Ontario · Grade 5
Mathematics, Grade 5
Ontario’s Grade 5 math course, from Number to Financial Literacy.
- Units
- 5
- Lessons
- 25
- Skills
- 54
- Provincial exam
- None
- Official curriculum
- Ontario Ministry of Education
Unit by unit
Every skill in the course, numbered by unit.
Unit 1 · 17 skills
Number
Whole Numbers to 100 000
Reading and representing numbers to 100 000
I can read, build, and break apart whole numbers up to 100 000.
Skill 1.1
Comparing and ordering numbers to 100 000
I can compare and order whole numbers up to 100 000.
Skill 1.2
Equivalent Fractions to Twelfths
Representing equivalent fractions, halves to twelfths
I can represent equivalent fractions from halves to twelfths, including improper fractions and mixed numbers.
Skill 1.3
Comparing and ordering fractions, halves to twelfths
I can compare and order fractions from halves to twelfths.
Skill 1.4
Decimals to Hundredths
Reading, representing, comparing, and ordering decimals to hundredths
I can read, represent, compare, and order decimals to hundredths.
Skill 1.5
Rounding decimals to the nearest tenth
I can round decimals to the nearest tenth.
Skill 1.6
Connecting Fractions, Decimals, and Percents
Equivalences between fractions and decimals
I can show equivalences between fractions and decimals up to hundredths.
Skill 1.7
Equivalences between decimals and whole-number percents
I can show equivalences between decimals and whole-number percents.
Skill 1.8
Properties of Operations and Mental Math
Using properties of operations to solve multi-operation problems
I can use properties of operations to solve and check multi-operation problems.
Skill 1.9
Recalling multiplication and division facts to 12 x 12
I can recall multiplication facts to 12 x 12 and related division facts.
Skill 1.10
Mental math: multiplying by 0.1 and 0.01, estimating with decimals
I can mentally multiply whole numbers by 0.1 and 0.01, and estimate decimal sums and differences.
Skill 1.11
Adding and Subtracting Whole Numbers, Decimals, and Fractions
Adding and subtracting whole numbers to 100 000 and decimals to hundredths
I can add and subtract whole numbers up to 100 000 and decimals to hundredths.
Skill 1.12
Adding and subtracting fractions with like denominators
I can add and subtract fractions with like denominators.
Skill 1.13
Multiplying and Dividing Larger Numbers
Multiplying two-digit numbers (area model and algorithm)
I can multiply two-digit numbers using the area model and algorithms.
Skill 1.14
Dividing three-digit numbers by two-digit numbers (area model and algorithm)
I can divide three-digit numbers by two-digit numbers using the area model and algorithms.
Skill 1.15
Operations with Unit Fractions, Ratios, and Rates
Multiplying and dividing whole numbers by unit fractions
I can multiply and divide whole numbers by unit fractions.
Skill 1.16
Representing and creating equivalent ratios and rates
I can represent and create equivalent ratios and rates.
Skill 1.17
The official wording · 17 outcomes
- 1.1
- read, represent, compose, and decompose whole numbers up to and including 100 000, using appropriate tools and strategies, and describe various ways they are used in everyday life
- 1.2
- compare and order whole numbers up to and including 100 000, in various contexts
- 1.3
- represent equivalent fractions from halves to twelfths, including improper fractions and mixed numbers, using appropriate tools, in various contexts
- 1.4
- compare and order fractions from halves to twelfths, including improper fractions and mixed numbers, in various contexts
- 1.5
- read, represent, compare, and order decimal numbers up to hundredths, in various contexts
- 1.6
- round decimal numbers to the nearest tenth, in various contexts
- 1.7
- describe relationships and show equivalences among fractions, decimal numbers up to hundredths
- 1.8
- decimal numbers up to hundredths, and whole number percents, using appropriate tools and drawings
- 1.9
- use the properties of operations, and the relationships between operations, to solve problems involving whole numbers and decimal numbers, including those requiring more than one operation, and check calculations
- 1.10
- recall and demonstrate multiplication facts from 0 × 0 to 12 × 12, and related division facts
- 1.11
- use mental math strategies to multiply whole numbers by 0.1 and 0.01 and estimate sums and differences of decimal numbers up to hundredths, and explain the strategies used
- 1.12
- represent and solve problems involving the addition and subtraction of whole numbers that add up to no more than 100 000, and of decimal numbers up to hundredths, using appropriate tools, strategies, and algorithms
- 1.13
- add and subtract fractions with like denominators, in various contexts
- 1.14
- represent and solve problems involving the multiplication of two-digit whole numbers by two- digit whole numbers using the area model and using algorithms, and make connections between the two methods
- 1.15
- represent and solve problems involving the division of three-digit whole numbers by two-digit whole numbers using the area model and using algorithms, and make connections between the two methods, while expressing any remainder appropriately
- 1.16
- multiply and divide one-digit whole numbers by unit fractions, using appropriate tools and drawings
- 1.17
- represent and create equivalent ratios and rates, using a variety of tools and models, in various contexts
Key ideas
Each digit in a number has a place value, and the digit's position tells you its value (the 5 in 51 981 is worth 50 000, not 5).
Equivalent fractions describe the same quantity, even though the numerator and denominator look different.
The first place after the decimal point is tenths, and the second is hundredths.
Fractions and decimals both describe a relationship to a whole — decimals just use place value (tenths, hundredths) instead of any denominator.
The commutative and associative properties mean numbers can be added or multiplied in a different order or grouping and still get the same result.
Watch out for
- Reading a number digit-by-digit ('seven eight zero three seven') instead of by its place-value groups.
- Thinking a fraction with bigger numbers (like 4/8) must be a bigger amount than a fraction with smaller numbers (like 1/2).
- Thinking a decimal with more digits after the point is always bigger (believing 0.9 < 0.15 because '15 > 9').
Every skill’s key ideas, worked examples and checks are in MapleMind.Practise this unit
Unit 2 · 10 skills
Algebra
Repeating, Growing, and Shrinking Patterns
Identifying and describing repeating, growing, and shrinking patterns
I can identify and describe repeating, growing, and shrinking patterns.
Skill 2.1
Creating and translating growing and shrinking patterns (tables and graphs)
I can create and translate growing and shrinking patterns using tables of values and graphs.
Skill 2.2
Determining pattern rules for repeating, growing, and shrinking patterns
I can determine pattern rules to extend patterns and make predictions.
Skill 2.3
Creating patterns to show relationships among whole numbers and decimals
I can create patterns to show relationships among whole numbers and decimals.
Skill 2.4
Expressions, Equations, and Inequalities
Translating among words, algebraic expressions, and visual representations
I can translate among words, algebraic expressions, and visual representations.
Skill 2.5
Evaluating algebraic expressions with whole numbers
I can evaluate algebraic expressions that involve whole numbers.
Skill 2.6
Solving equations with whole numbers up to 100
I can solve equations with whole numbers up to 100 and verify the solutions.
Skill 2.7
Solving and graphing one-operation inequalities up to 50
I can solve one-operation inequalities up to 50 and verify and graph the solutions.
Skill 2.8
Coding with Conditional Statements
Writing and running code with conditional statements and control structures
I can write and run code that uses conditional statements and control structures.
Skill 2.9
Reading and altering code with conditional statements and control structures
I can read and alter code that uses conditional statements and control structures.
Skill 2.10
The official wording · 10 outcomes
- 2.1
- identify and describe repeating, growing, and shrinking patterns, including patterns found in real-life contexts
- 2.2
- create and translate growing and shrinking patterns using various representations, including tables of values and graphs
- 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
- 2.4
- create and describe patterns to illustrate relationships among whole numbers and decimal tenths and hundredths
- 2.5
- translate among words, algebraic expressions, and visual representations that describe equivalent relationships
- 2.6
- evaluate algebraic expressions that involve whole numbers
- 2.7
- solve equations that involve whole numbers up to 100 in various contexts, and verify solutions
- 2.8
- solve inequalities that involve one operation and whole numbers up to 50, and verify and graph the solutions
- 2.9
- solve problems and create computational representations of mathematical situations by writing and executing code, including code that involves conditional statements and other control structures
- 2.10
- read and alter existing code, including code that involves conditional statements and other control structures, and describe how changes to the code affect the outcomes
Key ideas
A repeating pattern has a core that repeats over and over, while a growing pattern increases in size or number of elements each term.
An algebraic expression combines variables, numbers, and operations to generalize a relationship, like 4s for the perimeter of a square.
A conditional statement checks something that is true or false, and does different things depending on the answer.
A shrinking pattern decreases in size or number of elements from one term to the next.
The same relationship can be shown in words, as an algebraic expression, or with a visual model — and they all describe the same thing.
Watch out for
- Assuming every pattern must be repeating and missing growing or shrinking patterns.
- Writing '3a' as if it means '3 and a' instead of '3 times a.'.
- Writing a conditional statement without a clear true/false condition to check.
Every skill’s key ideas, worked examples and checks are in MapleMind.Practise this unit
Unit 3 · 8 skills
Data
Sampling Techniques and Collecting Data
Explaining why sampling techniques give a representative sample
I can explain why sampling techniques matter for a representative sample.
Skill 3.1
Collecting data with sampling and organizing it in relative-frequency tables
I can collect data using sampling and organize it in relative-frequency tables.
Skill 3.2
Stacked-Bar Graphs and Infographics
Selecting and justifying a graph type, including stacked-bar graphs
I can select and justify a graph type, including stacked-bar graphs.
Skill 3.3
Creating an infographic using relative-frequency tables and stacked-bar graphs
I can create an infographic using relative-frequency tables and stacked-bar graphs.
Skill 3.4
Mean, Median, Mode, and Analysing Data
Determining mean and median and identifying mode(s)
I can determine mean and median and identify mode(s) for a data set.
Skill 3.5
Analysing data in stacked-bar and misleading graphs
I can analyse data in stacked-bar and misleading graphs and draw conclusions.
Skill 3.6
Probability with Fractions
Using fractions and a probability line to make predictions
I can use fractions and a probability line to make predictions.
Skill 3.7
Comparing theoretical and experimental probability
I can compare theoretical and experimental probability.
Skill 3.8
The official wording · 8 outcomes
- 3.1
- explain the importance of various sampling techniques for collecting a sample of data that is representative of a population
- 3.2
- collect data, using appropriate sampling techniques as needed, to answer questions of interest about a population, and organize the data in relative-frequency tables
- 3.3
- select from among a variety of graphs, including stacked-bar 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 relative-frequency tables and stacked-bar graphs, and incorporating any other relevant information that helps to tell a story about the data
- 3.5
- determine the mean and the median and identify the mode(s), if any, for various data sets involving whole numbers and decimal numbers, and explain what each of these measures indicates about the data
- 3.6
- analyse different sets of data presented in various ways, including in stacked-bar 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
- use fractions to express the probability of events happening, represent this probability on a probability line, and use it to make predictions and informed decisions
- 3.8
- determine and compare the theoretical and experimental probabilities of an event happening
Key ideas
Sampling means gathering data from a smaller subset of a population instead of everyone, which is more efficient and practical.
A stacked-bar graph shows a whole bar divided into segments, each representing a different category, often using percent or relative frequency.
The mean, median, and mode can each be found for quantitative data, but only the mode works for qualitative (category) data.
Probability is measured with numbers from 0 (impossible) to 1 (certain), and fractions can express any probability along that line.
Simple random, stratified random, and systematic random sampling are different ways to choose a fair sample.
Watch out for
- Thinking any small group of easy-to-reach people counts as a fair sample.
- Choosing a graph type without considering whether the data is best shown as proportions of a whole.
- Confusing the median (the middle value once ordered) with the mean (the sum divided by the count).
Every skill’s key ideas, worked examples and checks are in MapleMind.Practise this unit
Unit 4 · 13 skills
Spatial Sense
Triangles and Congruent Shapes
Identifying triangle properties and constructing triangles
I can identify triangle properties and construct triangles from measurements.
Skill 4.1
Identifying and constructing congruent shapes
I can identify and construct congruent triangles, rectangles, and parallelograms.
Skill 4.2
Views of Objects
Drawing and matching top, front, and side views of objects
I can draw and match top, front, and side views of objects.
Skill 4.3
The Cartesian Plane and Translations
Plotting and reading coordinates in the first quadrant
I can plot and read coordinates in the first quadrant of a Cartesian plane.
Skill 4.4
Describing translations that move a point between coordinates
I can describe the translations that move a point from one coordinate to another.
Skill 4.5
Translations, Reflections, and Rotations up to 180°
Performing and predicting translations, reflections, and rotations up to 180°
I can perform and predict translations, reflections, and rotations up to 180°.
Skill 4.6
Metric Measurement and Conversions
Estimating and measuring with metric units
I can estimate and measure with appropriate metric units.
Skill 4.7
Converting larger metric units to smaller ones
I can convert larger metric units to smaller ones.
Skill 4.8
Angles and Protractors
Comparing angles by matching and with non-standard units
I can compare angles by matching and with non-standard units.
Skill 4.9
Using a protractor to measure and construct angles up to 180°
I can use a protractor to measure and construct angles up to 180°.
Skill 4.10
Area Formulas and Perimeter
Developing and using the area formula for a parallelogram
I can develop and use the area formula for a parallelogram.
Skill 4.11
Developing and using the area formula for a triangle
I can develop and use the area formula for a triangle.
Skill 4.12
Showing that equal-area shapes can have different perimeters
I can show that equal-area shapes can have different perimeters.
Skill 4.13
The official wording · 13 outcomes
- 4.1
- identify geometric properties of triangles, and construct different types of triangles when given side or angle measurements
- 4.2
- identify and construct congruent triangles, rectangles, and parallelograms
- 4.3
- draw top, front, and side views of objects, and match drawings with objects
- 4.4
- plot and read coordinates in the first quadrant of a Cartesian plane using various scales
- 4.5
- describe the translations that move a point from one coordinate to another
- 4.6
- describe and perform translations, reflections, and rotations up to 180° on a grid, and predict the results of these transformations
- 4.7
- use appropriate metric units to estimate and measure length, area, mass, and capacity
- 4.8
- solve problems that involve converting larger metric units into smaller ones, and describe the base ten relationships among metric units
- 4.9
- compare angles and determine their relative size by matching them and by measuring them using appropriate non-standard units
- 4.10
- explain how protractors work, use them to measure and construct angles up to 180°, and use benchmark angles to estimate the size of other angles
- 4.11
- use the area relationships among rectangles, parallelograms, and triangles to develop the formulas for the area of a parallelogram
- 4.12
- the area of a triangle, and solve related problems
- 4.13
- show that two-dimensional shapes with the same area can have different perimeters, and solve related problems
Key ideas
All triangles have three sides and three angles that add up to 180 degrees.
A three-dimensional object can be shown in two dimensions using its top, front, and side views.
The x-axis and y-axis are perpendicular number lines that meet at the origin, (0, 0).
A translation slides every point of a shape the same distance and direction.
The attribute being measured (length, area, mass, or capacity) determines which type of unit to use.
Watch out for
- Thinking a triangle's angles can add up to something other than 180 degrees.
- Drawing the same view from every angle instead of showing what is actually seen from each direction.
- Reversing the order of the coordinates, plotting (y, x) instead of (x, y).
Every skill’s key ideas, worked examples and checks are in MapleMind.Practise this unit
Unit 5 · 6 skills
Financial Literacy
Transferring Money and Calculating Transactions
Describing ways money can be transferred
I can describe several ways money can be transferred.
Skill 5.1
Estimating and calculating transaction costs, including sales tax
I can estimate and calculate transaction costs, including sales tax.
Skill 5.2
Budgets, Credit, and Debt
Designing sample basic budgets
I can design sample basic budgets for earning and spending scenarios.
Skill 5.3
Explaining credit and debt
I can explain credit and debt and how they affect financial decisions.
Skill 5.4
Unit Rates and Taxes in Canada
Calculating unit rates and identifying the best value
I can calculate unit rates and identify the best value.
Skill 5.5
Describing taxes collected by governments in Canada
I can describe types of taxes in Canada and how tax revenue provides services.
Skill 5.6
The official wording · 6 outcomes
- 5.1
- describe several ways money can be transferred among individuals, organizations, and businesses
- 5.2
- estimate and calculate the cost of transactions involving multiple items priced in dollars and cents, including sales tax, using various strategies
- 5.3
- design sample basic budgets to manage finances for various earning and spending scenarios
- 5.4
- explain the concepts of credit and debt, and describe how financial decisions may be impacted by each
- 5.5
- calculate unit rates for various goods and services, and identify which rates offer the best value
- 5.6
- describe the types of taxes that are collected by the different levels of government in Canada, and explain how tax revenue is used to provide services in the community
Key ideas
Money can move between people, organizations, and businesses in many ways — cash, cheques, e-transfers, cards, and more.
A budget is a financial planning tool that tracks money coming in (earnings) and money going out (expenses).
A unit rate compares a cost or amount to a single unit, like the price per item or price per 100 grams.
Different transfer methods work better for different situations, depending on things like security, speed, and available tools.
Designing a budget means considering earnings, expenses, and the goals the budget is meant to support.
Watch out for
- Thinking cash is the only 'real' way money can be transferred.
- Forgetting to include all sources of earnings or all expenses in a budget.
- Comparing total prices instead of unit rates when the package sizes are different.
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 5.
Textbooks
The textbooks Ontario Ministry of Education lists for Mathematics, Grade 5:
- Math Now Grade 5 Online Resource
- Mathology 5
- My Math Path 5
- MathUP Classroom, Grade 5
- D2L Ontario Math 5
From the Trillium List, read October 27, 2026. ontario.ca
Strands
| Strand | Outcomes | Taught in |
|---|---|---|
| BNumber | Outcomes 17 | Taught in Unit 1 |
| CAlgebra | Outcomes 10 | Taught in Unit 2 |
| DData | Outcomes 8 | Taught in Unit 3 |
| ESpatial Sense | Outcomes 13 | 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
Your year in one workbook
A fun way to keep Mathematics, Grade 5 organized, get to know your child better and see early when they need a hand. Fill it in on a screen, or print it.
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Questions about Mathematics, Grade 5
What is Mathematics, Grade 5?
Ontario’s Grade 5 math course: 5 units and 54 skills, from Number to Financial Literacy.
What units are in Mathematics, Grade 5?
1. Number, 2. Algebra, 3. Data, 4. Spatial Sense and 5. Financial Literacy.
Is there a provincial exam for Mathematics, Grade 5?
No. Ontario gives no provincial exam for Mathematics, Grade 5.
What textbook does Mathematics, Grade 5 use?
The textbooks Ontario Ministry of Education lists for Mathematics, Grade 5: Math Now Grade 5 Online Resource, GTK Press, Mathology 5, Pearson Education Canada, My Math Path 5, Nelson Education Ltd., MathUP Classroom, Grade 5, Rubicon Publishing, Inc. and D2L Ontario Math 5, D2L Corporation.
What comes after Mathematics, Grade 5?
Mathematics, Grade 6.
Can MapleMind help with Mathematics, Grade 5?
Yes. MapleMind teaches every skill of Mathematics, Grade 5, 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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