems, tables and graphs; connecting unit relates to proportional relationships and their representations in tables, graphs and equations; and fractional percents and percents greater than 100 percent.
Bisectors and Properties of Shapes (G)
Part A (Lessons 1–6)
Topics include constructions of angle bisectors and perpendicular bisectors, and the various properties of triangles, quadrilaterals, and more general polygons. In particular, different polygons are classified based on their side lengths and angle measurements.
Part B (Lessons 7–10)
Topics include quadrilateral diagonals, circle terminology and construction, and applications of circles in the real-world.
Area, Volume, and Angles (G)
Part A (Lessons 1–5)
Topics include calculating the area of parallelograms, triangles, trapezoids, and composite shapes; calculating the surface area, volume, and capacity of prisms; and representing 3D objects in different ways.
Part B (Lessons 6–10)
Topics include calculating the circumference and area of circles; calculating the volume and surface area of cylinders; and properties of angles formed by intersecting lines including parallel lines and transversals.
Transformations of Shapes (G)
Part A (Lessons 1–7)
Topics include congruence of polygons, triangle congruence rules, plotting points on the Cartesian plane, the image of a polygon on the Cartesian plane under translations, reflections and/or rotations on the Cartesian plane, and tessellations.
Part B (Lessons 8–11)
Topics include similarity of polygons, triangle similarity rules, dilatations of polygons, and indirect measurements.
Representing Patterns (A)
Part A (Lessons 1–6)
Topics include representing sequences using tables, general terms and graphs, describing patterns using variables and expressions, extending sequences, and solving problems involving unknown quantities.
Part B (Lessons 7–11)
Topics include equivalent expressions for the general term of a sequence, describing relationships and patterns using equations, and decreasing and naturally occurring sequences.
Equations and the Pythagorean Theorem (A)
Part A (Lessons 1–7)
Topics include using variables in expressions, equations, and inequalities, identifying and exploring linear relationships, solving equations and inequalities by inspection, trial and error, and using visual models, and simplifying expressions by collecting like terms.
Part B (Lessons 8-15)
Topics include solving equations and inequalities using algebraic techniques, comparing the differences between evaluating an expression and solving an equation, exploring equations with multiple variables, and the Pythagorean Theorem.
Data Collection and Graphs (D)
Part A (Lessons 1–5)
Topics include different types of data; population, sample and census; bias in data collection arising from question wording, accepted answers and choice of sample group; frequency and relative frequency tables and graphs; reading and creating circle graphs; choosing an appropriate graph type for a data set; bias in data representation arising from the chosen graph type, graph structure and shape, and axis labels and scales.
Part B (Lessons 6–9)
Topics include organizing continuous data into stem-and-leaf plots and frequency tables with intervals; as well as creating and reading histograms, and scatter plots.
Data Analysis (D)
Part A (Lessons 1–4)
Topics include determining the mean, median, and mode of data sets; studying the effects of adding data to a data set or removing data from a data set; exploring the effect of outliers on the mean, median, and mode; and practising drawing conclusions and making predictions from data in graphs.
Part B (Lessons 5–8)
Topics include interpreting data, histograms, and scatter plots and drawing conclusions from these graphs; describing relationships between the two variables in a scatter plot; estimating rates of change associated with scatter plots; making predictions supported by the data in histograms and scatter plots; and using appropriate measures of central tendency to compare two data sets.
Probability (D)
Part A (Lessons 1–4)
Topics include random experiments, outcomes, and events; calculating theoretical probabilities of single events; comparing probabilities of different events; independent events; experimental probability; and using probabilities to make predictions.
Part B (Lessons 5–8)
Topics include comparing theoretical probabilities and experimental probabilities; exploring how the number of trials impacts probability estimates; complementary events; setting up and running simulations using probability models; and revisiting independent events.