Grade 8 Math Practice (Ontario) — Free Skills & Solutions

Use mental math to multiply and divide decimal numbers by powers of ten, including negative exponents, and apply the order of operations to expressions containing them.

Add and subtract rational numbers

Add and subtract integers and fractions, including negative fractions, using appropriate strategies in various contexts.

Multiply and divide rational numbers

Multiply and divide integers and fractions, including negative fractions and mixed numbers, using appropriate strategies in various contexts.

Percents, ratios, and proportional reasoning

Use fractions, decimals, and percents interchangeably (including percents over 100% and under 1%), and solve proportional-reasoning problems.

Pattern rules for growing and shrinking patterns

Determine the pattern rule for growing and shrinking patterns involving rational numbers, extend patterns, solve for unknown term numbers, and compare patterns by their rate and initial value.

Linear patterns: tables, rate of change, and equations

Represent a linear growing or shrinking pattern with a table of values and an equation, find its rate of change and initial value, and use the equation to make predictions.

Simplify and evaluate algebraic expressions

Add and subtract monomials and binomials of degree 1 with integer coefficients, and evaluate algebraic expressions that involve rational numbers.

Solve multi-step equations

Solve equations that involve multiple terms, integers, and decimal numbers.

Equations in context: translate, solve, and verify

Translate a real-life situation into a linear equation, solve it, and verify the solution by substituting it back into the original equation.

Solve and graph inequalities

Solve inequalities that involve integers, verify a solution, and describe how to graph the solution on a number line.

Describe a scatter plot relationship

Describe the relationship between two variables in a scatter plot as strong or weak, positive or negative, or none.

Outliers and their effect on the mean

Identify an outlier in a small data set and determine how removing it changes the mean.

Probability of independent events

Find the probability of two independent events both happening, such as a coin flip and a die roll.

Dependent events: drawing without replacement

Find the probability of two dependent events, such as drawing two marbles without replacement.

Pythagorean theorem: find the hypotenuse

Apply the Pythagorean theorem to find the hypotenuse of a right triangle.

Pythagorean theorem: find a missing leg

Apply the Pythagorean theorem to find a missing leg of a right triangle.

Circumference and area of a circle

Find the circumference or area of a circle using 3.14 for pi.

Volume of a cylinder

Find the volume of a cylinder using V = pi * r^2 * h, with 3.14 for pi.

Angle properties with parallel lines

Solve for unknown angles using intersecting and parallel line properties.

Simple interest growth

Calculate simple interest earned on savings at a given annual rate.

Compound interest vs simple interest

Calculate compound interest growth year by year and compare it with simple interest.

Balance a monthly budget

Track income and expenses to determine whether a budget is balanced and by how much.

Sales, coupons, and best value

Compare a percent-off sale with a dollar-off coupon to find the better deal.

Grade 8 math practice

Number Sense

Represent and compare very large and very small numbers, including through the use of scientific notation

Describe, compare, and order numbers in the real number system (rational and irrational numbers), separately and in combination

Estimate and calculate square roots

Use fractions, decimal numbers, and percents, including percents of more than 100% or less than 1%, interchangeably and flexibly

Operations

Use properties and order of operations, and relationships between operations, to solve problems involving rational numbers, ratios, rates, and percents, including multi-step problems

Understand and recall commonly used square numbers and their square roots

Use mental math strategies to multiply and divide whole numbers and decimal numbers up to thousandths by powers of ten

Add and subtract integers

Add and subtract fractions

Multiply and divide fractions by fractions, as well as by whole numbers and mixed numbers

Multiply and divide integers

Compare proportional situations and determine unknown values in proportional situations, and apply proportional reasoning to solve problems in various contexts

Patterns and Relationships

Identify and compare repeating, growing, and shrinking patterns, including real-life contexts, and compare linear growing and shrinking patterns on the basis of constant rates and initial values

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

Determine pattern rules and use them to extend patterns, predict, and identify missing elements in growing and shrinking patterns involving rational numbers, and use algebraic representations to solve for unknown values in linear growing and shrinking patterns

Create and describe patterns to illustrate relationships among rational numbers

Equations and Inequalities

Add and subtract monomials with a degree of 1, and add binomials with a degree of 1 that involve integers, using tools

Evaluate algebraic expressions that involve rational numbers

Solve equations that involve multiple terms, integers, and decimal numbers in various contexts, and verify solutions

Solve inequalities that involve integers, and verify and graph the solutions

Coding

Write and execute code involving the analysis of data in order to inform and communicate decisions

Read and alter existing code involving the analysis of data in order to inform and communicate decisions, and describe the effect of changes on outcomes and efficiency

Mathematical Modelling

Apply the modelling process to represent, analyse, predict, and provide insight into real-life situations

Data Literacy

Identify situations involving one-variable data and situations involving two-variable data, and explain when each type is needed

Collect continuous data to answer questions of interest involving two variables, and organize the data sets as appropriate in a table of values

Select from a variety of graphs (including scatter plots) best suited to the data, display with proper sources, titles, labels, and scales, and justify the choice

Create an infographic about a data set, using appropriate representations (tables, scatter plots), and incorporating relevant information

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

Analyse data sets in scatter plots and misleading graphs, challenge preconceived notions, and make convincing arguments and informed decisions

Probability

Solve various problems that involve probability, using appropriate tools and strategies, including Venn and tree diagrams

Determine and compare the theoretical and experimental probabilities of multiple independent events happening and of multiple dependent events happening

Geometric and Spatial Reasoning

Identify geometric properties of tessellating shapes and identify the transformations that occur in the tessellations

Make objects and models using appropriate scales, given their top, front, and side views or perspective views

Use scale drawings to calculate actual lengths and areas, and reproduce scale drawings at different ratios

Describe and perform translations, reflections, rotations, and dilations on a Cartesian plane, and predict the results

Measurement

Represent very large (mega, giga, tera) and very small (micro, nano, pico) metric units using models, base ten relationships, and exponential notation

Solve problems involving angle properties, including the properties of intersecting and parallel lines and of polygons

Solve problems involving the perimeter, circumference, area, volume, and surface area of composite two-dimensional shapes and three-dimensional objects, using appropriate formulas

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

Money and Finances

Describe some advantages and disadvantages of various methods of payment used when dealing with multiple currencies and exchange rates

Create a financial plan to reach a long-term financial goal, accounting for income, expenses, and tax implications

Identify different ways to maintain a balanced budget, and use appropriate tools to track all income and spending, for several different scenarios

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

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

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

Endless practice

Convert to and from scientific notation

Compare and order numbers in scientific notation

Rational and irrational numbers

Square roots: exact values and estimation

Powers of ten and order of operations