The Ontario Grade 7 math curriculum: what your child learns

Your child works with whole numbers up to one billion (including powers of ten), perfect squares and square roots, and rational numbers: positive and negative fractions and decimals, which they compare and order. They simplify fractions, convert between fractions, decimals and percents, and increase or decrease amounts by common percents (like 10%, 25% or 50%) in their head. New operations include adding and subtracting integers, exponents, the greatest common factor and lowest common multiple, multiplying and dividing fractions by fractions and decimals by decimals, and proportional reasoning.

Typical homework, with a hint

What your child learns in Number

• Numbers to one billionB1.1

  Shows and compares numbers as large as one billion, including writing them in expanded form with powers of ten (like 3 × 10⁶ + 4 × 10⁵), and talks about where such numbers are used in daily life.

• Perfect squares and rootsB1.2

  Recognizes and shows perfect squares (like 49 = 7 × 7) and finds their square roots, in different situations.

• Comparing rational numbersB1.3

  Reads, shows, compares and orders rational numbers, including positive and negative fractions and decimals to thousandths, in different situations.

• Simplifying fractionsB1.4

  Simplifies fractions by finding an equal fraction in lowest terms (like 6/8 = 3/4) when it helps, in different situations.

• Numbers between two numbersB1.5

  Finds fractions and decimals that lie between any two numbers.

• Rounding decimalsB1.6

  Rounds decimals to the closest whole number, tenth or hundredth, as needed, in different situations.

• Fractions, decimals and percentsB1.7

  Changes fractions into decimals and percents, and back again, in different situations.

• Order of operationsB2.1

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

• Common percent equivalentsB2.2

  Understands and remembers common percents and their matching fractions and decimals (like 25% = 1/4 = 0.25).

• Mental math with percentsB2.3

  Makes a whole number bigger or smaller by 1%, 5%, 10%, 25%, 50% or 100% using mental math, and explains the strategies.

• Adding and subtracting integersB2.4

  Uses objects, drawings and number sentences to show and solve situations that add and subtract integers (positive and negative numbers).

• Adding and subtracting fractionsB2.5

  Adds and subtracts fractions, including by first rewriting them as equal fractions with a common denominator, in different situations.

• GCF and LCMB2.6

  Finds the lowest common multiple of two or three whole numbers, and the greatest common factor of whole numbers up to 144.

• ExponentsB2.7

  Writes repeated multiplication of whole numbers using exponents (2 × 2 × 2 = 2³) and works out its value, in different situations.

• Multiplying and dividing fractionsB2.8

  Multiplies and divides a fraction by another fraction, using tools, in different situations.

• Multiplying and dividing decimalsB2.9

  Multiplies and divides a decimal by another decimal, in different situations.

• Proportional reasoningB2.10

  Tells apart situations that are proportional (one amount grows at a fixed rate with another) from ones that are not, and uses proportional reasoning to solve problems.

Kids compare linear growing patterns by their constant rate and starting value, write them as algebraic expressions and equations, and use them to find unknown values. They add and subtract like terms (like 5x − 2x), evaluate expressions with decimals, solve equations with several terms and decimal numbers, and solve and graph inequalities with several terms. In coding, they use loops that run a set number of times and sub-programs to write efficient code.

Typical homework, with a hint

What your child learns in Algebra

• Comparing linear patternsC1.1

  Finds and compares repeating, growing and shrinking patterns, including patterns in everyday life, and compares linear growing patterns by their starting value and how much they grow each step.

• Patterns as expressionsC1.2

  Makes repeating, growing and shrinking patterns with whole numbers and decimals, shows them in different ways, and writes linear growing patterns as algebraic expressions and equations.

• Pattern rules and unknownsC1.3

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

• Integer patternsC1.4

  Makes and describes patterns that show how integers are related.

• Adding and subtracting monomialsC2.1

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

• Evaluating expressionsC2.2

  Works out the value of algebraic expressions with whole numbers and decimals.

• Solving equationsC2.3

  Solves equations with several terms, whole numbers and decimals (like 2.5x + 3 = 13) in different situations, and checks the answer.

• Solving inequalitiesC2.4

  Solves inequalities with several terms and whole numbers, 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 that repeats a set number of times, uses sub-programs, or uses other control structures.

• Reading and changing codeC3.2

  Reads and changes existing code that repeats a set number of times, uses sub-programs or 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 why percentages make large data sets easier to understand, collect and organise different kinds of data, choose the best graph (including circle graphs), and make infographics. They work out how adding or removing a value changes the mean, median and mode, and question misleading graphs. In probability, they learn the difference between independent events (flipping two coins) and dependent events (picking two marbles without putting the first one back), and compare theoretical and experimental probability.

Typical homework, with a hint

What your child learns in Data

• Percentages in dataD1.1

  Explains, with examples, why percents are used to show how a large set of data is spread across a population or a sample.

• Collecting and organizing dataD1.2

  Collects data in words or categories, and counted or measured numbers, to answer questions, and organizes it in a suitable way, including with percents.

• Circle graphsD1.3

  Picks the best type of graph for a set of data, including circle graphs (pie charts), gives it a title, labels, a suitable scale and the data source, and explains why that graph fits.

• Making infographicsD1.4

  Makes an infographic that tells the story of a data set, using tables, circle graphs and any other useful information.

• Changing data and averagesD1.5

  Works out how adding or removing data changes the mean, median or mode, and describes how that changes the shape and spread of the data.

• Analysing dataD1.6

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

• Independent and dependent eventsD2.1

  Explains, with examples, the difference between independent events (one doesn’t affect the other) and dependent events (one does), and how their probabilities differ.

• Theoretical and experimental probabilityD2.2

  Works out and compares what should happen (theoretical probability) and what does happen in experiments (experimental probability) for two independent events and for two dependent events.

Geometry covers prisms, pyramids and cylinders (including their symmetry), top, front, side and perspective drawings, dilations (enlarging or shrinking a shape), and translations, reflections and rotations on a coordinate grid. Measurement brings in circles: radius, diameter, circumference and area. Kids connect volume and capacity (1 cm³ holds 1 mL), convert metric units in perimeter, area and volume problems, find the surface area of a cylinder from its net, and find the volume of prisms and cylinders as the area of the base times the height.

Typical homework, with a hint

What your child learns in Spatial Sense

• Prisms, pyramids and cylindersE1.1

  Describes and sorts prisms, pyramids and cylinders by their properties, including their planes of symmetry and rotational symmetry.

• Top, front, side viewsE1.2

  Draws objects and spaces to scale from the top, front and side, and in perspective (3D-looking) views.

• DilationsE1.3

  Enlarges and shrinks shapes (dilations) and describes how the new shape is similar to the original.

• Transformations on a gridE1.4

  Describes and carries out slides, flips and turns on a coordinate grid, and predicts where a shape will end up.

• Volume and capacityE2.1

  Explains how volume and capacity are alike and different, and uses the fact that 1 mL equals 1 cm³ to solve problems.

• Converting metric unitsE2.2

  Solves perimeter, area and volume problems that need changing from one metric unit to another.

• CircumferenceE2.3

  Uses how a circle’s radius, diameter and circumference are related to explain the circumference formula and solve problems with it.

• Constructing circlesE2.4

  Draws circles when given the radius, the diameter or the circumference.

• Area of a circleE2.5

  Shows how a circle’s radius, diameter and area are related, uses that to explain the formula for a circle’s area, and solves problems with it.

• Surface area of cylindersE2.6

  Draws a cylinder as a net (two circles and a rectangle) and finds its surface area by adding the areas of the parts.

• Volume of prisms, cylindersE2.7

  Shows that you find the volume of a prism or cylinder by multiplying its base area by its height, and uses this to find the base area, volume or height when the other two are known.

Financial literacy in Grade 7 covers exchange rates and converting between Canadian dollars and other currencies, reliable sources of financial information, budgets for longer-term goals that kids create, track and adjust, what influences money decisions, how interest affects savings, investments and the cost of borrowing over time, and comparing interest rates and fees on accounts and loans.

Typical homework, with a hint

What your child learns in Financial Literacy

• Exchange ratesF1.1

  Finds and compares exchange rates, and converts other currencies into Canadian dollars and Canadian dollars into other currencies.

• Financial information sourcesF1.2

  Names and describes trustworthy sources of information that help with planning for and reaching a money goal.

• Making budgetsF1.3

  Makes sample budgets for longer-term money goals in different situations, then tracks and adjusts them.

• Influences on money choicesF1.4

  Names things in society and in someone’s own life that can influence money decisions, and describes how each might affect them.

• How interest worksF1.5

  Explains how interest rates affect savings, investments and the cost of borrowing money over time.

• Comparing accounts and loansF1.6

  Compares the interest rates and fees of different accounts and loans from different financial institutions, and picks the best option for different situations.

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 7 math at home

• Use a thermometer in winter, an elevator or a bank balance to talk about adding and subtracting negative numbers.
• When a rule for fractions or integers feels like magic, ask your child to show it with a drawing or a number line first.
• Look at real prices together: sale percentages, unit prices, and exchange rates when shopping online or travelling.
• Encourage one step per line when solving equations. It makes slips easy to find.
• Estimate first, then calculate. A quick estimate shows whether the answer makes sense.
• Expect some frustration as the math gets more abstract. Short, regular practice helps more than long sessions.

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

How Astuzo helps with Grade 7 math

Grade 7 homework often has several steps and new rules, like integer signs and the order of operations. Spark asks your child what each step should be and why, and when something goes wrong in the middle of a long calculation, it helps them find the slip themselves. That habit of checking their own work carries them through Grade 8 and into high school.

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.