Ontario · Grade 9
Mathematics, Grade 9 (De-streamed)
- MTH1W
Ontario’s Grade 9 math course, from Number to Financial Literacy.
- Units
- 5
- Lessons
- 49
- Skills
- 51
- Provincial exam
- 20% of the final mark
- Official curriculum
- Ontario Ministry of Education
Unit by unit
Every skill in the course, numbered by unit.
Unit 1 · 14 skills
Number
The Development and Use of Numbers
Telling the story of a number concept across cultures
I can research a number concept and tell the story of its development and use in a specific culture.
Skill 1.1
Number Sets
Describing how subsets of a number system are defined
I can describe how subsets of a number system are defined.
Skill 1.2
Comparing similarities and differences between number subsets
I can describe similarities and differences between different subsets of numbers.
Skill 1.3
Density, Infinity, and Limit
Using patterns to explain the density of a number set
I can use patterns and number relationships to explain the density of a number set.
Skill 1.4
Using patterns to explain infinity and limit
I can use patterns and number relationships to explain infinity and limit.
Skill 1.5
The Sign and Size of an Exponent
Analysing how the sign and size of an exponent affects the value of a power
I can use patterning to analyse how the sign and size of an exponent affects the value of a power.
Skill 1.6
Scientific Notation and Evaluating Powers
Using the exponent relationship to write scientific notation and evaluate powers
I can use the exponent relationship to express numbers in scientific notation and evaluate powers.
Skill 1.7
The Exponent Laws
Analysing the relationships between exponents and operations with powers
I can use patterning to analyse the relationships between exponents and operations with powers.
Skill 1.8
Simplifying Expressions with the Exponent Laws
Using the exponent laws to simplify numeric and algebraic expressions
I can use the exponent laws to simplify numeric and algebraic expressions.
Skill 1.9
Integers to Describe Location, Direction, Amount, and Change
Applying integers to describe location, direction, amount, and change
I can apply an understanding of integers to describe location, direction, amount, and change in different contexts.
Skill 1.10
Unit Fractions and Measuring Tools
Applying unit fractions and their relationship to other fractional amounts
I can apply an understanding of unit fractions and their relationship to other fractional amounts, using measuring tools.
Skill 1.11
Positive and Negative Signs on Ratios, Rates, Fractions, and Decimals
Explaining the effects of positive and negative signs on ratios, rates, fractions, and decimals
I can explain the effects that positive and negative signs have on ratios, rates, fractions, and decimals.
Skill 1.12
Operations with Positive and Negative Fractions and Mixed Numbers
Solving problems with operations on positive and negative fractions and mixed numbers
I can solve problems involving operations with positive and negative fractions and mixed numbers.
Skill 1.13
Rates, Percentages, and Proportions
Posing and solving problems involving rates, percentages, and proportions
I can pose and solve problems involving rates, percentages, and proportions.
Skill 1.14
The official wording · 14 outcomes
- 1.1
- research a number concept to tell a story about its development and use in a specific culture, and describe its relevance in a current context
- 1.2
- describe how various subsets of a number system are defined
- 1.3
- describe similarities and differences between these subsets
- 1.4
- use patterns and number relationships to explain density
- 1.5
- infinity, and limit as they relate to number sets
- 1.6
- analyse, through the use of patterning, the relationship between the sign and size of an exponent and the value of a power
- 1.7
- use this relationship to express numbers in scientific notation and evaluate powers
- 1.8
- analyse, through the use of patterning, the relationships between the exponents of powers and the operations with powers
- 1.9
- use these relationships to simplify numeric and algebraic expressions
- 1.10
- apply an understanding of integers to describe location, direction, amount, and changes in any of these, in various contexts
- 1.11
- apply an understanding of unit fractions and their relationship to other fractional amounts, in various contexts, including the use of measuring tools
- 1.12
- apply an understanding of integers to explain the effects that positive and negative signs have on the values of ratios, rates, fractions, and decimals, in various contexts
- 1.13
- solve problems involving operations with positive and negative fractions and mixed numbers, including problems involving formulas, measurements, and linear relations, using technology when appropriate
- 1.14
- pose and solve problems involving rates, percentages, and proportions in various contexts, including contexts connected to real-life applications of data, measurement, geometry, linear relations, and financial literacy
Key ideas
Number concepts (number systems, proportional reasoning, ratios like the golden ratio) were developed and used by many different cultures throughout history, often for practical purposes like trade or design.
Every number system is made up of a set of numbers as well as certain arithmetic operations defined on them.
A set's density describes the likelihood that a number of a particular type will be found within a given set of numbers — it's different from cardinality (just counting how many elements are in a set).
When the size of an exponent decreases by 1, the value of the power is divided by the base — this pattern reveals what a power with an exponent of 0 or a negative exponent means.
Scientific notation writes a number as a decimal between 1 and 10 multiplied by a power of ten, making very large or very small numbers easier to read and compare.
Watch out for
- Assuming a number concept was invented once by one person or culture, missing that similar ideas often developed independently in many cultures.
- Thinking a subset must be a completely separate, non-overlapping group, rather than understanding that the same number can belong to more than one subset.
- Confusing density with cardinality — thinking a 'denser' set must simply have more total numbers, rather than a higher likelihood of a particular type appearing.
Every skill’s key ideas, worked examples and checks are in MapleMind.Practise this unit
Unit 2 · 15 skills
Algebra
The Development and Use of Algebra
Telling the story of an algebraic concept across cultures
I can research an algebraic concept and tell the story of its development and use in a specific culture.
Skill 2.1
Creating Algebraic Expressions to Generalize Relationships
Creating algebraic expressions from words, numbers, and visuals
I can create algebraic expressions to generalize relationships expressed in words, numbers, and visuals.
Skill 2.2
Comparing Algebraic Expressions for Equivalence
Comparing expressions using concrete, numerical, graphical, and algebraic methods
I can compare algebraic expressions to identify whether they're equivalent, using concrete, numerical, graphical, or algebraic methods.
Skill 2.3
Simplifying Algebraic Expressions
Simplifying algebraic expressions using properties of operations
I can simplify algebraic expressions by applying properties of operations.
Skill 2.4
Creating and Solving Equations
Creating and solving equations, and verifying solutions
I can create and solve equations for different contexts, and verify my solutions.
Skill 2.5
Coding to Demonstrate Algebraic Concepts
Using coding to demonstrate variables, parameters, equations, and inequalities
I can use coding to demonstrate an understanding of variables, parameters, equations, and inequalities.
Skill 2.6
Decomposing Situations into Computational Steps
Creating code by decomposing a situation into computational steps
I can create code by decomposing situations into computational steps.
Skill 2.7
Reading and Altering Code
Reading code to predict its outcome and altering it for new situations
I can read code to predict its outcome, and alter code to represent a similar or new situation.
Skill 2.8
Comparing the Shapes of Graphs and Rates of Change
Comparing the shapes of linear and non-linear graphs to describe rates of change
I can compare the shapes of linear and non-linear graphs to describe rates of change and make predictions.
Skill 2.9
Representing Linear Relations Four Ways
Representing linear relations with materials, tables, graphs, and equations
I can represent linear relations using concrete materials, tables of values, graphs, and equations, connecting rate of change and initial value across all four.
Skill 2.10
Comparing Two Lines and Their Point of Intersection
Comparing two lines y = ax + b and interpreting their point of intersection
I can compare two linear relations of the form y = ax + b graphically and algebraically, and interpret their point of intersection.
Skill 2.11
Comparing Characteristics of Relations
Comparing characteristics of graphs, tables of values, and equations
I can compare characteristics of graphs, tables of values, and equations of linear and non-linear relations.
Skill 2.12
Graphing Equation Forms and Their Inequalities
Graphing relations of the forms x=k, y=k, x+y=k, x-y=k, ax+by=k, xy=k and their inequalities
I can graph relations of the forms x=k, y=k, x+y=k, x-y=k, ax+by=k, and xy=k, and their associated inequalities.
Skill 2.13
Transforming Lines y = ax
Translating, reflecting, and rotating lines y = ax
I can translate, reflect, and rotate lines y = ax and describe how each transformation affects the graph and equation.
Skill 2.14
Determining the Equation of a Line
Determining a line’s equation from rate of change and initial value
I can determine the equation of a line from a graph, table of values, or concrete representation by connecting rate of change to slope and initial value to y-intercept.
Skill 2.15
The official wording · 15 outcomes
- 2.1
- research an algebraic concept to tell a story about its development and use in a specific culture, and describe its relevance in a current context
- 2.2
- create algebraic expressions to generalize relationships expressed in words, numbers, and visual representations, in various contexts
- 2.3
- compare algebraic expressions using concrete, numerical, graphical, and algebraic methods to identify those that are equivalent, and justify their choices
- 2.4
- simplify algebraic expressions by applying properties of operations of numbers, using various representations and tools, in different contexts
- 2.5
- create and solve equations for various contexts, and verify their solutions
- 2.6
- use coding to demonstrate an understanding of algebraic concepts including variables, parameters, equations, and inequalities
- 2.7
- create code by decomposing situations into computational steps in order to represent mathematical concepts and relationships, and to solve problems
- 2.8
- read code to predict its outcome, and alter code to adjust constraints, parameters, and outcomes to represent a similar or new mathematical situation
- 2.9
- compare the shapes of graphs of linear and non-linear relations to describe their rates of change, to make connections to growing and shrinking patterns, and to make predictions
- 2.10
- represent linear relations using concrete materials, tables of values, graphs, and equations, and make connections between the various representations to demonstrate an understanding of rates of change and initial values
- 2.11
- compare two linear relations of the form y = ax + b graphically and algebraically, and interpret the meaning of their point of intersection in terms of a given context
- 2.12
- compare characteristics of graphs, tables of values, and equations of linear and non-linear relations
- 2.13
- graph relations represented as algebraic equations of the forms x = k, y = k, x + y = k, x – y = k, ax + by = k, and xy = k, and their associated inequalities, where a, b, and k are constants, to identify various characteristics and the points and/or regions defined by these equations and inequalities
- 2.14
- translate, reflect, and rotate lines defined by y = ax, where a is a constant, and describe how each transformation affects the graphs and equations of the defined lines
- 2.15
- determine the equations of lines from graphs, tables of values, and concrete representations of linear relations by making connections between rates of change and slopes, and between initial values and y- intercepts, and use these equations to solve problems
Key ideas
Algebraic concepts like variables, patterns, and generalizing relationships have been developed and used by many cultures — from ancient Egyptian symbols for unknowns to weaving patterns encoded in punch cards.
A relationship described in words (like 'three less than double the sum of two numbers') can be translated directly into an algebraic expression: 2(x + y) - 3.
Expressions can be compared using concrete tools (algebra tiles), numerically (substituting values or a table of values), graphically (checking if the graphs match), or algebraically (simplifying both to the same form).
The commutative, associative, and distributive properties that work for numbers also work for algebraic terms — for example, -2x + 3x = 3x + (-2x) just like -2 + 3 = 3 + (-2).
Equations can be created from real-life contexts — like determining the diagonal distance across a field, the fixed cost for a service, or the term of a pattern with a given value.
Watch out for
- Assuming algebra with symbols like x and y is a purely modern invention, missing centuries of earlier symbolic and pattern-based thinking.
- Translating a word relationship into the wrong order of operations (e.g., writing 'three less than double the sum' incorrectly as 2x + y - 3 instead of 2(x + y) - 3).
- Concluding two expressions are equivalent just because they give the same result for ONE tested value, without checking more values or using an algebraic method.
Every skill’s key ideas, worked examples and checks are in MapleMind.Practise this unit
Unit 3 · 9 skills
Data
Implications of Collecting and Using Large Amounts of Data
Describing implications of collecting, storing, and using large amounts of data
I can describe potential implications and consequences of collecting, storing, and using large amounts of data.
Skill 3.1
Single-Variable Data: Quartiles and Box Plots
Representing and analysing single-variable data with quartiles and box plots
I can represent and statistically analyse single-variable data using quartile values and box plots.
Skill 3.2
Creating a Scatter Plot for Two Variables
Creating a scatter plot to represent a relationship between two variables
I can create a scatter plot to represent the relationship between two variables.
Skill 3.3
Correlation, Regression Models, and Predictions
Determining correlation and testing regression models to make predictions
I can determine correlation between two variables and test regression models to make predictions.
Skill 3.4
The Value of Mathematical Modelling
Describing the value of mathematical modelling in real life
I can describe the value of mathematical modelling and how it's used in real life to inform decisions.
Skill 3.5
Modelling Step 1: Identify the Question
Identifying a question of interest and the information needed to answer it
I can identify a question of interest and the information needed to answer it, as the first step of mathematical modelling.
Skill 3.6
Modelling Step 2: Plan and Collect the Data
Creating a plan to collect data, identifying assumptions and what varies
I can create a plan to collect data for my question of interest, identifying assumptions and what may vary or stay the same.
Skill 3.7
Modelling Step 3: Display, Analyse, and Build the Model
Displaying and analysing data to build a mathematical model
I can determine ways to display and analyse data in order to build a mathematical model that answers my question of interest.
Skill 3.8
Modelling Step 4: Report, Evaluate, and Predict
Reporting how a model answers the question, its limitations, and what it predicts
I can report how a mathematical model answers my question, evaluate how well it fits, and describe its limitations and predictions.
Skill 3.9
The official wording · 9 outcomes
- 3.1
- identify a current context involving a large amount of data, and describe potential implications and consequences of its collection, storage, representation, and use
- 3.2
- represent and statistically analyse data from a real-life situation involving a single variable in various ways, including the use of quartile values and box plots
- 3.3
- create a scatter plot to represent the relationship between two variables
- 3.4
- determine the correlation between these variables by testing different regression models using technology, and use a model to make predictions when appropriate
- 3.5
- describe the value of mathematical modelling and how it is used in real life to inform decisions
- 3.6
- identify a question of interest requiring the collection and analysis of data, and identify the information needed to answer the question
- 3.7
- create a plan to collect the necessary data on the question of interest from an appropriate source, identify assumptions, identify what may vary and what may remain the same in the situation, and then carry out the plan
- 3.8
- determine ways to display and analyse the data in order to create a mathematical model to answer the original question of interest, taking into account the nature of the data, the context, and the assumptions made
- 3.9
- report how the model can be used to answer the question of interest, how well the model fits the context, potential limitations of the model, and what predictions can be made based on the model
Key ideas
Large amounts of data are collected in contexts like social media, online shopping, census data, fitness apps, and scientific research.
A box plot displays a five-number summary: the lowest value, the first quartile, the median, the third quartile, and the greatest value.
A scatter plot displays data points for two variables, with one variable on each axis, revealing whether a relationship exists between them.
The correlation coefficient r describes the strength (close to -1, 0, or 1) and direction (positive or negative) of a linear relationship between two variables.
Mathematical modelling helps develop understanding of a real-life situation, test the impact of potential changes, and support decision-making at every level of society.
Watch out for
- Assuming data collection is entirely good or entirely bad, missing that there are trade-offs and multiple perspectives to consider.
- Confusing the quartiles with simply dividing the data range into four equal-sized numeric intervals, rather than dividing the actual data into four equal-count groups.
- Plotting the two variables on the wrong axes or without a consistent scale, distorting the apparent relationship.
Every skill’s key ideas, worked examples and checks are in MapleMind.Practise this unit
Unit 4 · 8 skills
Geometry and Measurement
The Story of a Geometric Concept or Measurement System
Telling the story of a geometric concept or measurement system across cultures
I can research a geometric concept or measurement system and tell the story of its development and use in a specific culture.
Skill 4.1
Geometric Designs with Circle Properties
Creating and analysing designs using circle properties
I can create and analyse designs using circle properties.
Skill 4.2
Geometric Designs with Triangle and Angle Properties
Creating and analysing designs using triangle and angle properties
I can create and analyse designs using triangle and angle properties.
Skill 4.3
Converting Within and Between Measurement Systems
Solving problems converting units within and between measurement systems
I can solve problems involving different units within a measurement system and between measurement systems.
Skill 4.4
The Effect of Changing Dimensions
Showing how changing dimensions affects perimeter, area, surface area, and volume
I can show how changing dimensions of a 2D shape or 3D object affects perimeter, area, surface area, and volume.
Skill 4.5
Right Triangles in Real-Life and Composite Shapes
Solving right-triangle side-length problems in real life and composite shapes
I can solve problems involving the side-length relationship for right triangles in real life and in composite shapes.
Skill 4.6
The Volume Relationship Between Prisms and Pyramids
Applying the volume relationship between prisms and pyramids
I can apply the volume relationship between prisms and pyramids to solve problems.
Skill 4.7
The Volume Relationship Between Cylinders and Cones
Applying the volume relationship between cylinders and cones
I can apply the volume relationship between cylinders and cones to solve problems.
Skill 4.8
The official wording · 8 outcomes
- 4.1
- research a geometric concept or a measurement system to tell a story about its development and use in a specific culture or community, and describe its relevance in connection to careers and to other disciplines
- 4.2
- create and analyse designs involving geometric relationships and circle and triangle properties, using various tools
- 4.3
- create and analyse designs involving geometric relationships and circle and triangle properties, using various tools
- 4.4
- solve problems involving different units within a measurement system and between measurement systems, including those from various cultures or communities, using various representations and technology, when appropriate
- 4.5
- show how changing one or more dimensions of a two-dimensional shape and a three-dimensional object affects perimeter/circumference, area, surface area, and volume, using technology when appropriate
- 4.6
- solve problems involving the side-length relationship for right triangles in real-life situations, including problems that involve composite shapes
- 4.7
- the relationships between the volume of prisms and pyramids
- 4.8
- the volume of cylinders and cones, involving various units of measure
Key ideas
Geometric concepts (like the side-length relationship in right triangles) and measurement systems (like using a 'hand' to measure horse height) were developed and used by many cultures, often long before they were formally credited.
Inscribed angles subtended by the same arc are congruent, and the central angle is always twice the measure of an inscribed angle subtended from the same chord.
The interior angles of a triangle always sum to 180°, and its exterior angles always sum to 360°; the longest side is always opposite the largest angle.
Different measurement systems (metric, imperial, and others from various cultures) each have their own units for length, area, capacity, volume, mass, and time.
Changing one dimension of a shape (like doubling the length of a rectangle) does NOT necessarily double its area or perimeter in the same way — each measurement responds differently.
Watch out for
- Assuming a mathematical relationship (like the Pythagorean relationship) was discovered by only the person it's commonly named after.
- Assuming the central angle equals the inscribed angle rather than being exactly double it.
- Assuming a triangle's angles could sum to something other than 180° if the triangle looks unusual (very thin or very wide).
Every skill’s key ideas, worked examples and checks are in MapleMind.Practise this unit
Unit 5 · 5 skills
Financial Literacy
How a Financial Situation Informs Decisions
Explaining how a past or current financial situation informs decisions
I can identify a financial situation and explain how it can inform financial decisions.
Skill 5.1
Appreciation and Depreciation
Using graphs to answer questions about appreciation and depreciation
I can use graphs of appreciation and depreciation to answer related questions.
Skill 5.2
How Interest Rate and Calculation Method Affect Cost
Comparing how interest rate and calculation method affect overall cost
I can compare how different interest rates and calculation methods (simple vs compound) affect the overall cost of a purchase.
Skill 5.3
How Borrowing Time and Down Payment Affect Cost
Comparing how borrowing time and down payment amount affect overall cost
I can compare how borrowing time and down payment amount affect the overall cost of a purchase.
Skill 5.4
Modifying a Budget for Changed Circumstances
Modifying a budget to reflect changed circumstances, with a rationale
I can modify a budget to reflect changed circumstances and explain my rationale.
Skill 5.5
The official wording · 5 outcomes
- 5.1
- identify a past or current financial situation and explain how it can inform financial decisions, by applying an understanding of the context of the situation and related mathematical knowledge
- 5.2
- identify financial situations that involve appreciation and depreciation, and use associated graphs to answer related questions
- 5.3
- compare the effects that different interest rates, lengths of borrowing time, ways in which interest is calculated, and amounts of down payments have on the overall costs associated with purchasing goods or services, using appropriate tools
- 5.4
- compare the effects that different interest rates, lengths of borrowing time, ways in which interest is calculated, and amounts of down payments have on the overall costs associated with purchasing goods or services, using appropriate tools
- 5.5
- modify budgets displayed in various ways to reflect specific changes in circumstances, and provide a rationale for the modifications
Key ideas
Financial situations can be systemic, current, or historical events at a global, national, local, or individual level.
Appreciation means an asset's value increases over time (like some collectibles or real estate); depreciation means it decreases (like most vehicles and electronics).
Interest can be calculated as simple interest (based only on the original amount) or compound interest (based on the growing amount, at different compounding periods like monthly or annually).
A longer borrowing time generally increases the total interest paid, even at the same interest rate, because interest accumulates over more periods.
Budgets can be displayed in different ways — a template, a circle graph, or a digital spreadsheet — and can belong to an individual, family, business, or government.
Watch out for
- Discussing a financial situation without connecting it to any specific mathematical concept that could help understand it.
- Assuming all valuable items appreciate over time, missing that most everyday purchases (like electronics and vehicles) depreciate.
- Assuming a lower stated interest rate always means a lower total cost, without checking the compounding method and frequency.
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.
The official curriculum
This page follows Ontario’s own curriculum for Mathematics, Grade 9 (De-streamed).
Textbooks
The textbooks Ontario Ministry of Education lists for Mathematics, Grade 9 (De-streamed):
- Mathology 9
- MathUp Classroom, Grade 9
- D2L Ontario Math 9
From the Trillium List, read October 27, 2026. ontario.ca
Strands
| Strand | Outcomes | Taught in |
|---|---|---|
| BNumber | Outcomes 14 | Taught in Unit 1 |
| CAlgebra | Outcomes 15 | Taught in Unit 2 |
| DData | Outcomes 9 | Taught in Unit 3 |
| EGeometry and Measurement | Outcomes 8 | Taught in Unit 4 |
| FFinancial Literacy | Outcomes 5 | 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
MapleMind teaches Mathematics, Grade 9 (De-streamed) one skill at a time. Each skill gets a short lesson, practice as you go and a check worth up to three stars. It remembers where you stopped.
Course Companion
Your year in one workbook
A fun way to keep Mathematics, Grade 9 (De-streamed) organized, get to know your child better and see early when they need a hand. Fill it in on a screen, or print it.
- Pages
- 45
- Fillable fields
- 1,853
- Price
- $4.99
Questions about Mathematics, Grade 9 (De-streamed)
What is Mathematics, Grade 9 (De-streamed)?
Ontario’s Grade 9 math course: 5 units and 51 skills, from Number to Financial Literacy.
What units are in Mathematics, Grade 9 (De-streamed)?
1. Number, 2. Algebra, 3. Data, 4. Geometry and Measurement and 5. Financial Literacy.
Is there a provincial exam for Mathematics, Grade 9 (De-streamed)?
Yes. The EQAO Grade 9 Assessment of Mathematics counts for 20% of the final mark. Next sitting: January 12, 2027.
What textbook does Mathematics, Grade 9 (De-streamed) use?
The textbooks Ontario Ministry of Education lists for Mathematics, Grade 9 (De-streamed): Mathology 9, Pearson Education Canada, MathUp Classroom, Grade 9, Rubicon Publishing and D2L Ontario Math 9, D2L Corporation.
What comes after Mathematics, Grade 9 (De-streamed)?
Principles of Mathematics, Grade 10 (Academic) and Foundations of Mathematics, Grade 10 (Applied).
Can MapleMind help with Mathematics, Grade 9 (De-streamed)?
Yes. MapleMind teaches every skill of Mathematics, Grade 9 (De-streamed), 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.
Get ready for Mathematics, Grade 9 (De-streamed)
Practise every skill of Mathematics, Grade 9 (De-streamed) in MapleMind, free with daily limits.
