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Grade 9 Math Courses - Ontario Curriculum

Explore Ontario's Grade 9 math curriculum, covering essential topics in algebra, geometry, and data management. Prepare for success with our comprehensive course offerings aligned with provincial standards.

Ontario Grade 9 Math Curriculum - StudyPug

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OE_ID	Expectations	StudyPug Topic
ON.OE.9.B.1.1	B1.1 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: 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	Understanding the number systems

ON.OE.9.B.1.2

B1.2 describe how various subsets of a number system are defined, and describe similarities and differences between these subsets: Describe how various subsets of a number system are defined, and describe similarities and differences between these subsets

Rational vs. Irrational numbers

Comparing and ordering rational numbers

Comparing and ordering numbers

ON.OE.9.B.1.3

B1.3 use patterns and number relationships to explain density, infinity, and limit as they relate to number sets: Use patterns and number relationships to explain density, infinity, and limit as they relate to number sets

Using exponents to describe numbers

ON.OE.9.B.2.1

B2.1 analyse, through the use of patterning, the relationship between the sign and size of an exponent and the value of a power, and use this relationship to express numbers in scientific notation and evaluate powers: Analyse the relationship between the sign and size of an exponent and the value of a power, and use this relationship to express numbers in scientific notation and evaluate powers

Scientific notation

Product rule of exponents

ON.OE.9.B.2.2

B2.2 analyse, through the use of patterning, the relationships between the exponents of powers and the operations with powers, and use these relationships to simplify numeric and algebraic expressions: Analyse the relationships between the exponents of powers and the operations with powers, and use these relationships to simplify numeric and algebraic expressions

Quotient rule of exponents

Power of a product rule

Power of a quotient rule

Power of a power rule

Negative exponent rule

Combining the exponent rules

Order of operations with exponents

Using exponents to solve problems

ON.OE.9.B.3.1

B3.1 apply an understanding of integers to describe location, direction, amount, and changes in any of these, in various contexts: Apply an understanding of integers to describe location, direction, amount, and changes in any of these, in various contexts

Applications of integer operations

Subtracting integers

ON.OE.9.B.3.2

B3.2 apply an understanding of unit fractions and their relationship to other fractional amounts, in various contexts, including the use of measuring tools: Apply an understanding of unit fractions and their relationship to other fractional amounts, in various contexts, including the use of measuring tools

Converting repeating decimals to fractions

Solving problems with rational numbers in fraction form

Applications of fraction operations

ON.OE.9.B.3.3

B3.3 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: 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

Solving problems with rational numbers in decimal form

ON.OE.9.B.3.4

B3.4 solve problems involving operations with positive and negative fractions and mixed numbers, including problems involving formulas, measurements, and linear relations, using technology when appropriate: Solve problems involving operations with positive and negative fractions and mixed numbers, including problems involving formulas, measurements, and linear relations, using technology when appropriate

Fractions: Multiplying proper fractions

Multiplying improper fractions and mixed numbers

Dividing fractions and mixed numbers

Adding and subtracting decimals

Multiplying decimals

Dividing decimals

Order of operations (PEMDAS)

ON.OE.9.B.3.5

B3.5 solve problems involving ratios, rates, and percent in various contexts, including contexts connected to real-life applications of data, measurement, geometry, linear relations, and financial literacy: Solve problems involving ratios, rates, and percent in various contexts, including contexts connected to real-life applications of data, measurement, geometry, linear relations, and financial literacy

Representing percents

Percents, fractions, and decimals

Percent of a number

Adding and multiplying percents

Taxes, discounts, tips and more

Simple interest

ON.OE.9.C.1.1

C1.1 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: 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

What is a polynomial?

ON.OE.9.C.1.2

C1.2 create algebraic expressions to generalize relationships expressed in words, numbers, and visual representations, in various contexts: Create algebraic expressions to generalize relationships expressed in words, numbers, and visual representations, in various contexts

Characteristics of polynomials

Representing patterns in linear relations

Evaluating algebraic expressions

ON.OE.9.C.1.3

C1.3 compare algebraic expressions using concrete, numerical, graphical, and algebraic methods to identify those that are equivalent, and justify their choices: Compare algebraic expressions using concrete, numerical, graphical, and algebraic methods to identify those that are equivalent, and justify their choices

Polynomial components

Equivalent expressions of polynomials

ON.OE.9.C.1.4

C1.4 simplify algebraic expressions by applying properties of operations of numbers, using various representations and tools, in different contexts: Simplify algebraic expressions by applying properties of operations of numbers, using various representations and tools, in different contexts

Multiplying monomial by monomial

Multiplying monomial by binomial

Multiplying binomial by binomial

Multiplying polynomial by polynomial

Adding and subtracting polynomials

Multiplying and dividing monomials

Multiplying polynomials by monomials

Dividing polynomials by monomials

ON.OE.9.C.1.5

C1.5 create and solve equations for various contexts, and verify their solutions: Create and solve equations for various contexts, and verify their solutions

Solving linear equations using multiplication and division

Solving two-step linear equations: ax + b = c, x/a + b = c

Solving linear equations using distributive property: a(x + b) = c

Solving linear equations with variables on both sides

Solving one - step equations: x + a = b

Solving literal equations

ON.OE.9.C.2.1

C2.1 use coding to demonstrate an understanding of algebraic concepts including variables, parameters, equations, and inequalities: Use coding to demonstrate an understanding of algebraic concepts including variables, parameters, equations, and inequalities

Applications of polynomials

ON.OE.9.C.2.2

C2.2 create code by decomposing situations into computational steps in order to represent mathematical concepts and relationships, and to solve problems: Create code by decomposing situations into computational steps in order to represent mathematical concepts and relationships, and to solve problems

Common factors of polynomials

ON.OE.9.C.2.3

C2.3 read code to predict its outcome, and alter code to adjust constraints, parameters, and outcomes to represent a similar or new mathematical situation: Read code to predict its outcome, and alter code to adjust constraints, parameters, and outcomes to represent a similar or new mathematical situation

Find the difference of squares: (a - b)(a + b) = (a^2 - b^2)

ON.OE.9.C.3.1

C3.1 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: 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

Evaluating polynomials

Reading linear relation graphs

ON.OE.9.C.3.2

C3.2 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: 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

Using algebra tiles to factor polynomials

ON.OE.9.C.3.3

C3.3 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: 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

Solving polynomial equations

Solving linear equations by graphing

ON.OE.9.C.4.1

C4.1 compare characteristics of graphs, tables of values, and equations of linear and non-linear relations: Compare characteristics of graphs, tables of values, and equations of linear and non-linear relations

Word problems of polynomials

ON.OE.9.C.4.2

C4.2 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: Graph relations represented as algebraic equations of various forms and their associated inequalities to identify characteristics and defined points/regions

Factoring polynomials by grouping

Express linear inequalities graphically and algebraically

Solving one-step linear inequalities

Solving multi-step linear inequalities

Compound inequalities

ON.OE.9.C.4.3

C4.3 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: 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

Solving polynomials with unknown coefficients

Rotational symmetry and transformations

ON.OE.9.C.4.4

C4.4 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: Determine line equations from graphs, tables, and concrete representations by connecting rates of change to slopes and initial values to y-intercepts, and use these equations to solve problems

Solving polynomials with unknown constant terms

ON.OE.9.D.1.1

D1.1 identify a current context involving a large amount of data, and describe potential implications and consequences of its collection, storage, representation, and use: Identify a current context involving a large amount of data, and describe potential implications and consequences of its collection, storage, representation, and use

Influencing factors in data collection

ON.OE.9.D.1.2

D1.2 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: 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

Data collection

Advantages and disadvantages of different graphs

Critiquing data presentation

ON.OE.9.D.1.3

D1.3 create a scatter plot to represent the relationship between two variables, determine the correlation between these variables by testing different regression models using technology, and use a model to make predictions when appropriate: Create a scatter plot to represent the relationship between two variables, determine correlation by testing regression models using technology, and use a model to make predictions when appropriate

Box-and-whisker plots and scatter plots

ON.OE.9.D.2.1

D2.1 describe the value of mathematical modelling and how it is used in real life to inform decisions: Describe the value of mathematical modelling and how it is used in real life to inform decisions

Classification of data

ON.OE.9.D.2.2

D2.2 identify a question of interest requiring the collection and analysis of data, and identify the information needed to answer the question: Identify a question of interest requiring data collection and analysis, and identify the information needed to answer the question

Sampling methods

ON.OE.9.D.2.3

D2.3 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: Create and execute a plan to collect necessary data, identifying assumptions and variables

Census and bias

ON.OE.9.D.2.4

D2.4 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: Determine ways to display and analyse data to create a mathematical model answering the original question, considering data nature, context, and assumptions

Bivariate, scatter plots and correlation

ON.OE.9.E.1.2

E1.2 create and analyse designs involving geometric relationships and circle and triangle properties, using various tools: Create and analyse designs involving geometric relationships and circle and triangle properties, using various tools

Angles in a circle

Chord properties

Tangent properties

ON.OE.9.E.1.3

E1.3 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: Solve problems involving different units within and between measurement systems, including those from various cultures, using representations and technology when appropriate

Conversions between metric and imperial systems

Introduction to surface area of 3-dimensional shapes

Nets of 3-dimensional shapes

Imperial systems

Conversions involving squares and cubic

ON.OE.9.E.1.4

E1.4 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: Show how changing dimensions of 2D shapes and 3D objects affects perimeter/circumference, area, surface area, and volume, using technology when appropriate

Surface area of 3-dimensional shapes

Volume of prisms

Volume of cylinders

Upper and lower bound

ON.OE.9.E.1.5

E1.5 solve problems involving the side-length relationship for right triangles in real-life situations, including problems that involve composite shapes: Solve problems involving the side-length relationship for right triangles in real-life situations, including problems with composite shapes

Surface area and volume of prisms

Surface area and volume of pyramids

Surface area and volume of cylinders

Surface area and volume of cones

Surface area and volume of spheres

Pythagorean theorem

Using the pythagorean relationship

Applications of pythagorean theorem

ON.OE.9.E.1.6

E1.6 solve problems using the relationships between the volume of prisms and pyramids and between the volume of cylinders and cones, involving various units of measure: Solve problems using relationships between volumes of prisms and pyramids, and between cylinders and cones, involving various units of measure

Word problems relating volume of prisms and cylinders

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