Ontario · Grade 8
Mathematics, Grade 8
Ontario’s Grade 8 math course, from Number to Financial Literacy.
- Units
- 5
- Lessons
- 41
- Skills
- 45
- Provincial exam
- None
- Official curriculum
- Ontario Ministry of Education
Unit by unit
Every skill in the course, numbered by unit.
Unit 1 · 12 skills
Number
Very Large and Very Small Numbers
Representing and comparing numbers with scientific notation
I can represent and compare very large and very small numbers using scientific notation.
Skill 1.1
The Real Number System
Describing, comparing, and ordering rational and irrational numbers
I can describe, compare, and order rational and irrational numbers in the real number system.
Skill 1.2
Square Roots
Estimating and calculating square roots
I can estimate and calculate square roots, including for numbers that aren't perfect squares.
Skill 1.3
Recalling commonly used square numbers and their square roots
I can quickly recall commonly used square numbers and their square roots.
Skill 1.4
Fractions, Decimals, and Percents — Flexibly
Using fractions, decimals, and percents flexibly, including over 100% and under 1%
I can use fractions, decimals, and percents flexibly to solve problems, including percents over 100% and under 1%.
Skill 1.5
Order of Operations in Multi-Step Problems
Using order of operations to solve multi-step problems with rational numbers, ratios, rates, and percents
I can use order of operations and how operations connect to solve multi-step problems with rational numbers, ratios, rates, and percents.
Skill 1.6
Mental Math with Powers of Ten
Using mental math to multiply and divide by powers of ten
I can use mental math to multiply and divide whole numbers and decimals up to thousandths by powers of ten.
Skill 1.7
Adding and Subtracting Integers
Adding and subtracting integers using appropriate strategies
I can add and subtract integers using appropriate strategies in different contexts.
Skill 1.8
Adding and Subtracting Fractions
Adding and subtracting fractions using appropriate strategies
I can add and subtract fractions using appropriate strategies in different contexts.
Skill 1.9
Multiplying and Dividing Fractions
Multiplying and dividing fractions by fractions, whole numbers, and mixed numbers
I can multiply and divide fractions by fractions, whole numbers, and mixed numbers.
Skill 1.10
Multiplying and Dividing Integers
Multiplying and dividing integers using appropriate strategies
I can multiply and divide integers using appropriate strategies in different contexts.
Skill 1.11
Proportional Reasoning
Comparing proportional situations and finding unknown values
I can compare proportional situations and determine unknown values using proportional reasoning.
Skill 1.12
The official wording · 12 outcomes
- 1.1
- represent and compare very large and very small numbers, including through the use of scientific notation, and describe various ways they are used in everyday life
- 1.2
- describe, compare, and order numbers in the real number system (rational and irrational numbers), separately and in combination, in various contexts
- 1.3
- estimate and calculate square roots, in various contexts
- 1.4
- understand and recall commonly used square numbers and their square roots
- 1.5
- use fractions, decimal numbers, and percents, including percents of more than 100% or less than 1%, interchangeably and flexibly to solve a variety of problems
- 1.6
- use the properties and order of operations, and the relationships between operations, to solve problems involving rational numbers, ratios, rates, and percents, including those requiring multiple steps or multiple operations
- 1.7
- use mental math strategies to multiply and divide whole numbers and decimal numbers up to thousandths by powers of ten, and explain the strategies used
- 1.8
- add and subtract integers, using appropriate strategies, in various contexts
- 1.9
- add and subtract fractions, using appropriate strategies, in various contexts
- 1.10
- multiply and divide fractions by fractions, as well as by whole numbers and mixed numbers, in various contexts
- 1.11
- multiply and divide integers, using appropriate strategies, in various contexts
- 1.12
- compare proportional situations and determine unknown values in proportional situations, and apply proportional reasoning to solve problems in various contexts
Key ideas
In scientific notation, there is exactly one non-zero digit to the left of the decimal point (e.g., 3.624 × 10^13, not 36.24 × 10^12).
Rational numbers can be written as a fraction a/b where a and b are integers; every whole number, integer, and terminating or repeating decimal is rational.
Every positive number has two square roots (positive and negative), but the √ symbol by itself means only the positive one — useful because side lengths can't be negative.
Fractions, decimals, and percents all describe the same relationship to a whole — decimal units are powers of ten, and percent means 'per hundred.'.
The order of operations is: brackets first, then exponents and roots, then multiplication and division left to right, then addition and subtraction left to right.
Watch out for
- Writing a number like 36.24 × 10^12 and thinking it counts as scientific notation, when the digit before the decimal must be a single non-zero digit.
- Thinking a decimal that looks messy (like 3.14159...) must automatically be irrational, without checking whether it actually terminates, repeats, or is just a long rational decimal.
- Forgetting that a positive number has two square roots and only reporting the positive one when the context (like comparing two numbers) actually calls for both.
Every skill’s key ideas, worked examples and checks are in MapleMind.Practise this unit
Unit 2 · 11 skills
Algebra
Comparing Growing and Shrinking Patterns
Comparing patterns using rate and initial value
I can compare linear growing and shrinking patterns using their constant rate and initial value.
Skill 2.1
Creating and Translating Patterns with Algebra
Creating and translating patterns using algebraic expressions and equations
I can create and translate patterns involving rational numbers using algebraic expressions and equations.
Skill 2.2
Pattern Rules and Solving for Unknowns
Using pattern rules to extend patterns and solve for unknown values
I can use pattern rules to extend patterns, justify predictions, and solve for unknown values in linear patterns.
Skill 2.3
Patterns Showing Relationships Among Rational Numbers
Creating patterns that show relationships among rational numbers
I can create and describe patterns that show relationships among rational numbers.
Skill 2.4
Monomials and Binomials
Adding and subtracting monomials with a degree of 1
I can add and subtract monomials with a degree of 1.
Skill 2.5
Adding binomials with a degree of 1 that involve integers
I can add binomials with a degree of 1 that involve integers, using tools.
Skill 2.6
Evaluating Algebraic Expressions
Evaluating algebraic expressions with rational numbers
I can evaluate algebraic expressions that involve rational numbers.
Skill 2.7
Solving Multi-Term Equations
Solving and verifying equations with multiple terms, integers, and decimal numbers
I can solve and verify equations with multiple terms, integers, and decimal numbers.
Skill 2.8
Solving and Graphing Inequalities
Solving, verifying, and graphing inequalities with integers
I can solve, verify, and graph inequalities that involve integers.
Skill 2.9
Coding to Analyse Data
Writing and running code that analyses data to inform decisions
I can write and run code that analyses data to inform and communicate decisions.
Skill 2.10
Reading and changing code that analyses data
I can read and alter existing code that analyses data, and describe how the changes affect the outcome and efficiency.
Skill 2.11
The official wording · 11 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 and shrinking patterns on the basis of their constant rates and initial values
- 2.2
- create and translate repeating, growing, and shrinking patterns involving rational numbers using various representations, including algebraic expressions and equations for linear growing and shrinking patterns
- 2.3
- determine pattern rules and use them to extend patterns, make and justify predictions, and identify missing elements in growing and shrinking patterns involving rational numbers, and use algebraic representations of the pattern rules to solve for unknown values in linear growing and shrinking patterns
- 2.4
- create and describe patterns to illustrate relationships among rational numbers
- 2.5
- add and subtract monomials with a degree of 1
- 2.6
- and add binomials with a degree of 1 that involve integers, using tools
- 2.7
- evaluate algebraic expressions that involve rational numbers
- 2.8
- solve equations that involve multiple terms, integers, and decimal numbers in various contexts, and verify solutions
- 2.9
- solve inequalities that involve integers, and verify and graph the solutions
- 2.10
- solve problems and create computational representations of mathematical situations by writing and executing code, including code that involves the analysis of data in order to inform and communicate decisions
- 2.11
- read and alter existing code involving the analysis of data in order to inform and communicate decisions, and describe how changes to the code affect the outcomes and the efficiency of the code
Key ideas
A constant rate means the change between terms is always the same amount — like an hourly wage of $15 per hour.
Growing and shrinking patterns can involve rational numbers (fractions, decimals, integers), not just whole numbers.
A 'near prediction' extends a pattern just beyond what's shown; a 'far prediction' extends it much further and usually needs a calculation to justify.
Patterns can be used to show number properties, like how exponents work in scientific notation.
A monomial with a degree of 1 has a variable with an exponent of one, like 2m (where the exponent 1 is just not written).
Watch out for
- Comparing patterns only by their starting values and ignoring the rate of change, or vice versa.
- Assuming a pattern only has one correct algebraic expression, when several equivalent expressions can describe the same pattern.
- Making a far prediction by just guessing or extending visually, rather than using the algebraic rule to calculate it precisely.
Every skill’s key ideas, worked examples and checks are in MapleMind.Practise this unit
Unit 3 · 8 skills
Data
One-Variable and Two-Variable Data
Telling one-variable and two-variable data situations apart
I can identify situations involving one-variable data and situations involving two-variable data.
Skill 3.1
Collecting Continuous Two-Variable Data
Collecting continuous two-variable data and organizing it in a table of values
I can collect continuous two-variable data and organize it in a table of values.
Skill 3.2
Choosing Graphs, Including Scatter Plots
Choosing and justifying the best graph, including scatter plots
I can select and justify the best graph, including scatter plots, for a data set.
Skill 3.3
Building an Infographic with Tables and Scatter Plots
Creating an infographic using tables and scatter plots
I can create an infographic about a data set using tables and scatter plots.
Skill 3.4
Describing Relationships Between Two Variables
Using correlation language to describe two-variable relationships
I can use mathematical language to describe the relationship between two variables shown in a scatter plot.
Skill 3.5
Analysing Data in Scatter Plots and Misleading Graphs
Analysing data in scatter plots and misleading graphs to draw conclusions
I can analyse data in scatter plots and misleading graphs to draw conclusions and make informed decisions.
Skill 3.6
Solving Probability Problems with Diagrams
Solving probability problems using Venn and tree diagrams
I can solve probability problems using Venn and tree diagrams.
Skill 3.7
Comparing Probabilities of Multiple Events
Comparing theoretical and experimental probabilities of multiple independent and dependent events
I can determine and compare theoretical and experimental probabilities of multiple independent and dependent events.
Skill 3.8
The official wording · 8 outcomes
- 3.1
- identify situations involving one-variable data and situations involving two-variable data, and explain when each type of data is needed
- 3.2
- collect continuous data to answer questions of interest involving two variables, and organize the data sets as appropriate in a table of values
- 3.3
- select from among a variety of graphs, including scatter plots, 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 scatter plots, and incorporating any other relevant information that helps to tell a story about the data
- 3.5
- use mathematical language, including the terms “strong”, “weak”, “none”, “positive”, and “negative”, to describe the relationship between two variables for various data sets with and without outliers
- 3.6
- analyse different sets of data presented in various ways, including in scatter plots 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
- solve various problems that involve probability, using appropriate tools and strategies, including Venn and tree diagrams
- 3.8
- determine and compare the theoretical and experimental probabilities of multiple independent events happening and of multiple dependent events happening
Key ideas
A variable is any attribute, number, or quantity that can be measured or counted.
Continuous data (like height, time, or temperature) can take any value within a range, not just whole numbers.
Scatter plots display data points for two continuous variables, with one variable on each axis.
Infographics share data and information clearly and concisely, often for a specific audience.
When data points form close to a line or curve, there's a strong relationship; when they cluster with no clear pattern, there's no relationship.
Watch out for
- Assuming any data with two numbers (like two different people's heights) counts as two-variable data, rather than checking whether there's a relationship being investigated.
- Collecting data for only one variable when the question of interest actually requires two, corresponding measurements.
- Defaulting to a bar graph for every data set, without considering whether a scatter plot or another graph type fits better.
Every skill’s key ideas, worked examples and checks are in MapleMind.Practise this unit
Unit 4 · 8 skills
Spatial Sense
Tessellations
Identifying properties of tessellating shapes and their transformations
I can identify the properties of tessellating shapes and the transformations used to create them.
Skill 4.1
Scale Models and Scale Drawings
Making objects and models from views using appropriate scales
I can make objects and models from top, front, side, or perspective views using appropriate scales.
Skill 4.2
Using scale drawings to calculate actual lengths and areas
I can use scale drawings to calculate actual lengths and areas, and reproduce drawings at different ratios.
Skill 4.3
Transformations on the Cartesian Plane
Performing and predicting translations, reflections, rotations, and dilations
I can describe and perform translations, reflections, rotations, and dilations on a Cartesian plane and predict their results.
Skill 4.4
Very Large and Very Small Metric Units
Representing very large and very small metric units with exponential notation
I can represent very large and very small metric units using base ten relationships and exponential notation.
Skill 4.5
Angle Properties
Solving angle problems with intersecting and parallel lines and polygons
I can solve problems involving angle properties of intersecting and parallel lines and of polygons.
Skill 4.6
Composite Shapes and Objects
Solving perimeter, area, volume, and surface area problems for composite shapes and objects
I can solve perimeter, area, volume, and surface area problems for composite 2D shapes and 3D objects.
Skill 4.7
The Pythagorean Relationship
Describing and applying the Pythagorean relationship to find an unknown side length
I can describe the Pythagorean relationship and apply it to find an unknown side length in a right triangle.
Skill 4.8
The official wording · 8 outcomes
- 4.1
- identify geometric properties of tessellating shapes and identify the transformations that occur in the tessellations
- 4.2
- make objects and models using appropriate scales, given their top, front, and side views or their perspective views
- 4.3
- use scale drawings to calculate actual lengths and areas, and reproduce scale drawings at different ratios
- 4.4
- describe and perform translations, reflections, rotations, and dilations on a Cartesian plane, and predict the results of these transformations
- 4.5
- represent very large (mega, giga, tera) and very small (micro, nano, pico) metric units using models, base ten relationships, and exponential notation
- 4.6
- solve problems involving angle properties, including the properties of intersecting and parallel lines and of polygons
- 4.7
- solve problems involving the perimeter, circumference, area, volume, and surface area of composite two-dimensional shapes and three-dimensional objects, using appropriate formulas
- 4.8
- describe the Pythagorean relationship using various geometric models, and apply the theorem to solve problems involving an unknown side length for a given right triangle
Key ideas
A tessellation covers an area with tiles leaving no gaps or overlaps; the angles where tiles meet always add up to 360°.
Top, front, and side views are 'flat drawings' without perspective, used in technical drawings for faithful 3D reproduction.
Each transformation has a mapping rule: translations shift (x,y) by (a,b); reflections flip across an axis; rotations turn around the origin by 90°, 180°, or 270°; dilations scale by a factor from the origin.
Metric prefixes describe the relative size of a unit: kilo- to milli- scale by powers of 10, but units beyond these (mega, giga, tera, micro, nano, pico) scale by powers of 1000.
Angle properties include: a straight angle is 180° (supplementary angles), a right angle is 90° (complementary angles), and interior angles of polygons sum to a set total based on the number of sides.
Watch out for
- Assuming any repeating pattern of shapes is a tessellation, without checking that there are no gaps or overlaps.
- Assuming a perspective drawing preserves true angles, when isometric and cabinet projections both distort angles to create the illusion of depth.
- Mixing up the mapping rules for reflection in the x-axis versus the y-axis.
Every skill’s key ideas, worked examples and checks are in MapleMind.Practise this unit
Unit 5 · 6 skills
Financial Literacy
Payment Methods, Currencies, and Exchange Rates
Weighing methods of payment across currencies and exchange rates
I can describe advantages and disadvantages of payment methods used with multiple currencies and exchange rates.
Skill 5.1
Creating a Long-Term Financial Plan
Creating a financial plan that accounts for income, expenses, and taxes
I can create a financial plan to reach a long-term financial goal, accounting for income, expenses, and taxes.
Skill 5.2
Maintaining a Balanced Budget
Identifying ways to keep a balanced budget and track income and spending
I can identify ways to maintain a balanced budget and track income and spending.
Skill 5.3
Simple and Compound Interest
Determining the growth of simple and compound interest and its long-term impact
I can determine the growth of simple and compound interest and explain its impact on long-term financial planning.
Skill 5.4
Getting More Value for Your Money
Comparing ways consumers can get more value for their money
I can compare ways consumers can get more value for their money, including sales and loyalty programs.
Skill 5.5
Comparing Credit Cards and Consumer Contracts
Comparing credit card interest rates, fees, and rewards to find the best value
I can compare credit card interest rates, fees, and rewards to determine the best value.
Skill 5.6
The official wording · 6 outcomes
- 5.1
- describe some advantages and disadvantages of various methods of payment that can be used when dealing with multiple currencies and exchange rates
- 5.2
- create a financial plan to reach a long-term financial goal, accounting for income, expenses, and tax implications
- 5.3
- identify different ways to maintain a balanced budget, and use appropriate tools to track all income and spending, for several different scenarios
- 5.4
- determine the growth of simple and compound interest at various rates using digital tools, and explain the impact interest has on long-term financial planning
- 5.5
- compare various ways for consumers to get more value for their money when spending, including taking advantage of sales and customer loyalty and incentive programs, and determine the best choice for different scenarios
- 5.6
- compare interest rates, annual fees, and rewards and other incentives offered by various credit card companies and consumer contracts to determine the best value and the best choice for different scenarios
Key ideas
There are different ways to pay in a foreign currency (cash exchange, credit card, prepaid travel card), each with its own advantages and disadvantages.
Income and expenses affect short-, medium-, and long-term financial goals differently — a long-term goal needs sustained planning over time.
Balancing a budget requires tracking income, fixed and variable expenses, spending, and saving.
Simple interest is calculated only on the original amount each period, while compound interest is calculated on the original amount PLUS any interest already earned.
Discounts and loyalty or incentive programs are offered by businesses so consumers feel they're getting more perceived value for their money.
Watch out for
- Assuming exchange rates never change or don't need to be checked before a purchase.
- Planning a budget using gross income without considering that taxes reduce the amount actually available.
- Confusing fixed expenses (that stay the same each month) with variable expenses (that change), leading to inaccurate tracking.
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 8.
Textbooks
The textbooks Ontario Ministry of Education lists for Mathematics, Grade 8:
- Math Now Grade 8
- MathUp Classroom, Grade 8
- Mathology 8
- My Math Path 8
- D2L Ontario Math 8
From the Trillium List, read October 27, 2026. ontario.ca
Strands
| Strand | Outcomes | Taught in |
|---|---|---|
| BNumber | Outcomes 12 | Taught in Unit 1 |
| CAlgebra | Outcomes 11 | Taught in Unit 2 |
| DData | Outcomes 8 | Taught in Unit 3 |
| ESpatial Sense | Outcomes 8 | 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.
Study it in MapleMind
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Course Companion
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Questions about Mathematics, Grade 8
What is Mathematics, Grade 8?
Ontario’s Grade 8 math course: 5 units and 45 skills, from Number to Financial Literacy.
What units are in Mathematics, Grade 8?
1. Number, 2. Algebra, 3. Data, 4. Spatial Sense and 5. Financial Literacy.
Is there a provincial exam for Mathematics, Grade 8?
No. Ontario gives no provincial exam for Mathematics, Grade 8.
What textbook does Mathematics, Grade 8 use?
The textbooks Ontario Ministry of Education lists for Mathematics, Grade 8: Math Now Grade 8, GTK Press, MathUp Classroom, Grade 8, Rubicon Publishing, Mathology 8, Pearson Education Canada, My Math Path 8, Nelson Education Ltd. and D2L Ontario Math 8, D2L Corporation.
What comes after Mathematics, Grade 8?
Mathematics, Grade 9 (De-streamed).
Can MapleMind help with Mathematics, Grade 8?
Yes. MapleMind teaches every skill of Mathematics, Grade 8, 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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