The Ontario Grade 6 math curriculum: what your child learns

Your child reads whole numbers to one million, places integers (including negative numbers) on number lines, and compares integers, decimals and fractions. They use divisibility rules, find percents mentally (like 10%, 15% and 25%), add and subtract fractions with unlike denominators, make factor trees, multiply and divide by decimal tenths and by fractions, and solve ratio, rate and percent problems.

Typical homework, with a hint

What your child learns in Number

• Numbers to one millionB1.1

  Reads and shows numbers as large as one million with suitable tools and strategies, and talks about where such numbers are used in daily life.

• Integers on number linesB1.2

  Reads and shows integers (positive and negative whole numbers) with different tools and strategies, including number lines that go across and up and down.

• Comparing integers, decimals, fractionsB1.3

  Puts integers, decimals and fractions in order and compares them, both on their own and mixed together, in different situations.

• Decimals to thousandthsB1.4

  Reads, shows, compares and orders decimals with up to three decimal places (thousandths, like 2.375), in different situations.

• Rounding decimalsB1.5

  Rounds decimals, including ones that end and ones that repeat (like 0.333…), to the closest whole number, tenth or hundredth as needed, in different situations.

• Fractions and decimalsB1.6

  Uses tools and drawings to show how fractions and decimals to thousandths are related and when they are equal (like 3/8 = 0.375), in different situations.

• Properties of operationsB2.1

  Uses how the operations work and relate to each other to solve problems with whole numbers, decimals, fractions, ratios, rates and whole-number percents, including problems with several steps or operations.

• Divisibility rulesB2.2

  Understands the divisibility rules and uses them to tell whether a number can be divided evenly by 2, 3, 4, 5, 6, 8, 9 or 10.

• Mental math percentsB2.3

  Works out percents of whole numbers in their head, such as 1%, 5%, 10%, 15%, 25% and 50%, and explains the strategies.

• Adding and subtracting decimalsB2.4

  Solves adding and subtracting problems with whole numbers and decimals, estimating first and using written methods.

• Adding fractions, unlike denominatorsB2.5

  Adds and subtracts fractions with the same or different denominators (like 1/2 + 1/3), using suitable tools, in different situations.

• Prime factors and treesB2.6

  Writes composite numbers as a product of prime numbers, for example with a factor tree (24 = 2 × 2 × 2 × 3).

• Multiplying by decimal tenthsB2.7

  Solves problems that multiply a three-digit whole number by a decimal tenth (like 245 × 0.3), using written methods.

• Dividing by decimal tenthsB2.8

  Solves problems that divide a three-digit whole number by a decimal tenth (like 360 ÷ 0.4), using suitable tools, strategies and written methods, and writes remainders in a way that fits the problem.

• Multiplying by fractionsB2.9

  Multiplies whole numbers by proper fractions (like 12 × 3/4), using suitable tools and strategies.

• Dividing by fractionsB2.10

  Divides whole numbers by proper fractions (like 6 ÷ 2/3), using suitable tools and strategies.

• Dividing decimalsB2.11

  Solves problems that divide a decimal with up to three decimal places by a whole number up to 10 (like 4.536 ÷ 6), using suitable tools and strategies.

• Ratios, rates, and percentsB2.12

  Solves ratio problems, including ones about percents and rates, using suitable tools and strategies.

Kids identify linear growing patterns and describe them with algebraic expressions and equations, then use those rules to find unknown values. They add like terms with a variable (like 2x + 3x), evaluate expressions with decimals, solve equations with several terms, and solve two-step inequalities. In coding, they write and improve efficient code.

Typical homework, with a hint

What your child learns in Algebra

• Linear growing patternsC1.1

  Finds and describes patterns that repeat, grow or shrink, including patterns in everyday life, and says which growing patterns are linear (grow by the same amount each step).

• Patterns as equationsC1.2

  Makes repeating, growing and shrinking patterns and shows them in different ways, including tables of values and graphs, and writes linear growing patterns as algebraic expressions and equations.

• Pattern rules and unknownsC1.3

  Works out pattern rules to continue repeating, growing and shrinking patterns, predict what comes next (and explain why) and find missing pieces, and uses an algebraic rule to find unknown values in linear growing patterns.

• Decimal number patternsC1.4

  Makes and describes patterns that show how whole numbers and decimals are related.

• Adding monomialsC2.1

  Uses tools to add simple algebra terms with one variable and whole numbers (like 2x + 3x = 5x).

• Evaluating expressionsC2.2

  Works out the value of algebraic expressions with whole numbers and decimal tenths (like 3n + 1.5 when n = 4).

• Solving multi-term equationsC2.3

  Solves equations with several terms and whole numbers (like 2x + 5 = x + 9) in different situations, and checks the answer.

• Two-step inequalitiesC2.4

  Solves two-step inequalities with whole numbers up to 100, checks the answers, and shows them on a number line.

• Writing efficient codeC3.1

  Writes and runs efficient code to solve problems and show math situations, including code with “if… then” conditions and other control structures.

• Reading and improving codeC3.2

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

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 the difference between discrete data (counted, like number of siblings) and continuous data (measured, like height), group data into intervals, and use histograms and broken-line graphs. They find the range and the mean, median and mode to compare data sets, spot misleading graphs, and find the probability of two independent events, like flipping a coin and rolling a die.

Typical homework, with a hint

What your child learns in Data

• Discrete vs continuous dataD1.1

  Explains the difference between discrete data (counted, like number of siblings) and continuous data (measured, like height), and gives examples of each.

• Collecting data in intervalsD1.2

  Collects data in words or categories, and counted or measured numbers, to answer questions about a group, and organizes it in a suitable way, including in intervals (like ages 0–4, 5–9).

• Histograms and line graphsD1.3

  Picks the best type of graph for a set of data, including histograms and broken-line 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 tables, histograms, broken-line graphs and any other useful information.

• Range and central tendencyD1.5

  Works out the range (how spread out the data is) and the mean, median and mode, and uses them to compare two or more sets of data.

• Spotting misleading graphsD1.6

  Questions data shown in histograms, broken-line 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 percentsD2.1

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

• Probability of two eventsD2.2

  Works out and compares what should happen (theoretical probability) and what does happen in experiments (experimental probability) for two independent events, like flipping a coin and rolling a die.

Geometry covers the properties of quadrilaterals (including diagonals and symmetry), building objects from top, front and side views, plotting points in all four quadrants, and combining translations, reflections and rotations. Measurement includes metric conversions both ways, angles up to 360°, unknown angles (supplementary, complementary, opposite), areas of trapezoids, rhombuses and kites, nets, and surface area of prisms and pyramids.

Typical homework, with a hint

What your child learns in Spatial Sense

• Properties of quadrilateralsE1.1

  Makes lists of the properties of different quadrilaterals (four-sided shapes), including their diagonals, rotational symmetry and lines of symmetry.

• Building from viewsE1.2

  Builds 3D objects from drawings of their top, front and side views.

• Four-quadrant coordinatesE1.3

  Plots and reads points in all four quadrants of a coordinate grid, and describes the slides that move a point from one spot to another.

• Combining transformationsE1.4

  Describes and carries out combinations of slides, flips and turns (up to 360°) on a grid, and predicts where a shape will end up.

• Converting metric unitsE2.1

  Measures length, area, mass and capacity in suitable metric units, and solves problems that change smaller units into larger ones and larger into smaller.

• Protractor to 360°E2.2

  Uses a protractor to measure and draw angles up to 360°, and explains how an angle measured clockwise relates to the same angle measured counterclockwise.

• Finding unknown anglesE2.3

  Finds missing angles using the properties of supplementary, complementary and opposite angles, and of interior and exterior angles.

• Area of composite shapesE2.4

  Finds the area of trapezoids, rhombuses, kites and combined shapes by splitting them into shapes whose area they already know how to find.

• Nets and surface areaE2.5

  Makes and uses nets (flat patterns that fold into a 3D shape) to show how the faces of prisms and pyramids add up to their surface area.

• Surface area of prismsE2.6

  Finds the surface area of prisms and pyramids by working out the area of each flat face and adding them up.

Financial literacy in Grade 6 covers the pros and cons of different ways to pay, setting earning and saving goals and what helps or gets in the way of reaching them, interest rates and bank fees, and different ways to share resources (trading, lending, borrowing and donating).

Typical homework, with a hint

What your child learns in Financial Literacy

• Comparing ways to payF1.1

  Describes the pros and cons of different ways to pay for things, such as cash, debit and credit cards.

• Setting financial goalsF1.2

  Names different kinds of money goals, including earning and saving goals, and lists key steps to reach them.

• Reaching financial goalsF1.3

  Describes things that can help or get in the way of reaching a money goal.

• Interest rates and feesF1.4

  Explains what an interest rate is, and the kinds of interest rates and fees that banks and other financial institutions charge on accounts and loans.

• Trading, lending, donatingF1.5

  Describes how people and organizations share money and other resources by trading, lending, borrowing and donating.

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 6 math at home

• Talk about negative numbers with temperatures in winter and bank balances.
• For unlike denominators, go back to drawings or fraction strips before the rule.
• Encourage neat, step-by-step work. In Grade 6 the method matters as much as the answer.
• Keep practice calm and routine. Short, regular sessions beat cramming.

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

Grade 6 is an EQAO year in Ontario. Read our parent guide: EQAO Grade 6 math: what parents should know.

How Astuzo helps with Grade 6 math

Grade 6 problems are often multi-step. Spark keeps your child moving one step at a time: what do you know, what’s the first step, does the answer make sense? Those are the habits they’ll need in Grades 7 and 8.

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.