Grade 8 Math Curriculum Ontario

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Core Grade 8 Math Study Points

Number Sense & Operations: Working with scientific notation, classifying rational and irrational numbers, estimating and calculating square roots, and solving multi-step problems involving fractions, decimals, and percents.
Algebra & Coding: Comparing linear growing and shrinking patterns, graphing proportional relationships, adding and subtracting monomials and binomials (degree 1), solving multi-step equations and inequalities, and writing code for data analysis.
Data Literacy & Probability: Creating and analyzing scatter plots, identifying data trends (strong, weak, positive, negative), and determining theoretical and experimental probabilities for independent and dependent events.+1
Spatial Sense (Geometry & Measurement): Performing transformations (translations, reflections, rotations, dilations) on a Cartesian plane, calculating the surface area and volume of cylinders and composite figures, and applying the Pythagorean theorem.+1
Financial Literacy: Managing multiple currencies and exchange rates, creating long-term financial plans, balancing budgets, and calculating simple and compound interest.

Skills available for Ontario grade 8 math tutoring curriculum
Objectives: Ontario Curriculum
8.B Number
8.B1 Number Sense
Rational and Irrational Numbers
8.B1.1 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
Convert between standard and scientific notation (8-H.1)
Compare numbers written in scientific notation (8-H.2)
8.B1.2 describe, compare, and order numbers in the real number system (rational and irrational numbers), separately and in combination, in various contexts
Classify numbers (8-A.8)
Integers on number lines (8-B.1)
Graph integers on horizontal and vertical number lines (8-B.2)
Compare and order integers (8-B.7)
Identify rational and irrational numbers (8-E.1)
Compare positive rational numbers (8-E.5)
Compare rational numbers (8-E.6)
Put rational numbers in order (8-E.7)
Compare and order rational and irrational numbers (8)
8.B1.3 estimate and calculate square roots, in various contexts
Square roots of perfect squares (8-G.11)
Estimate square roots (8-G.12)
Relationship between squares and square roots (8-G.13)
Solve equations involving squares and square roots (8-G.14)
Fractions, Decimals and Percents
8.B1.4 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
Find what percent one number is of another (8-K.3)
Find what percent one number is of another: word problems (8-K.4)
Percents of numbers and money amounts (8-K.6)
Percents of numbers: word problems (8-K.7)
Percent of a number: tax, discount and more (8-L.4)
Find the percent: tax, discount and more (8-L.5)
Multi-step problems with percents (8-L.7)
8.B2 Operations
Properties and Relationships
8.B2.1 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
Evaluate numerical expressions involving integers (8-C.11)
Evaluate numerical expressions involving fractions (8-D.25)
Evaluate numerical expressions involving positive and negative decimals (8-F.7)
Evaluate numerical expressions involving rational numbers (8-F.8)
Price lists (8-L.1)
Unit prices: find the total price (8-L.3)
Multi-step word problems (8-N.1)
Properties of addition and multiplication (8-W.12)
Multiply using the distributive property (8-W.13)
Math Facts
8.B2.2 understand and recall commonly used square numbers and their square roots
Square roots of perfect squares (8-G.11)
Relationship between squares and square roots (8-G.13)
Mental Math
8.B2.3 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
Multiply a whole number by a power of ten: with exponents (8-G.4)
Multiply a decimal by a power of ten: with exponents (8-G.5)
Divide by a power of ten: with exponents (8-G.6)
Multiply and divide by a power of ten: with exponents (8-G.7)
Addition and Subtraction
8.B2.4 add and subtract integers, using appropriate strategies, in various contexts
Add and subtract integers using counters (8-C.2)
Add and subtract integers (8-C.3)
Complete addition and subtraction sentences with integers (8-C.4)
Add and subtract three or more integers (8-C.5)
Add and subtract integers: word problems (8-C.6)
8.B2.5 add and subtract fractions, using appropriate strategies, in various contexts
Add and subtract fractions with like denominators (8-D.3)
Add fractions with unlike denominators using models (8-D.4)
Add fractions with unlike denominators (8-D.5)
Subtract fractions with unlike denominators using models (8-D.6)
Subtract fractions with unlike denominators (8-D.7)
Add and subtract fractions with unlike denominators: word problems (8-D.8)
Add and subtract mixed numbers (8-D.9)
Add and subtract mixed numbers: word problems (8-D.10)
Multiplication and Division
8.B2.6 multiply and divide fractions by fractions, as well as by whole numbers and mixed numbers, in various contexts
Reciprocals and multiplicative inverses (8-D.12)
Multiply fractions and whole numbers (8-D.13)
Multiply two fractions using models (8-D.14)
Multiply fractions (8-D.15)
Multiply fractions: word problems (8-D.16)
Multiply mixed numbers (8-D.17)
Multiply mixed numbers: word problems (8-D.18)
Divide whole numbers by unit fractions using models (8-D.19)
Divide whole numbers and unit fractions (8-D.20)
Divide fractions (8-D.21)
Divide fractions: word problems (8-D.22)
Divide mixed numbers (8-D.23)
Divide mixed numbers: word problems (8-D.24)
8.B2.7 multiply and divide integers, using appropriate strategies, in various contexts
Multiply and divide integers (8-C.8)
Complete multiplication and division sentences with integers (8-C.9)
8.B2.8 compare proportional situations and determine unknown values in proportional situations, and apply proportional reasoning to solve problems in various contexts
Compare ratios: word problems (8-I.10)
Compare rates: word problems (8-I.11)
Ratios and rates: word problems (8-I.12)
Do the ratios form a proportion? (8-I.13)
Do the ratios form a proportion: word problems (8-I.14)
Solve proportions (8-I.15)
Estimate population size using proportions (8-I.16)
Write and solve equations for proportional relationships (8-J.10)
8.C Algebra
8.C1 Patterns and Relationships
Patterns
8.C1.1 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
Find the constant of proportionality from a table (8-J.1)
Find the constant of proportionality from a graph (8-J.4)
Identify proportional relationships from graphs and equations (8-J.6)
Identify proportional relationships from tables (8-J.7)
Identify arithmetic and geometric sequences (8-V.1)
Constant rate of change (8-Z.4)
8.C1.2 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
Graph proportional relationships (8-J.8)
Interpret graphs of proportional relationships (8-J.9)
Arithmetic sequences (8-V.2)
Geometric sequences (8-V.3)
Number sequences: mixed review (8-V.4)
Number sequences: word problems (8-V.5)
Evaluate variable expressions for number sequences (8-V.6)
Complete a table for a linear function (8-Z.5)
Complete a table and graph a linear function (8-Z.6)
Graph a line from an equation (8-Z.7)
Interpret the graph of a linear function: word problems (8-Z.8)
8.C1.3 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
Write equations for proportional relationships from tables (8-J.2)
Write equations for proportional relationships from graphs (8-J.5)
Write variable expressions for arithmetic sequences (8-V.7)
Write a linear function from a table (8-Z.9)
Write linear functions: word problems (8-Z.10)
8.C1.4 create and describe patterns to illustrate relationships among rational numbers
Integer addition and subtraction rules (8-C.1)
Integer multiplication and division rules (8-C.7)
Apply addition and subtraction rules (8-F.9)
Apply multiplication and division rules (8-F.10)
Apply addition, subtraction, multiplication and division rules (8-F.11)
8.C2 Equations and Inequalities
Variables and Expressions
8.C2.1 add and subtract monomials with a degree of 1, and add binomials with a degree of 1 that involve integers, using tools
Add and subtract like terms (8-W.15)
Simplify linear expressions (8-W.16)
Identify equivalent linear expressions using algebra tiles (8-W.18)
Identify equivalent linear expressions (8-W.19)
Identify equivalent linear expressions: word problems (8-W.20)
8.C2.2 evaluate algebraic expressions that involve rational numbers
Evaluate linear one-variable expressions (8-W.4)
Evaluate one-variable expressions (8-W.5)
Evaluate multi-variable expressions (8-W.6)
Evaluate rational expressions (8-W.9)
Equalities and Inequalities
8.C2.3 solve equations that involve multiple terms, integers, and decimal numbers in various contexts, and verify solutions
Which x satisfies an equation? (8-X.1)
Model and solve equations using algebra tiles (8-X.3)
Write and solve equations that represent diagrams (8-X.4)
Solve one-step equations (8-X.6)
Solve two-step equations (8-X.7)
Solve multi-step equations (8-X.8)
Solve equations involving like terms (8-X.9)
Solve equations with variables on both sides (8-X.10)
Solve equations: complete the solution (8-X.11)
Solve equations: word problems (8-X.12)
8.C2.4 solve inequalities that involve integers, and verify and graph the solutions
Solutions to inequalities (8-Y.1)
Solve one-step inequalities (8-Y.4)
Graph solutions to one-step inequalities (8-Y.5)
Solve two-step inequalities (8-Y.6)
Graph solutions to two-step inequalities (8-Y.7)
Solve multi-step inequalities (8-Y.8)
Graph solutions to multi-step inequalities (8-Y.9)
8.C3 Coding
Coding Skills
8.C3.1 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
8.C3.2 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
8.D Data
8.D1 Data Literacy
Data Collection and Organization
8.D1.1 identify situations involving one-variable data and situations involving two-variable data, and explain when each type of data is needed
8.D1.2 collect continuous data to answer questions of interest involving two variables, and organize the data sets as appropriate in a table of values
Data Visualization
8.D1.3 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
Choose the best type of graph (8-AA.18)
8.D1.4 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
Create scatter plots (8-AA.13)
Data Analysis
8.D1.5 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
Identify trends with scatter plots (8-AA.14)
8.D1.6 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
Interpret tables (8-AA.1)
Make predictions with scatter plots (8-AA.15)
8.D2 Probability
Probability
8.D2.1 solve various problems that involve probability, using appropriate tools and strategies, including Venn and tree diagrams
Probability of simple events (8-CC.1)
Probability of opposite, mutually exclusive and overlapping events (8-CC.2)
Experimental probability (8-CC.3)
Compound events: find the number of outcomes (8-CC.5)
Counting principle (8-CC.6)
8.D2.2 determine and compare the theoretical and experimental probabilities of multiple independent events happening and of multiple dependent events happening
Probability of independent events (8-CC.8)
Probability of independent and dependent events (8-CC.9)
8.E Spatial Sense
8.E1 Geometric and Spatial Reasoning
Geometric Reasoning
8.E1.1 identify geometric properties of tessellating shapes and identify the transformations that occur in the tessellations
8.E1.2 make objects and models using appropriate scales, given their top, front, and side views or their perspective views
Front, side and top view (8-T.3)
Base plans (8-T.4)
8.E1.3 use scale drawings to calculate actual lengths and areas, and reproduce scale drawings at different ratios
Scale drawings: word problems (8-I.17)
Dilations: scale factor and classification (8-R.4)
Location and Movement
8.E1.4 describe and perform translations, reflections, rotations, and dilations on a Cartesian plane, and predict the results of these transformations
Identify reflections, rotations and translations (8-Q.2)
Describe a sequence of transformations (8-Q.3)
Translations: graph the image (8-Q.4)
Translations: find the coordinates (8-Q.5)
Reflections: graph the image (8-Q.6)
Reflections: find the coordinates (8-Q.7)
Rotations: graph the image (8-Q.8)
Rotations: find the coordinates (8-Q.9)
Describe transformations (8-Q.10)
Compositions of congruence transformations: graph the image (8-Q.11)
Sequences of congruence transformations: choose the sequence (8-Q.12)
8.E2 Measurement
The Metric System
8.E2.1 represent very large (mega, giga, tera) and very small (micro, nano, pico) metric units using models, base ten relationships, and exponential notation
Lines and Angles
8.E2.2 solve problems involving angle properties, including the properties of intersecting and parallel lines and of polygons
Find missing angles in triangles (8-P.7)
Find missing angles in triangles using ratios (8-P.8)
Triangle Angle-Sum Theorem (8-P.9)
Find missing angles in quadrilaterals I (8-P.11)
Find missing angles in quadrilaterals II (8-P.12)
Interior angles of polygons (8-P.13)
Identify complementary, supplementary, vertical, adjacent and congruent angles (8-P.14)
Find measures of complementary, supplementary, vertical and adjacent angles (8-P.15)
Transversals of parallel lines: name angle pairs (8-P.16)
Transversals of parallel lines: find angle measures (8-P.17)
Find lengths and measures of bisected line segments and angles (8-P.18)
Length, Area and Volume
8.E2.3 solve problems involving the perimeter, circumference, area, volume, and surface area of composite two-dimensional shapes and three-dimensional objects, using appropriate formulas
Perimeter (8-U.1)
Area (8-U.2)
Area between two shapes (8-U.3)
Area and perimeter: word problems (8-U.4)
Area of circles (8-U.5)
Circumference of circles (8-U.6)
Area and perimeter of semicircles and quarter circles (8-U.7)
Circles: word problems (8-U.8)
Area of compound figures with triangles, semicircles and quarter circles (8-U.9)
Volume (8-U.10)
Volume of compound figures (8-U.12)
Surface area of prisms and cylinders (8-U.13)
Surface area of pyramids (8-U.14)
8.E2.4 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
Pythagorean theorem: find the length of the hypotenuse (8-S.1)
Pythagorean theorem: find the missing leg length (8-S.2)
Pythagorean theorem: find the missing leg or hypotenuse length (8-S.3)
Pythagorean theorem: find the perimeter (8-S.4)
Pythagorean theorem: word problems (8-S.5)
Converse of the Pythagorean theorem: is it a right triangle? (8-S.6)
8.F Financial Literacy
8.F1 Money and Finances
Money Concepts
8.F1.1 describe some advantages and disadvantages of various methods of payment that can be used when dealing with multiple currencies and exchange rates
Financial Management
8.F1.2 create a financial plan to reach a long-term financial goal, accounting for income, expenses, and tax implications
8.F1.3 identify different ways to maintain a balanced budget, and use appropriate tools to track all income and spending, for several different scenarios
Balance a budget (8-L.11)
Adjust a budget (8-L.12)
8.F1.4 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
Simple interest (8-L.9)
Compound interest (8-L.10)
Consumer and Civic Awareness
8.F1.5 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
8.F1.6 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
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