Mathematics

In this unit you will grow your number sense in two directions: very big and in between.

First you will read, write, compare and round whole numbers up to one billion, and write them in expanded form using powers of ten (like 3 × 10⁸ + 4 × 10⁶). You will see how big numbers are used in everyday life, from distances in space to computer storage. Next you will meet perfect squares (like 144 = 12²) and find their square roots (√144 = 12), for example to find the side of a square backyard rink.

Then you will work with rational numbers: positive and negative fractions and decimals, like −3/4 and −4.5°C. You will place them on number lines, compare and order them, simplify fractions with equivalent fractions, find fractions and decimals between any two numbers, round decimals in real situations, and convert between fractions, decimals and percents, including percents over 100% and under 1%.

Remember from Grade 6: you worked with numbers to one million, integers, decimals to thousandths, rounding, and fractions and decimals to thousandths. Grade 7 builds on all of it. 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, B1.5, B1.6, B1.7, with A1 woven in (Ontario Mathematics, Grade 7, 2020). Operations (B2), including general exponents, greatest common factor, percent increases and decreases, and operations with integers, fractions and decimals, are in the Operations unit.

In this unit you will become a stronger and faster Grade 7 problem solver. You will write repeated multiplication with exponents and use the full order of operations (BEDMAS). You will find the greatest common factor and lowest common multiple of two or three numbers, and use them to add and subtract fractions. Then you will multiply and divide fractions by fractions and decimals by decimals. You will add and subtract integers with chips and number lines, learn common percent, fraction and decimal equivalents by heart, increase and decrease numbers by a percent in your head, and tell proportional situations from non-proportional ones.

Remember from Grade 6: you used the order of operations without exponents, made factor trees, added and subtracted fractions with unlike denominators, multiplied and divided with decimal tenths and whole numbers by fractions, compared integers on a number line, and solved ratio, rate and percent problems. Grade 7 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: B2.1, B2.2, B2.3, B2.4, B2.5, B2.6, B2.7, B2.8, B2.9, B2.10, with A1 (social-emotional learning skills and mathematical processes) woven in (Ontario Mathematics, Grade 7, 2020). Number sense (B1) is in its own unit.

In this unit, Grade 7 students build on the patterns, equations, inequalities, coding and modelling they learned in Grade 6. New this year: comparing linear patterns by their constant rate and initial value; patterns with decimal numbers and with integers; subtracting as well as adding monomials; evaluating expressions with any decimals and more than one variable; equations with decimals and inequalities with multiple terms, graphed with open or closed circles; and code with events influenced by a defined count and sub-programs.

• Patterns and relationships (C1): identify and compare repeating, growing and shrinking patterns, including real-life ones; compare linear patterns by constant rate and initial value; create and translate patterns using objects, words, tables, graphs, expressions and equations; find missing elements and solve for unknown values; and create patterns that show relationships among integers.
• Equations and inequalities (C2): add and subtract monomials with a degree of 1, using tools; evaluate expressions with whole numbers and decimals; solve equations with multiple terms, whole numbers and decimals, and verify; and solve inequalities with multiple terms, then verify and graph the solutions.
• Coding (C3): write and run efficient code with counters and sub-programs, and read and alter code, describing how changes affect its 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 choose a plan for a winter ski club.

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 7, 2020).

In this unit, Grade 7 data scientists use percentages to describe the distribution of data for a population or a sample, and explain why percentages make large data sets and groups of different sizes easier to understand and compare. They plan how to collect qualitative, discrete and continuous data with fair samples and unbiased questions, and organize it in tables with a percentage column. They learn a new kind of graph, the circle graph: reading it, connecting percentages to angles (1% = 3.6°), and drawing it with a protractor. They choose and justify the best graph for a data set, build infographics with tables and circle graphs, and see how adding or removing data changes the mean, median and mode and the shape of a distribution (clusters, gaps, outliers, symmetric or skewed). They analyse circle graphs and misleading graphs, challenge preconceived notions, and make convincing arguments and informed decisions.

The unit ends with probability: telling independent events from dependent events (with and without replacement), finding the theoretical probability of two independent or two dependent events with tables and tree diagrams, and comparing it with experimental probability from real experiments.

Remember from Grade 6: you made relative-frequency tables, histograms and broken-line graphs, found the mean, median, mode and range, built infographics, caught misleading bar and line graphs, and found probabilities of two independent events. Grade 7 builds on all of it. Planning, giving and using feedback, questioning respectfully, working together 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 7, 2020).

In this unit you will become a 3D object classifier, a scale designer, a transformation expert and a circle and cylinder pro!

In geometry, you will describe and classify prisms, pyramids and cylinders by their properties, including planes of symmetry and rotational symmetry. You will draw top, front, side and perspective views using a scale, and build scale models. You will perform dilations and explain why the image is similar to the original, and you will describe translations, reflections and rotations on the Cartesian plane with coordinate rules and predict where shapes will land.

In measurement, you will compare volume and capacity (1 cm³ = 1 mL), convert metric units of length, area and volume in real problems, discover the number π and use it to find the circumference of a circle, construct circles from a radius, diameter or circumference, explain and use the formula for the area of a circle, find the surface area of cylinders from their nets, and show that the volume of any prism or cylinder is the area of its base times its height.

Remember from Grade 6: you described quadrilaterals and their symmetry, built objects from views, transformed shapes in all four quadrants, converted metric units, worked with angles, and found the areas of polygons and the surface areas of prisms and pyramids. Grade 7 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, E2.5, E2.6, E2.7, with A1 (social-emotional learning skills and mathematical processes) woven in (Ontario Mathematics, Grade 7, 2020).

In this unit you'll learn to make informed financial decisions. First you'll compare exchange rates and convert money between Canadian dollars and other currencies, including buy and sell rates and fees. Next you'll learn to find reliable sources of financial information and spot scams. Then you'll create, track and adjust budgets for longer-term goals for students and families. You'll describe the personal and societal factors (like feelings, values, advertising, inflation and technology) that shape money decisions. Finally, you'll see how interest rates affect savings, investments and the cost of borrowing over time.

Remember from Grade 6: you compared methods of payment, set financial goals, explored what helps or gets in the way of those goals, and learned about interest rates and fees for one year. Grade 7 builds on all of it. All exchange rates, interest rates, prices 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, with A1 (social-emotional learning skills and mathematical processes) woven in (Ontario Mathematics, Grade 7, 2020).