Mathematics

In this unit, children grow their number sense from 10 000 (in Grade 4) all the way to 100 000, and connect fractions and decimals to hundredths and to percents (percents are new this year).

They learn to read and write numbers to 100 000 and describe how big numbers are used in everyday life; use place value to build and break apart numbers in many ways; and compare and order numbers to 100 000.

Next they find equivalent fractions from halves to twelfths, change between improper fractions and mixed numbers, and compare and order fractions and mixed numbers using benchmarks and equivalent fractions.

Then they meet decimal hundredths: reading, writing and showing them with hundred grids, money and metre sticks; comparing and ordering them; and rounding them to the nearest tenth. Finally, they connect fractions, decimals and whole-number percents (for example 3/4 = 0.75 = 75%).

Along the way, children practise the social-emotional skills and mathematical processes of Strand A: explaining their thinking, trying more than one strategy, checking their work, persevering with tricky tasks 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. Whole-number and decimal calculations are in the separate Operations unit.

Curriculum expectations covered: A1, B1.1, B1.2, B1.3, B1.4, B1.5, B1.6, B1.7 (Ontario Mathematics, Grade 5, 2020).

In this unit you will become a powerful Grade 5 calculator and problem solver! First you will use the properties of operations to make math with whole numbers and decimals easier, and to check your work. You will learn all your multiplication and division facts up to 12 × 12, use mental math to multiply by 0.1 and 0.01, and estimate sums and differences of decimals. Then you will add and subtract whole numbers up to 100 000 and decimals to hundredths, and add and subtract fractions with like denominators. You will multiply 2-digit by 2-digit numbers and divide 3-digit by 2-digit numbers using area models and algorithms, and decide what to do with remainders. Finally you will solve multi-step problems, multiply and divide whole numbers by unit fractions (like 6 × 1/3 and 3 ÷ 1/4), and make equivalent ratios and rates.

Remember from Grade 4: you added and subtracted to 10 000 and with decimal tenths, learned facts to 10 × 10, multiplied and divided by 1-digit numbers, multiplied unit fractions by whole numbers, and used rates. Grade 5 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, with A1 (social-emotional learning skills and mathematical processes) woven in (Ontario Mathematics, Grade 5, 2020). Number sense (B1) is in its own unit.

In this unit, Grade 5 students build on the patterns, equations, inequalities, nested loops and modelling they learned in Grade 4. New this year: shrinking patterns in tables and graphs, term-number rules, hundredths, equivalent expressions, evaluating expressions, equations up to 100, inequalities with any one operation up to 50, and conditional statements in code.

• Patterns and relationships (C1): identify and describe repeating, growing and shrinking patterns, including real-life ones; create and translate growing and shrinking patterns with tables of values and graphs; determine pattern rules to extend patterns, make and justify predictions, and find missing elements; and create patterns that show relationships among whole numbers, tenths and hundredths.
• Equations and inequalities (C2): translate among words, algebraic expressions and pictures that describe equivalent relationships; evaluate expressions with whole numbers; solve equations with whole numbers up to 100 and verify them; and solve inequalities with one operation and whole numbers up to 50, then verify and graph the solutions.
• Coding (C3): write, run, read and change code that uses conditional statements (IF ... THEN ... ELSE) and other control structures like loops and REPEAT UNTIL, and describe how changes affect the outcome. All coding is done unplugged, on paper; no software is needed.
• Mathematical modelling (C4): use the steps understand, assume, model and solve, check and revise, share to plan a real-life event.

Throughout the unit, children practise 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 5, 2020).

In this unit, Grade 5 data scientists learn why who you ask matters. They explain populations and samples and use simple random, systematic random and stratified random sampling to get representative data. They collect data and organize it in relative-frequency tables, using fractions and decimals so groups of different sizes can be compared fairly. They read, choose and make graphs, including stacked-bar graphs (new this year), with proper titles, labels, legends, scales and sources, and justify their choices. They find the mean, median and mode of data with whole numbers and decimal numbers, create infographics, spot misleading graphs and claims, and use data to challenge preconceived notions and make convincing arguments and informed decisions.

The unit ends with probability: writing probabilities as fractions on a probability line from 0 to 1, making predictions and decisions, and comparing theoretical and experimental probability. Planning carefully, giving and using feedback, questioning respectfully 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 5, 2020).

In this unit you will become an angle measurer, a triangle builder, a transformation expert and an area problem-solver!

In geometry, you will compare angles with paper wedges, then measure and draw them in degrees with a protractor, using benchmark angles to estimate. You will sort triangles by their sides and angles, construct triangles from measurements, and check whether triangles, rectangles and parallelograms are congruent. You will draw top, front and side views of objects, plot points on coordinate grids with different scales, and translate, reflect and rotate shapes.

In measurement, you will choose metric units to estimate and measure length, area, mass and capacity, convert larger units to smaller ones, discover the formulas for the area of a parallelogram and a triangle, and show that shapes with the same area can have different perimeters.

Remember from Grade 4: you named angles as acute, right, obtuse or straight, plotted points on a grid, slid and flipped shapes, used metric prefixes, and found the area of rectangles. Grade 5 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, E1.5, 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 5, 2020).

In this unit you will learn how money works in the real world. First you will follow money as it moves between individuals, businesses and organizations: direct deposit, automatic payments, e-transfers, cards and more, and you will weigh the advantages and disadvantages of each. Next you will estimate and calculate totals and change with dollars and cents, including rounding cash totals to the nearest 5 cents. Then you will add Ontario's 13% HST (sales tax) to a purchase. After that you will design budgets for different earning and spending situations, learn what credit, debt and interest are and how they change people's choices, and use unit rates to find the best value when shopping for goods and services.

Remember from Grade 4: you learned methods of payment, found totals and change for whole-dollar prices, sorted needs and wants, made a saving plan, and compared pack sizes. Grade 5 builds on all of it. 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 5, 2020).