Ontario · Grade 7
Mathematics, Grade 7
Ontario’s Grade 7 math course, from Number to Financial Literacy.
- Units
- 5
- Lessons
- 29
- Skills
- 53
- Provincial exam
- None
- Official curriculum
- Ontario Ministry of Education
Unit by unit
Every skill in the course, numbered by unit.
Unit 1 · 18 skills
Number
Whole Numbers to One Billion
Representing and comparing whole numbers to one billion using powers of ten
I can represent and compare whole numbers up to one billion using powers of ten.
Skill 1.1
Perfect Squares and Square Roots
Identifying and representing perfect squares
I can identify and represent perfect squares.
Skill 1.2
Determining square roots of perfect squares
I can determine the square roots of perfect squares.
Skill 1.3
Rational Numbers
Reading, representing, comparing, and ordering rational numbers, including negatives
I can read, represent, compare, and order rational numbers, including negatives.
Skill 1.4
Simplifying Fractions and Generating Numbers Between Quantities
Using equivalent fractions to simplify fractions
I can use equivalent fractions to simplify fractions.
Skill 1.5
Generating fractions and decimals between any two quantities
I can generate fractions and decimals between any two quantities.
Skill 1.6
Rounding and Converting Fractions, Decimals, and Percents
Rounding decimals to the nearest tenth, hundredth, or whole number
I can round decimals to the nearest tenth, hundredth, or whole number.
Skill 1.7
Converting between fractions, decimals, and percents
I can convert between fractions, decimals, and percents.
Skill 1.8
Order of Operations and Multi-Step Problems
Using order of operations to solve multi-step problems
I can use order of operations to solve multi-step problems with rational numbers, ratios, rates, and percents.
Skill 1.9
Recalling commonly used percent, fraction, and decimal equivalents
I can recall commonly used percent, fraction, and decimal equivalents.
Skill 1.10
Mental math: increasing and decreasing by a percent
I can mentally increase and decrease a whole number by common percents.
Skill 1.11
Adding and Subtracting Integers
Representing and solving addition and subtraction of integers
I can represent and solve addition and subtraction of integers.
Skill 1.12
Adding and Subtracting Fractions, GCF, and LCM
Adding and subtracting fractions, including by creating equivalent fractions
I can add and subtract fractions, including by creating equivalent fractions.
Skill 1.13
Determining the greatest common factor and lowest common multiple
I can determine the greatest common factor and lowest common multiple.
Skill 1.14
Exponential Notation
Expressing repeated multiplication using exponential notation
I can express repeated multiplication using exponential notation.
Skill 1.15
Multiplying and Dividing Fractions and Decimals
Multiplying and dividing fractions by fractions
I can multiply and divide fractions by fractions.
Skill 1.16
Multiplying and dividing decimals by decimals
I can multiply and divide decimal numbers by decimal numbers.
Skill 1.17
Proportional Reasoning
Identifying proportional situations and applying proportional reasoning
I can identify proportional situations and apply proportional reasoning.
Skill 1.18
The official wording · 18 outcomes
- 1.1
- represent and compare whole numbers up to and including one billion, including in expanded form using powers of ten, and describe various ways they are used in everyday life
- 1.2
- identify and represent perfect squares
- 1.3
- and determine their square roots, in various contexts
- 1.4
- read, represent, compare, and order rational numbers, including positive and negative fractions and decimal numbers to thousandths, in various contexts
- 1.5
- use equivalent fractions to simplify fractions, when appropriate, in various contexts
- 1.6
- generate fractions and decimal numbers between any two quantities
- 1.7
- round decimal numbers to the nearest tenth, hundredth, or whole number, as applicable, in various contexts
- 1.8
- convert between fractions, decimal numbers, and percents, in various contexts
- 1.9
- use the properties and order of operations, and the relationships between operations, to solve problems involving whole numbers, decimal numbers, fractions, ratios, rates, and percents, including those requiring multiple steps or multiple operations
- 1.10
- understand and recall commonly used percents, fractions, and decimal equivalents
- 1.11
- use mental math strategies to increase and decrease a whole number by 1%, 5%, 10%, 25%, 50%, and 100%, and explain the strategies used
- 1.12
- use objects, diagrams, and equations to represent, describe, and solve situations involving addition and subtraction of integers
- 1.13
- add and subtract fractions, including by creating equivalent fractions, in various contexts
- 1.14
- determine the greatest common factor for a variety of whole numbers up to 144 and the lowest common multiple for two and three whole numbers
- 1.15
- evaluate and express repeated multiplication of whole numbers using exponential notation, in various contexts
- 1.16
- multiply and divide fractions by fractions, using tools in various contexts
- 1.17
- multiply and divide decimal numbers by decimal numbers, in various contexts
- 1.18
- identify proportional and non-proportional situations and apply proportional reasoning to solve problems
Key ideas
Expanded notation with powers of ten shows a number as an expression using addition, multiplication, and exponents, like 307 020 050 = 3 x 10^8 + 7 x 10^6 + 2 x 10^4 + 5 x 10.
A perfect square is the result of multiplying a whole number by itself, like 3 x 3 = 9.
A rational number is any number that can be written as a fraction a/b, where a and b are integers and b is not zero — this includes whole numbers, integers, and both positive and negative fractions and decimals.
A fraction is simplified (in lowest terms) when the numerator and denominator share no common factor other than 1.
Rounding makes a number simpler to work with, and is based on which reference point (tenth, hundredth, or whole number) the decimal is closest to.
Watch out for
- Miscounting the number of zeros or place-value periods in a very large number.
- Thinking any even number, or any number that 'looks square,' is automatically a perfect square.
- Thinking negative fractions and decimals can't be compared the same way as positive ones.
Every skill’s key ideas, worked examples and checks are in MapleMind.Practise this unit
Unit 2 · 10 skills
Algebra
Comparing Linear Growing Patterns
Comparing patterns, including linear growing patterns by rate and initial value
I can compare patterns, including linear growing patterns by rate and initial value.
Skill 2.1
Creating and translating patterns with whole and decimal numbers, using algebra for linear patterns
I can create and translate patterns with whole and decimal numbers, using algebra for linear patterns.
Skill 2.2
Pattern Rules and Patterns Among Integers
Determining pattern rules and solving for unknowns in linear growing patterns
I can determine pattern rules and solve for unknowns in linear growing patterns.
Skill 2.3
Creating patterns to show relationships among integers
I can create patterns to show relationships among integers.
Skill 2.4
Monomials, Expressions, Equations, and Inequalities
Adding and subtracting monomials with a degree of 1
I can add and subtract monomials with a degree of 1.
Skill 2.5
Evaluating algebraic expressions with whole and decimal numbers
I can evaluate algebraic expressions with whole and decimal numbers.
Skill 2.6
Solving multi-term equations with whole and decimal numbers
I can solve multi-term equations with whole and decimal numbers and verify solutions.
Skill 2.7
Solving and graphing multi-term inequalities
I can solve and graph multi-term inequalities with whole numbers.
Skill 2.8
Coding with a Defined Count and Sub-Programs
Writing and running efficient code involving a defined count and/or sub-program
I can write and run efficient code involving a defined count and/or sub-program.
Skill 2.9
Reading and altering code involving a defined count and/or sub-program
I can read and alter code involving a defined count and/or sub-program.
Skill 2.10
The official wording · 10 outcomes
- 2.1
- identify and compare a variety of repeating, growing, and shrinking patterns, including patterns found in real-life contexts, and compare linear growing patterns on the basis of their constant rates and initial values
- 2.2
- create and translate repeating, growing, and shrinking patterns involving whole numbers and decimal numbers using various representations, including algebraic expressions and equations for linear growing patterns
- 2.3
- determine pattern rules and use them to extend patterns, make and justify predictions, and identify missing elements in repeating, growing, and shrinking patterns involving whole numbers and decimal numbers, and use algebraic representations of the pattern rules to solve for unknown values in linear growing patterns
- 2.4
- create and describe patterns to illustrate relationships among integers
- 2.5
- add and subtract monomials with a degree of 1 that involve whole numbers, using tools
- 2.6
- evaluate algebraic expressions that involve whole numbers and decimal numbers
- 2.7
- solve equations that involve multiple terms, whole numbers, and decimal numbers in various contexts, and verify solutions
- 2.8
- solve inequalities that involve multiple terms and whole numbers, and verify and graph the solutions
- 2.9
- solve problems and create computational representations of mathematical situations by writing and executing efficient code, including code that involves events influenced by a defined count and/or sub-program and other control structures
- 2.10
- read and alter existing code, including code that involves events influenced by a defined count and/or sub-program and other control structures, and describe how changes to the code affect the outcomes and the efficiency of the code
Key ideas
A linear growing pattern has a constant rate (how much it grows each term) and an initial value (its starting value when the term number is zero).
The algebraic expression for a linear pattern (the general term) can be used to solve for the term value given the term number, or the reverse.
Only monomials with the same variable (like terms) can be added or subtracted, like 10y - 8y = 2y.
A defined count repeats an instruction either a set number of times or until a condition is met.
In a comparison of linear patterns, the one with the greater constant rate grows faster and has a steeper line on a graph.
Watch out for
- Confusing the initial value (starting point) with the constant rate (how fast it grows).
- Extending a pattern term-by-term for a far prediction instead of substituting into its equation.
- Trying to combine monomials with different variables into a single term.
Every skill’s key ideas, worked examples and checks are in MapleMind.Practise this unit
Unit 3 · 8 skills
Data
Percentages for Data Distribution
Explaining why percentages represent data distribution
I can explain why percentages represent the distribution of a variable in large data sets.
Skill 3.1
Collecting qualitative and quantitative data, organizing using percentages
I can collect qualitative and quantitative data, organizing it using percentages.
Skill 3.2
Circle Graphs and Infographics
Selecting and justifying a graph type, including circle graphs
I can select and justify a graph type, including circle graphs.
Skill 3.3
Creating an infographic using tables and circle graphs
I can create an infographic using tables and circle graphs.
Skill 3.4
Impact on Central Tendency and Analysing Data
Determining the impact of adding or removing data on central tendency
I can determine the impact of adding or removing data on central tendency.
Skill 3.5
Analysing data in circle graphs and misleading graphs
I can analyse data in circle graphs and misleading graphs.
Skill 3.6
Independent and Dependent Events
Describing the difference between independent and dependent events
I can describe the difference between independent and dependent events.
Skill 3.7
Comparing probabilities of two independent events and of two dependent events
I can compare probabilities of two independent events and of two dependent events.
Skill 3.8
The official wording · 8 outcomes
- 3.1
- explain why percentages are used to represent the distribution of a variable for a population or sample in large sets of data, and provide examples
- 3.2
- collect qualitative data and discrete and continuous quantitative data to answer questions of interest, and organize the sets of data as appropriate, including using percentages
- 3.3
- select from among a variety of graphs, including circle graphs, the type of graph best suited to represent various sets of data; display the data in the graphs with proper sources, titles, and labels, and appropriate scales; and justify their choice of graphs
- 3.4
- create an infographic about a data set, representing the data in appropriate ways, including in tables and circle graphs, and incorporating any other relevant information that helps to tell a story about the data
- 3.5
- determine the impact of adding or removing data from a data set on a measure of central tendency, and describe how these changes alter the shape and distribution of the data
- 3.6
- analyse different sets of data presented in various ways, including in circle graphs and in misleading graphs, by asking and answering questions about the data, challenging preconceived notions, and drawing conclusions, then make convincing arguments and informed decisions
- 3.7
- describe the difference between independent and dependent events, and explain how their probabilities differ, providing examples
- 3.8
- determine and compare the theoretical and experimental probabilities of two independent events happening and of two dependent events happening
Key ideas
When comparing categories of a large population, it's easier to compare relative amounts (percentages) than exact quantities.
A circle graph shows how categories represent parts of a whole data set, with each sector's angle calculated as a percentage of 360 degrees.
Adding or removing a data value that is not the most frequent value in the set will not impact the mode.
Two events are independent when the outcome of one does not affect the outcome of the other.
Percentages let data sets or samples of different sizes be compared fairly, on the same relative scale.
Watch out for
- Comparing raw counts from populations of very different sizes as if the comparison were fair.
- Forgetting to convert a percentage into a corresponding angle of 360° when building a circle graph.
- Assuming adding or removing any single data value will always change every measure of central tendency the same amount.
Every skill’s key ideas, worked examples and checks are in MapleMind.Practise this unit
Unit 4 · 11 skills
Spatial Sense
Classifying Cylinders, Pyramids, and Prisms
Describing and classifying cylinders, pyramids, and prisms by geometric properties
I can describe and classify cylinders, pyramids, and prisms by their geometric properties.
Skill 4.1
Views with Scales, Including Perspective
Drawing top, front, side, and perspective views using scales
I can draw top, front, side, and perspective views using scales.
Skill 4.2
Dilations and Transformations on the Cartesian Plane
Performing dilations and describing similarity
I can perform dilations and describe similarity between the image and original.
Skill 4.3
Performing translations, reflections, and rotations on a Cartesian plane
I can perform translations, reflections, and rotations on a Cartesian plane.
Skill 4.4
Volume, Capacity, and Metric Conversions
Describing volume and capacity and relating millilitres to cubic centimetres
I can describe volume and capacity and relate millilitres to cubic centimetres.
Skill 4.5
Solving perimeter, area, and volume problems requiring metric conversions
I can solve perimeter, area, and volume problems requiring metric conversions.
Skill 4.6
Circles: Circumference, Area, and Construction
Using radius, diameter, and circumference relationships to explain the circumference formula
I can use radius, diameter, and circumference relationships to explain the circumference formula.
Skill 4.7
Constructing circles given radius, diameter, or circumference
I can construct circles given radius, diameter, or circumference.
Skill 4.8
Using radius, diameter, and area relationships to explain the area-of-a-circle formula
I can use radius, diameter, and area relationships to explain the area-of-a-circle formula.
Skill 4.9
Cylinder Nets and the Volume of Prisms and Cylinders
Representing cylinders as nets and determining their surface area
I can represent cylinders as nets and determine their surface area.
Skill 4.10
Determining the volume of a prism or cylinder from base area and height
I can determine the volume of a prism or cylinder from base area and height.
Skill 4.11
The official wording · 11 outcomes
- 4.1
- describe and classify cylinders, pyramids, and prisms according to their geometric properties, including plane and rotational symmetry
- 4.2
- draw top, front, and side views, as well as perspective views, of objects and physical spaces, using appropriate scales
- 4.3
- perform dilations and describe the similarity between the image and the original shape
- 4.4
- describe and perform translations, reflections, and rotations on a Cartesian plane, and predict the results of these transformations
- 4.5
- describe the differences and similarities between volume and capacity, and apply the relationship between millilitres (mL) and cubic centimetres (cm3) to solve problems
- 4.6
- solve problems involving perimeter, area, and volume that require converting from one metric unit of measurement to another
- 4.7
- use the relationships between the radius, diameter, and circumference of a circle to explain the formula for finding the circumference and to solve related problems
- 4.8
- construct circles when given the radius, diameter, or circumference
- 4.9
- show the relationships between the radius, diameter, and area of a circle, and use these relationships to explain the formula for measuring the area of a circle and to solve related problems
- 4.10
- represent cylinders as nets and determine their surface area by adding the areas of their parts
- 4.11
- show that the volume of a prism or cylinder can be determined by multiplying the area of its base by its height, and apply this relationship to find the area of the base, volume, and height of prisms and cylinders when given two of the three measurements
Key ideas
Cylinders have two parallel, congruent bases; prisms are a special type of cylinder with polygon bases; pyramids have one base with triangular faces meeting at an apex.
Top, front, and side views are flat drawings without perspective, used to faithfully reproduce an object in three dimensions.
A dilation enlarges or reduces a figure by a scale factor, and unlike translations, reflections, and rotations, it does not produce a congruent image.
Volume is the amount of space something takes up; capacity is how much a container can hold — an object always has volume, but may not have capacity.
The diameter of a circle is twice its radius (d = 2r), and the circumference is a little more than 3 times the diameter — this constant ratio is called pi (π).
Watch out for
- Thinking a prism and a cylinder are unrelated categories instead of understanding a prism is a special cylinder.
- Applying the scale inconsistently across different dimensions of the same drawing.
- Confusing a dilation (changes size) with the other transformations (which keep size the same).
Every skill’s key ideas, worked examples and checks are in MapleMind.Practise this unit
Unit 5 · 6 skills
Financial Literacy
Exchange Rates and Currency Conversion
Identifying and comparing exchange rates and converting foreign currencies
I can identify and compare exchange rates and convert foreign currencies.
Skill 5.1
Reliable Sources and Longer-Term Budgets
Identifying reliable sources of information for financial planning
I can identify reliable sources of information for financial planning.
Skill 5.2
Creating, tracking, and adjusting sample budgets for longer-term goals
I can create, track, and adjust sample budgets for longer-term goals.
Skill 5.3
Factors in Financial Decisions and Interest Over Time
Identifying societal and personal factors influencing financial decisions
I can identify societal and personal factors influencing financial decisions.
Skill 5.4
Explaining how interest rates impact savings, investments, and borrowing over time
I can explain how interest rates impact savings, investments, and borrowing over time.
Skill 5.5
Comparing Financial Institutions
Comparing interest rates and fees to determine the best financial option
I can compare interest rates and fees to determine the best financial option.
Skill 5.6
The official wording · 6 outcomes
- 5.1
- identify and compare exchange rates, and convert foreign currencies to Canadian dollars and vice versa
- 5.2
- identify and describe various reliable sources of information that can help with planning for and reaching a financial goal
- 5.3
- create, track, and adjust sample budgets designed to meet longer-term financial goals for various scenarios
- 5.4
- identify various societal and personal factors that may influence financial decision making, and describe the effects that each might have
- 5.5
- explain how interest rates can impact savings, investments, and the cost of borrowing to pay for goods and services over time
- 5.6
- compare interest rates and fees for different accounts and loans offered by various financial institutions, and determine the best option for different scenarios
Key ideas
International currencies have different values compared to Canadian currency, and this relationship is expressed as an exchange rate.
Managing finances, including setting financial goals, often requires gathering information from various sources — and it's important to tell reliable sources from unreliable ones.
Many factors — personal, family, cultural, and societal — can impact financial decision making.
Financial institutions offer a range of accounts and loan products, each with its own interest rates and fees.
Exchange rates can fluctuate daily, so the same amount of foreign currency can be worth a different amount of Canadian dollars from day to day.
Watch out for
- Assuming exchange rates stay the same over time instead of fluctuating daily.
- Assuming all financial information found online is equally trustworthy.
- Assuming financial decisions are made in isolation, without considering personal or societal context.
Every skill’s key ideas, worked examples and checks are in MapleMind.Practise this unit
Plan the term
Pick your term and the days you study. Each unit gets its share of the weeks and comes back a week later for a review. The last two weeks go over the whole course.
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The official curriculum
This page follows Ontario’s own curriculum for Mathematics, Grade 7.
Textbooks
The textbooks Ontario Ministry of Education lists for Mathematics, Grade 7:
- Math Now Grade 7
- MathUp Classroom, Grade 7
- Mathology 7
- My Math Path 7
- D2L Ontario Math 7
From the Trillium List, read October 27, 2026. ontario.ca
Strands
| Strand | Outcomes | Taught in |
|---|---|---|
| BNumber | Outcomes 18 | Taught in Unit 1 |
| CAlgebra | Outcomes 10 | Taught in Unit 2 |
| DData | Outcomes 8 | Taught in Unit 3 |
| ESpatial Sense | Outcomes 11 | Taught in Unit 4 |
| FFinancial Literacy | Outcomes 6 | Taught in Unit 5 |
Ontario’s Strand A, social-emotional learning skills and the mathematical processes, is taught through every other strand.
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Questions about Mathematics, Grade 7
What is Mathematics, Grade 7?
Ontario’s Grade 7 math course: 5 units and 53 skills, from Number to Financial Literacy.
What units are in Mathematics, Grade 7?
1. Number, 2. Algebra, 3. Data, 4. Spatial Sense and 5. Financial Literacy.
Is there a provincial exam for Mathematics, Grade 7?
No. Ontario gives no provincial exam for Mathematics, Grade 7.
What textbook does Mathematics, Grade 7 use?
The textbooks Ontario Ministry of Education lists for Mathematics, Grade 7: Math Now Grade 7, GTK Press, MathUp Classroom, Grade 7, Rubicon Publishing, Mathology 7, Pearson Education Canada, My Math Path 7, Nelson Education Ltd. and D2L Ontario Math 7, D2L Corporation.
What comes after Mathematics, Grade 7?
Mathematics, Grade 8.
Can MapleMind help with Mathematics, Grade 7?
Yes. MapleMind teaches every skill of Mathematics, Grade 7, step by step, with practice and checks, and its tutor answers questions about any of them. It’s free with daily limits, on iPhone, Android and the web.
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