Mathematics

In this unit you will stretch your number sense in three directions: very big and very small, the whole number line, and flexible forms.

First you will write very large numbers (like the distance to the Sun) and very small numbers (like the width of a red blood cell) in scientific notation, such as 1.5 × 10⁸ and 7.5 × 10⁻⁶. You will compare them and see how they are used every day, from phone storage to metric prefixes.

Next you will explore the real number system: natural numbers, whole numbers, integers, rational numbers and the new irrational numbers, like √2 and π, whose decimals never end and never repeat. You will compare and order all kinds of real numbers on a number line.

Then you will estimate square roots that are not whole numbers, like √50 ≈ 7.07, and use square roots of decimals and fractions to solve real problems with squares and circles.

Finally, you will use fractions, decimals and percents interchangeably, including percents over 100% and under 1%, to solve problems with sales tax, discounts, snowfall, savings and recipes.

Remember from Grade 7: you worked with numbers to one billion and powers of ten, perfect squares and their square roots, rational numbers, and conversions between fractions, decimals and percents. Grade 8 builds on all of it, and gets you ready for high school math. Every lesson has hands-on activities you can do at home, lots of practice and a short quiz. Strand A skills (social-emotional learning and mathematical processes) are woven in: explaining your thinking, choosing strategies, checking and persevering.

Curriculum expectations covered: B1.1, B1.2, B1.3, B1.4, with A1 woven in (Ontario Mathematics, Grade 8, 2020). Operations (B2), including recalling square numbers, multiplying and dividing by powers of ten mentally, and operations with integers, fractions and proportions, are in the Operations unit.

In this unit you will become a confident Grade 8 calculator and problem solver. You will use properties of operations and the order of operations with fractions, decimals and exponents, recall square numbers and square roots by heart, and multiply and divide by powers of ten in your head. You will choose strategies to add and subtract integers, and you will learn something brand new: how to multiply and divide integers. You will add, subtract, multiply and divide fractions and mixed numbers, including some negative fractions. Finally, you will compare rates and ratios to find the better choice and use proportional reasoning to solve problems with maps, recipes, discounts and 13% HST.

Remember from Grade 7: you used exponents and BEDMAS, found the GCF and LCM, added and subtracted fractions, multiplied and divided fractions by fractions and decimals by decimals, added and subtracted integers, and told proportional situations from non-proportional ones. Grade 8 builds on all of it and gets you ready for Grade 9 math. Every lesson has hands-on activities you can do at home, lots of practice and a short quiz.

Curriculum expectations covered: B2.1, B2.2, B2.3, B2.4, B2.5, B2.6, B2.7, B2.8, with A1 (social-emotional learning skills and mathematical processes) woven in (Ontario Mathematics, Grade 8, 2020). Number sense (B1) is in its own unit.

In this unit, Grade 8 students build on the patterns, equations, inequalities, coding and modelling they learned in Grade 7. New this year: patterns with all rational numbers (fractions, decimals and integers); using patterns to explain relationships such as why a negative times a negative is positive; adding binomials with algebra tiles and zero pairs; evaluating expressions with negatives and fractions; equations with integers, including variables on both sides; inequalities with integers, including reversing the sign when dividing by a negative; and code that analyses data to inform decisions.

• Patterns and relationships (C1): identify and compare repeating, growing and shrinking patterns, including linear patterns by their constant rate and initial value; create and translate patterns with rational numbers using tables, graphs, expressions and equations; determine pattern rules, justify predictions, find missing terms and solve for unknown values; and create patterns that show relationships among rational numbers.
• Equations and inequalities (C2): add and subtract monomials and add binomials with algebra tiles; evaluate expressions with rational numbers; solve and verify equations with multiple terms, integers and decimals; and solve, verify and graph inequalities with integers.
• Coding (C3): write code with lists and loops to find totals, means, highest values and counts, and use the results to make decisions; read and alter data code, describing how changes affect the outcome and efficiency. All coding is unplugged: written on paper and run by hand, so no software or device is needed.
• Mathematical modelling (C4): use the steps understand, assume, model, check and revise, share to plan a maple syrup project, revising the model when real data comes in.

Throughout the unit, students practise perseverance, checking their work, managing frustration while debugging, and explaining their reasoning (Strand A).

Curriculum expectations covered: C1.1, C1.2, C1.3, C1.4, C2.1, C2.2, C2.3, C2.4, C3.1, C3.2, C4, with A1 (social-emotional learning skills and the mathematical processes) woven in (Ontario Mathematics, Grade 8, 2020).

In this unit, Grade 8 data scientists move from describing one variable to exploring how two variables are related. They decide when a question needs one-variable or two-variable data, plan investigations and collect continuous two-variable data in a table of values, and make scatter plots with proper titles, labels, scales and sources. They choose and justify the best graph for a data set, describe relationships as strong or weak and positive, negative or none, with and without outliers, and use simple trend lines to make predictions (a first look at the lines of best fit in Grade 9). They learn that a relationship does not prove a cause, spot misleading graphs and claims, challenge preconceived notions, and build infographics with tables and scatter plots.

The unit ends with probability: using Venn diagrams for and, or and not, and tree diagrams to find and compare the theoretical and experimental probabilities of multiple independent and multiple dependent events.

Remember from Grade 7: you used percentages and circle graphs, saw how adding or removing data changes the mean, median and mode, and found probabilities of two independent or two dependent events. Grade 8 builds on all of it. Thinking critically, communicating, giving and using feedback, and persevering (Strand A) are woven through the lessons.

Curriculum expectations covered: D1.1, D1.2, D1.3, D1.4, D1.5, D1.6, D2.1, D2.2, with A1 (Ontario Mathematics, Grade 8, 2020).

In this unit you will become an angle detective, a tessellation designer, a transformation expert, a model builder and a measurement pro!

In geometry, you will use the angles formed when a transversal crosses parallel lines, find the interior and exterior angles of any polygon, discover which shapes tessellate and the translations, reflections and rotations inside tessellations, and perform and predict reflections, rotations and dilations on the Cartesian plane, including centres other than the origin. You will choose appropriate scales to build models from views, and use scale drawings to find real lengths and areas and to redraw plans at new scales.

In measurement, you will work with very large and very small metric units (mega, giga, tera, micro, nano, pico) using powers of 10, describe the Pythagorean relationship with squares on the sides of a right triangle and use it to find unknown side lengths, and find the perimeter, area, surface area and volume of composite shapes and objects.

Remember from Grade 7: you classified 3D objects, drew views and built scale models, dilated shapes from the origin, used coordinate rules for transformations, converted metric units, and found circumference, the area of a circle, and the surface area and volume of prisms and cylinders (with π ≈ 3.14). Grade 8 builds on all of it. Every lesson has hands-on activities you can do at home, lots of practice and a short quiz.

Curriculum expectations covered: E1.1, E1.2, E1.3, E1.4, E2.1, E2.2, E2.3, E2.4, with A1 (social-emotional learning skills and mathematical processes) woven in (Ontario Mathematics, Grade 8, 2020).

In this unit you'll make informed financial decisions like a smart consumer about to start high school. First you'll compare ways to pay when other currencies and exchange rates are involved. Next you'll create a financial plan for a long-term goal, including income, expenses and taxes (HST, income tax and paycheque deductions). Then you'll learn ways to keep a budget balanced and tools to track income and spending for different scenarios. You'll compare simple and compound interest, use spreadsheets to explore growth at different rates, and see how interest affects long-term plans. Finally, you'll find better value when shopping (sales, unit prices, loyalty programs) and compare credit cards and consumer contracts.

Remember from Grade 7: you converted currencies, found reliable sources of financial information, created and adjusted budgets, explored personal and societal factors in money decisions, and saw how interest affects savings and borrowing over time. Grade 8 builds on all of it. All exchange rates, interest rates, prices, wages and fees in this unit are example amounts in Canadian dollars; real ones vary and change over time. Every lesson has hands-on activities, lots of practice and a short quiz.

Curriculum expectations covered: F1.1, F1.2, F1.3, F1.4, F1.5, F1.6, with A1 (social-emotional learning skills and mathematical processes) woven in (Ontario Mathematics, Grade 8, 2020).