The Ontario Grade 5 math curriculum: what your child learns

Your child works with numbers to 100 000, fractions from halves to twelfths (including improper fractions and mixed numbers), and decimals to hundredths, and connects fractions, decimals and whole-number percents. They recall facts to 12 × 12, multiply two-digit by two-digit numbers with the area model and a written method, divide three-digit numbers by two-digit numbers, add and subtract fractions with like denominators, and work with equivalent ratios and rates.

Typical homework, with a hint

What your child learns in Number

• Reading numbers to 100 000B1.1

  Reads and shows numbers up to 100 000, breaks them into parts and puts them back together using suitable tools and strategies, and talks about where numbers are used in daily life.

• Comparing numbers to 100 000B1.2

  Compares numbers up to 100 000 and puts them in order, in different situations.

• Equivalent fractionsB1.3

  Shows equal fractions from halves to twelfths with suitable tools, including improper fractions (like 7/4) and mixed numbers (like 1 3/4), in different situations.

• Comparing fractionsB1.4

  Puts fractions from halves to twelfths in order from smallest to largest, including mixed numbers and improper fractions, in different situations.

• Decimals to hundredthsB1.5

  Reads, shows, compares and orders decimals with up to two decimal places (hundredths, like 3.47), in different situations.

• Rounding decimals to tenthsB1.6

  Rounds decimals to the closest tenth, in different situations.

• Fractions, decimals, and percentsB1.7

  Uses tools and drawings to show how fractions, decimals to hundredths and whole-number percents are related and when they are equal (like 1/4 = 0.25 = 25%), in different situations.

• Properties of operationsB2.1

  Uses how the operations work and relate to each other to solve problems with whole numbers and decimals (including ones that need more than one step) and check answers.

• Times tables to 12×12B2.2

  Knows the times tables from 0 × 0 to 12 × 12 by heart, and the division facts that go with them.

• Mental math with decimalsB2.3

  Multiplies a whole number by 0.1 or 0.01 in their head, estimates the answers to adding and subtracting decimals to hundredths mentally, and explains the strategies.

• Adding and subtracting decimalsB2.4

  Solves adding and subtracting problems with whole numbers that add up to 100 000 or less, and with decimals to hundredths, using suitable tools, strategies and written methods.

• Adding fractions, like denominatorsB2.5

  Adds and subtracts fractions that have the same denominator (like 2/8 + 3/8), in different situations.

• Two-digit multiplicationB2.6

  Solves problems that multiply a two-digit number by a two-digit number, both with the area model and with a written method, and explains how the two methods connect.

• Dividing by two digitsB2.7

  Solves problems that divide a three-digit number by a two-digit number, both with the area model and with a written method, explains how the two connect, and writes any remainder in a way that fits the problem.

• Multiplying by unit fractionsB2.8

  Uses tools and drawings to multiply and divide a one-digit number by a unit fraction (like 3 × 1/4 or 2 ÷ 1/3).

• Equivalent ratios and ratesB2.9

  Uses different tools and models to show and make equal ratios and rates (like 2:3 = 4:6), in different situations.

Patterns can now shrink as well as grow. Kids translate between words and algebraic expressions (“3 more than a number” becomes n + 3), evaluate expressions by substituting a value, solve equations with whole numbers up to 100, and solve one-step inequalities. Code uses conditional statements (“if this, then that”).

Typical homework, with a hint

What your child learns in Algebra

• Growing and shrinking patternsC1.1

  Finds and describes patterns that repeat, grow or shrink, including patterns in everyday life.

• Patterns in tables, graphsC1.2

  Makes growing and shrinking patterns, and shows them in different ways, including in tables of values and on graphs.

• Pattern rules and predictionsC1.3

  Works out the rule of a repeating, growing or shrinking pattern, and uses it to continue the pattern, predict what comes next (and explain why), and find missing pieces.

• Decimal number patternsC1.4

  Makes and describes patterns that show how whole numbers, decimal tenths and decimal hundredths are related.

• Words to algebraic expressionsC2.1

  Turns words into algebraic expressions and pictures, and back again, when they describe the same relationship (like “3 more than a number” and n + 3).

• Evaluating expressionsC2.2

  Works out the value of algebraic expressions with whole numbers (like 4n + 2 when n = 5).

• Solving equationsC2.3

  Solves equations with whole numbers up to 100 in different situations, and checks the answer.

• Solving inequalitiesC2.4

  Solves one-step inequalities with whole numbers up to 50, checks the answers, and shows them on a number line.

• Code with conditionsC3.1

  Writes and runs code to solve problems and show math situations, including code with “if… then” conditions and other ways of controlling what the code does.

• Reading and changing codeC3.2

  Reads and changes existing code with conditions and other control structures, and describes how the changes affect what happens.

Math modelling (C4): Turns a real-life situation into math (a model) to represent it, analyse it, make predictions and understand it better.

Kids learn why a good sample matters, organise data in relative-frequency tables, choose graphs (including stacked-bar graphs), and spot misleading graphs. They find the mean, median and mode with decimals too. Probability is written as a fraction, and they compare what should happen (theoretical) with what did happen (experimental).

Typical homework, with a hint

What your child learns in Data

• Sampling techniquesD1.1

  Explains why the way you choose a sample matters, so that the data you collect fairly represents the whole group.

• Relative-frequency tablesD1.2

  Collects data about a group (using a sample when needed) to answer questions, and organizes it in relative-frequency tables (showing each count as a fraction, decimal or percent of the total).

• Choosing the right graphD1.3

  Picks the best type of graph for a set of data, including stacked-bar graphs, gives it a title, labels, a suitable scale and the data source, and explains why that graph fits.

• Making an infographicD1.4

  Makes an infographic that tells the story of a data set, using relative-frequency tables, stacked-bar graphs and any other useful information.

• Mean, median, and modeD1.5

  Works out the mean (average) and median (middle value) and finds the mode (most common value, if any) of sets of whole-number and decimal data, and explains what each one tells you.

• Spotting misleading graphsD1.6

  Questions data shown in stacked-bar graphs and other ways, spots graphs that mislead, challenges assumptions, draws conclusions, and uses them to back up arguments and make good decisions.

• Probability as fractionsD2.1

  Writes the chance of something happening as a fraction, marks it on a probability line, and uses it to make predictions and decisions.

• Theoretical vs experimental probabilityD2.2

  Works out and compares the theoretical probability of an event (what should happen) and the experimental probability (what happens when you try it).

Geometry covers types of triangles, congruent shapes, and drawing top, front and side views. Kids plot points with different scales and do translations, reflections and rotations up to 180°. In measurement they convert metric units (like metres to centimetres), use a protractor, find the area of triangles and parallelograms, and see that shapes with the same area can have different perimeters.

Typical homework, with a hint

What your child learns in Spatial Sense

• Types of trianglesE1.1

  Describes the properties of triangles, and draws different kinds of triangles from given side lengths or angles.

• Congruent shapesE1.2

  Recognizes and draws congruent (identical) triangles, rectangles and parallelograms.

• Top, front, side viewsE1.3

  Draws an object as seen from the top, the front and the side, and matches drawings like these to the objects.

• Coordinates with scalesE1.4

  Plots and reads points on a coordinate grid (first quadrant) with different scales, and describes the slides that move a point from one spot to another.

• Translations, reflections, rotationsE1.5

  Describes and carries out slides (translations), flips (reflections) and turns (rotations) of up to 180° on a grid, and predicts where a shape will end up.

• Choosing metric unitsE2.1

  Estimates and measures length, area, mass and capacity in suitable metric units.

• Converting metric unitsE2.2

  Solves problems that change bigger metric units into smaller ones (like metres to centimetres), and explains how metric units are related by powers of ten.

• Comparing anglesE2.3

  Compares angles to see which is bigger, by laying one on another and by measuring with everyday units.

• Using a protractorE2.4

  Explains how a protractor works, uses one to measure and draw angles up to 180°, and estimates other angles from known ones (like 45° and 90°).

• Area of triangles, parallelogramsE2.5

  Uses how rectangles, parallelograms and triangles are related to work out the area formulas for a parallelogram and a triangle, and solves problems with them.

• Same area, different perimeterE2.6

  Shows that two shapes can cover the same area but have different perimeters, and solves problems about it.

Money gets real: how money moves between people and businesses, totals with sales tax, simple budgets, credit and debt, unit rates to find the best value, and the kinds of taxes collected by different levels of government in Canada.

Typical homework, with a hint

What your child learns in Financial Literacy

• How money movesF1.1

  Describes several ways money moves between people, organizations and businesses (like e-transfers, cheques or cards).

• Costs with sales taxF1.2

  Estimates and works out what several items cost together, with prices in dollars and cents and sales tax added, using different strategies.

• Making a budgetF1.3

  Plans simple sample budgets for different situations of earning and spending money.

• Credit and debtF1.4

  Explains what credit and debt are, and how each one can affect money decisions.

• Unit rates, best valueF1.5

  Works out unit rates (like the price per 100 g) for different goods and services, and finds which is the best value.

• Taxes in CanadaF1.6

  Describes the kinds of taxes collected by the federal, provincial and local governments in Canada, and how that money pays for community services.

The Ontario curriculum also has a strand A that runs through all the others. It’s about how kids approach math: managing frustration, keeping at a hard problem, and using the mathematical processes (such as problem solving, reasoning, connecting, representing and communicating). It has no homework of its own, but it’s exactly what a patient, hint-based tutor helps build.

How to help with Grade 5 math at home

• Use money to make decimals and percents concrete: 25¢ is 0.25 of a dollar and 25% of a dollar.
• For fractions, draw it. A quick sketch of pieces clears up most confusion.
• Ask “is your answer reasonable?” after every calculation. Estimating first catches big mistakes.
• Let your child compare unit prices at the grocery store.

More ideas: how to help with math homework without giving the answer.

How Astuzo helps with Grade 5 math

In Grade 5 many mistakes hide in the middle of a long calculation. When an answer is off, Spark doesn’t just say “wrong”. It asks your child to walk through their steps and helps them find the slip themselves, which is how kids learn to check their own work.

You set your child’s grade once, and Spark pitches every hint at that level. You get a short email each evening they use it, showing what they worked on. See how Astuzo works.