Grade 9 Math Curriculum Ontario

Ontario Grade 9 Math (MTH1W) Tutoring

Our comprehensive SprintMind Math Tutoring program is specifically aligned with the Grade 9 Math Curriculum Ontario. We help students transition smoothly into the De-streamed Grade 9 Math classroom by focusing on foundational skills and advanced applications.

Key Grade 9 Curriculum Topics We Cover:

Number & Algebra: Master Grade 9 algebra concepts, work with rational numbers and integers, understand powers and scientific notation, solve linear equations, and explore linear and non-linear relations. We also introduce Grade 9 math coding.
Data & Mathematical Modelling: Learn Grade 9 mathematical modelling, analyze scatter plots and correlation, and perform detailed data analysis and quartile values.
Geometry & Measurement: Explore Grade 9 geometry properties, solve Pythagorean theorem word problems, calculate the volume of prisms, pyramids, and cylinders, and master metric and imperial unit conversions.
Financial Literacy: Build real-world skills with Grade 9 financial literacy. Learn about simple and compound interest, practice modifying and balancing budgets, and understand asset appreciation and depreciation.

Skills available for Ontario grade 9 math curriculum

Objectives: Ontario Curriculum
9.B Number
9.B1 Development of Numbers and Number Sets: demonstrate an understanding of the development and use of numbers, and make connections between sets of numbers
Development and Use of Numbers
9.B1.1 research a number concept to tell a story about its development and use in a specific culture, describe its relevance in a current context
Number Sets
9.B1.2 describe how various subsets of a number system are defined, and describe similarities and differences between these subsets
Classify numbers (9-A.1)
9.B1.3 use patterns and number relationships to explain density, infinity, and limit as they relate to number sets
Arithmetic sequences (9-L.2)
Geometric sequences (9-L.3)
9.B2 Powers: represent numbers in various ways, evaluate powers, and simplify expressions by using the relationships between powers and their exponents
Powers
9.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
Understanding exponents (9-I.1)
Powers with integer bases (9-I.2)
Powers with decimal and fractional bases (9-I.3)
Negative exponents (9-I.4)
Convert between standard and scientific notation (9-J.1)
Compare numbers written in scientific notation (9-J.2)
9.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
Multiplication with exponents – integral bases (9-I.5)
Division with exponents – integral bases (9-I.6)
Multiplication and division with exponents – integral bases (9-I.7)
Power rule – integral bases (9-I.8)
Multiplication with exponents – variable bases (9-I.9)
Division with exponents – variable bases (9-I.10)
Multiplication and division with exponents – variable bases (9-I.11)
Power rule – variable bases (9-I.12)
Identify equivalent expressions involving exponents (9-I.14)
Evaluate expressions using properties of exponents (10-B.8)
9.B3 Number Sense and Operations: apply an understanding of rational numbers, ratios, rates, percentages, and proportions, in various mathematical contexts, and to solve problems
Rational Numbers
9.B3.1 apply an understanding of integers to describe location, direction, amount, and changes in any of these, in various contexts
Understanding opposite integers (8-B.3)
Understanding absolute value (8-B.4)
Absolute value and integers: word problems (8-B.6)
Compare and order integers (8-B.7)
Number lines (9-A.4)
9.B3.2 apply an understanding of unit fractions and their relationship to other fractional amounts, in various contexts, including the use of measuring tools
Unit rates (9-C.3)
9.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
Compare rational numbers (9-A.2)
Put rational numbers in order (9-A.3)
Applications
9.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
Add and subtract rational numbers (9-B.4)
Add and subtract rational numbers: word problems (9-B.5)
Multiply and divide rational numbers (9-B.6)
Multiply and divide rational numbers: word problems (9-B.7)
Evaluate numerical expressions involving rational numbers (9-B.8)
Evaluate variable expressions involving rational numbers (9-B.9)
9.B3.5 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
Unit prices (9-C.4)
Solve proportions: word problems (9-C.6)
Scale drawings: word problems (9-C.7)
Percent word problems (9-D.3)
Percent of change (9-D.4)
Percent of change: word problems (9-D.5)
9.C Algebra
9.C1 Algebraic Expressions and Equations: demonstrate an understanding of the development and use of algebraic concepts and of their connection to numbers, using various tools and representations
Develpment and Use of Algebra
9.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
Algebraic Expressions and Equations
9.C1.2 create algebraic expressions to generalize relationships expressed in words, numbers, and visual representations, in various contexts
Write variable expressions for arithmetic sequences (9-L.5)
Write variable expressions for geometric sequences (9-L.6)
Write variable expressions (9-M.1)
9.C1.3 compare algebraic expressions using concrete, numerical, graphical, and algebraic methods to identify those that are equivalent, and justify their choices
Identify equivalent linear expressions (9-M.3)
9.C1.4 simplify algebraic expressions by applying properties of operations of numbers, using various representations and tools, in different contexts
Distributive property (9-H.2)
Simplify variable expressions using properties (9-H.3)
Simplify variable expressions involving like terms and the distributive property (9-M.2)
9.C1.5 create and solve equations for various contexts, and verify their solutions
Write variable equations (9-M.4)
Does x satisfy the equation? (9-M.5)
Model and solve equations using algebra tiles (9-N.1)
Write and solve equations that represent diagrams (9-N.2)
Solve two-step linear equations (9-N.4)
Solve advanced linear equations (9-N.5)
Solve equations with variables on both sides (9-N.6)
Solve equations: complete the solution (9-N.7)
Solve linear equations: word problems (9-N.10)
Solve linear equations: mixed review (9-N.11)
9.C2 Coding: apply coding skills to represent mathematical concepts and relationships dynamically, and to solve problems, in algebra and across the other strands
Coding
9.C2.1 use coding to demonstrate an understanding of algebraic concepts including variables, parameters, equations, and inequalities
9.C2.2 create code by decomposing situations into computational steps in order to represent mathematical concepts and relationships, and to solve problems
9.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
9.C3 Application of Relations: represent and compare linear and non-linear relations that model real-life situations, and use these representations to make predictions
Application of Linear and Non-Linear Relations
9.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
Rate of change: graphs (8-Z.3)
Identify linear functions (9-S.1)
Find the slope of a graph (9-S.2)
9.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
Slope-intercept form: graph an equation (9-S.6)
Slope-intercept form: write an equation from a graph (9-S.7)
Slope-intercept form: write an equation from a table (9-S.9)
Complete a table and graph a linear function (9-S.13)
9.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
Solve a system of equations by graphing (9-T.2)
Solve a system of equations by graphing: word problems (9-T.3)
9.C4 Characteristics of Relations: demonstrate an understanding of the characteristics of various representations of linear and non-linear relations, using tools, including coding when appropriate
Characteristics of Linear and Non-Linear Relations
9.C4.1 compare characteristics of graphs, tables of values, and equations of linear and non-linear relations
Complete a function table from a graph (9-Q.8)
Complete a function table from an equation (9-Q.9)
Compare linear functions: graphs, tables and equations (9-S.14)
9.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
Slope-intercept form: graph an equation (9-S.6)
Standard form: graph an equation (9-S.17)
Graph a horizontal or vertical line (9-S.19)
Graph a linear inequality in the coordinate plane (11-C.2)
Graph solutions to linear inequalities (11-C.6)
9.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
Transformations of linear functions (9-S.25)
9.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
Slope-intercept form: write an equation from a graph (9-S.7)
Slope-intercept form: write an equation (9-S.8)
Slope-intercept form: write an equation from a table (9-S.9)
Slope-intercept form: write an equation from a word problem (9-S.10)
Write linear functions to solve word problems (9-S.12)
9.D Data
9.D1 Collection, Representation, and Analysis of Data: describe the collection and use of data, and represent and analyse data involving one and two variables
Application of Data
9.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
Representation and Analysis of Data
9.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
Interpret box-and-whisker plots (9-P.5)
Calculate mean, median, mode and range (9-Y.1)
Interpret charts to find mean, median, mode and range (9-Y.2)
Quartiles (9-Y.4)
9.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
Interpret a scatter plot (9-P.6)
Scatter plots: line of best fit (9-P.8)
9.D2 Mathematical Modelling: apply the process of mathematical modelling, using data and mathematical concepts from other strands, to represent, analyse, make predictions, and provide insight into real-life situations
Application of Mathematical Modelling
9.D2.1 describe the value of mathematical modelling and how it is used in real life to inform decisions
Process of Mathematical Modelling
9.D2.2 identify a question of interest requiring the collection and analysis of data, and identify the information needed to answer the question
9.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
Identify biased samples (9-Y.5)
9.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
Interpret bar graphs, line graphs and histograms (9-P.1)
Create bar graphs, line graphs and histograms (9-P.2)
Interpret circle graphs (9-P.3)
Interpret stem-and-leaf plots (9-P.4)
9.D2.5 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
9.E Geometry and Measurement
9.E1 Geometric and Measurement Relationships: demonstrate an understanding of the development and use of geometric and measurement relationships, and apply these relationships to solve problems, including problems involving real-life situations
Geometric and Measurement Relationships
9.E1.1 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
9.E1.2 create and analyse designs involving geometric relationships and circle and triangle properties, using various tools
Circles: calculate area, circumference, radius and diameter (9-F.2)
Central angles (9-F.4)
Arc measure and arc length (9-F.5)
Area of sectors (9-F.6)
Circle measurements: mixed review (9-F.7)
Arcs and chords (9-F.8)
Tangent lines (9-F.9)
Inscribed angles (9-F.11)
Angles in inscribed right triangles (9-F.12)
Triangle Angle-Sum Theorem (10-BB.2)
9.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
Estimate metric measurements (10-W.1)
Convert rates and measurements: metric units (10-W.2)
Estimate imperial measurements of length (10-W.3)
Convert rates and measurements: imperial units of length (10-W.4)
Unit prices with imperial length conversions (10-W.6)
Imperial mixed units of length (10-W.7)
Convert between metric and imperial units of length (10-W.8)
Scale drawings: word problems (10-W.9)
9.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
Area and perimeter of similar figures (9-E.19)
Volume and surface area of similar solids (9-E.21)
Perimeter, area and volume: changes in scale (9-E.22)
9.E1.5 solve problems involving the side-length relationship for right triangles in real-life situations, including problems that involve composite shapes
Pythagorean theorem (9-E.27)
Pythagorean theorem: word problems (9-E.28)
Converse of the Pythagorean theorem: is it a right triangle? (9-E.29)
Special right triangles (10-DD.4)
9.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
Volume of prisms and pyramids (9-E.10)
Volume of cones and cylinders (9-E.11)
9.F Financial Literacy
9.F1 Financial Decisions: demonstrate the knowledge and skills needed to make informed financial decisions
Financial Decisions
9.F1.1 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
9.F1.2 identify financial situations that involve appreciation and depreciation, and use associated graphs to answer related questions
9.F1.3 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
Simple interest (8-L.9)
Compound interest (8-L.10)
9.F1.4 modify budgets displayed in various ways to reflect specific changes in circumstances, and provide a rationale for the modifications
Balance a budget (8-L.11)
Adjust a budget (8-L.12)
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