Mathematics

In this unit, children grow their number sense from 100 000 (in Grade 5) all the way to one million, meet integers (numbers below zero), and extend decimals from hundredths to thousandths.

They learn to read and write whole numbers to one million, use place value to build and break them apart, compare and order them and describe how big numbers are used in everyday life. Next they read and represent integers on horizontal and vertical number lines (temperature, elevation, building floors) and compare and order them.

Then they read, write, compare and order decimals to thousandths, round terminating and repeating decimals to the nearest whole number, tenth or hundredth, and show equivalences between fractions and decimals up to thousandths (for example 3/8 = 0.375). The unit ends by comparing and ordering integers, decimals and fractions together.

Along the way, children practise the social-emotional skills and mathematical processes of Strand A: explaining their thinking, choosing and checking strategies, persevering when a problem is tricky and being a good sport in games. Each lesson includes worked examples, pictures, a hands-on activity with things from home, practice questions with answers, a short quiz and notes for the grown-up helping. Calculations, including ratios, rates and percents, are in the separate Operations unit.

Curriculum expectations covered: A1, B1.1, B1.2, B1.3, B1.4, B1.5, B1.6 (Ontario Mathematics, Grade 6, 2020).

In this unit you will become a powerful Grade 6 problem solver! You will use the order of operations and the properties of operations to work with whole numbers, decimals and fractions. You will learn divisibility rules for 2, 3, 4, 5, 6, 8, 9 and 10, and break numbers into prime factors with factor trees. You will find percents like 1%, 5%, 10%, 15%, 25% and 50% in your head. Then you will add and subtract whole numbers up to one million and decimals to thousandths, and fractions and mixed numbers with unlike denominators. You will multiply and divide three-digit whole numbers by decimal tenths (like 324 × 0.7 and 240 ÷ 0.6), divide decimals by whole numbers, and multiply and divide whole numbers by proper fractions. Finally you will solve problems with ratios, rates and percents, including sale prices and sales tax, and put everything together in multi-step problems.

Remember from Grade 5: you used properties, learned facts to 12 × 12, added and subtracted fractions with like denominators, multiplied and divided whole numbers by unit fractions, multiplied by 0.1 and 0.01, and made equivalent ratios and rates. Grade 6 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, B2.11, B2.12, with A1 (social-emotional learning skills and mathematical processes) woven in (Ontario Mathematics, Grade 6, 2020). Number sense (B1) is in its own unit.

In this unit, Grade 6 students build on the patterns, expressions, equations, inequalities, conditional code and modelling they learned in Grade 5. New this year: linear growing patterns and their algebraic expressions and equations (like t = 3n + 1), solving for unknown term numbers, patterns with thousandths, adding monomials with tools, evaluating expressions with decimal tenths, equations with multiple terms, inequalities with two operations up to 100, efficient code with ELSE IF, and describing how code changes affect efficiency.

• Patterns and relationships (C1): identify and describe repeating, growing and shrinking patterns, including real-life ones, and say which growing patterns are linear; represent patterns with tables of values, graphs, expressions and equations; use pattern rules to extend patterns, justify predictions, find missing elements and solve for unknown values; and create patterns that relate whole numbers and decimals.
• Equations and inequalities (C2): add monomials with a degree of 1, using tools; evaluate expressions with whole numbers and decimal tenths; solve equations with multiple terms and verify; and solve inequalities with two operations, then verify and graph the solutions.
• Coding (C3): write and execute efficient code with conditional statements and other control structures, and read and alter code, describing how changes affect its outcome and efficiency. All coding is unplugged, written on paper and run by hand; no software is needed.
• Mathematical modelling (C4): use the steps understand, assume, model and solve, check and revise, share to plan a winter carnival hot chocolate stand.

Throughout the unit, children practise reasoning, explaining their thinking, checking their work and keeping going when something is hard (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 6, 2020).

In this unit, Grade 6 data scientists learn the difference between discrete data (counted) and continuous data (measured). They plan how to collect qualitative, discrete and continuous data about a population and organize it in frequency tables, including equal intervals. They make and read two new kinds of graphs, histograms and broken-line graphs, and learn to choose and justify the best graph, with proper titles, labels, scales and sources. They find the range (a measure of spread, new this year) along with the mean, median and mode, and use these measures to compare two or more data sets and make informed decisions. They build infographics, catch misleading graphs, challenge preconceived notions and make convincing arguments.

The unit ends with probability: writing probabilities as fractions, decimals and percents on a probability line, making predictions and informed decisions, and finding and comparing the theoretical and experimental probabilities of two independent events, using tree diagrams and tables. Planning carefully, 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 6, 2020).

In this unit you will become a shape detective, a builder, a grid navigator, an angle expert and a surface-area problem-solver!

In geometry, you will list the properties of quadrilaterals, including their diagonals, lines of symmetry and rotational symmetry. You will build 3D objects when you are given their top, front and side views. You will plot and read points in all four quadrants of the Cartesian plane, using negative numbers, and you will perform and combine translations, reflections and rotations (up to 360°) and predict where shapes will land.

In measurement, you will convert metric units from smaller to larger and back again, measure and draw angles up to 360°, and use complementary, supplementary, opposite, interior and exterior angles to find unknown angles without measuring. You will find the areas of trapezoids, rhombuses, kites and composite polygons by decomposing them, make nets of prisms and pyramids, and calculate surface area.

Remember from Grade 5: you measured angles up to 180° with a protractor, drew views of objects, plotted points in the first quadrant with different scales, translated, reflected and rotated shapes by quarter and half turns, converted larger units to smaller ones, and found the areas of parallelograms and triangles. Grade 6 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, with A1 (social-emotional learning skills and mathematical processes) woven in (Ontario Mathematics, Grade 6, 2020).

In this unit you will learn to make informed money decisions. First you'll compare methods of payment (cash, debit, credit, prepaid and gift cards, mobile wallets, e-transfers, cheques and "buy now, pay later") and find the real cost of a purchase once tax, fees and interest are added. Next you'll set earning and saving goals and plan the steps to reach them, and look at the factors that help or get in the way, including your own feelings and advertising. Then you'll learn what interest rates are, how you can earn interest on savings or pay it on loans, and which fees banks and credit unions charge. Finally you'll explore trading, lending, borrowing and donating as ways people and organizations share money and other resources.

Remember from Grade 5: you followed money between individuals, businesses and organizations, added 13% HST, designed budgets, learned about credit, debt and interest, and used unit rates. Grade 6 builds on all of it. All fees and interest rates in this unit are example amounts; 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 6, 2020).