Grade 8 Math Worksheets: Free Practice Problems with Answers

Grade 8 is the most consequential year of elementary school mathematics. Everything your child learns this year — algebra, the Pythagorean theorem, linear relations, integers, and geometry — is exactly what Grade 9 mathematics (MTH1W) builds on directly. A student who finishes Grade 8 with strong foundations arrives in high school ready. One who finishes with gaps finds those gaps immediately in September. This page provides free Grade 8 math worksheets and practice problems across every major curriculum strand, with full answers. Use them for test preparation, homework support, or to identify where your child needs focused work before the transition to Grade 9.

What Grade 8 Math Covers in Ontario

The Ontario Grade 8 mathematics curriculum covers five main strands:

Number — fractions, decimals, integers, percentages, ratio and rate, perfect squares and square roots
Algebra — evaluating expressions with integers, solving multi-step equations, linear relations
Data — probability (theoretical and experimental), data collection, scatter plots, trends
Spatial Sense (Geometry) — Pythagorean theorem, surface area and volume, geometric transformations
Measurement — volume of cylinders, spheres, and cones; unit rates and conversions

For a complete breakdown of the Ontario Grade 8 curriculum by strand, see our Grade 8 math curriculum Ontario guide.

Grade 8 Math Worksheets: Number Practice Problems

Fractions and Percentages

Practice Set 1 — Operations with Fractions

3/4 + 2/5 = ___
5/6 − 3/8 = ___
2 2/3 + 1 3/4 = ___
3 1/2 − 1 5/6 = ___
3/4 × 8/9 = ___
2/3 ÷ 4/5 = ___
1 3/4 × 2 2/5 = ___
3 1/3 ÷ 1 2/3 = ___
A tank is 3/4 full. It holds 240 L when full. How much water is in it? ___
A piece of wood is 5 1/2 m long. It is cut into pieces of 3/4 m each. How many pieces can be cut? ___

Answers: 1) 23/20 = 1 3/20 2) 11/24 3) 4 5/12 4) 1 2/3 5) 2/3 6) 5/6 7) 4 1/5 8) 2 9) 180 L 10) 7 pieces (with 1/4 m left over)

Practice Set 2 — Percentages and Proportions

What is 35% of 120? ___
48 is what percent of 160? ___
A price increases from $80 to $96. What is the percent increase? ___
A jacket is $240. It is discounted by 30%. What is the sale price? ___
A student scored 54/72 on a test. What percent is this? ___
A population of 4,500 decreases by 12%. What is the new population? ___
The price of a phone drops from $650 to $520. What is the percent decrease? ___
A store marks up an item by 25% and sells it for $75. What was the original price? ___

Answers: 1) 42 2) 30% 3) 20% 4) $168 5) 75% 6) 3,960 7) 20% 8) $60

Integers

Practice Set 3 — Integer Operations

(−8) × (−7) = ___
−144 ÷ (−12) = ___
(−6)² = ___
−6² = ___
(−3)³ = ___
−5 × (−4) ÷ (−2) = ___
(−2)⁴ = ___
−(−3)² = ___
Evaluate: −4 × 3 + (−6) ÷ 2 − (−5) = ___
The temperature is −8°C. It falls by 5°C each hour for 3 hours, then rises 12°C. What is the final temperature? ___

Answers: 1) 56 2) 12 3) 36 4) −36 5) −27 6) −10 7) 16 8) −9 9) −10 10) −11°C

Square Roots and Perfect Squares

Practice Set 4 — Perfect Squares and Square Roots

What is √64? ___
What is √144? ___
Is 75 a perfect square? ___
What is the smallest perfect square greater than 50? ___
Between which two whole numbers does √50 lie? ___
Estimate √30 to one decimal place. ___
A square has an area of 169 cm². What is the side length? ___
Simplify: √(36 × 4) = ___
Is √2 rational or irrational? ___
Order from smallest to largest: √25, √10, √36, √18 ___

Answers: 1) 8 2) 12 3) No 4) 64 5) 7 and 8 6) 5.5 7) 13 cm 8) 12 9) Irrational 10) √10, √18, √25, √36

Grade 8 Math Worksheets: Algebra Practice Problems

Evaluating and Simplifying Expressions

Practice Set 5 — Algebraic Expressions

If x = −3, evaluate 4x² − 2x + 1. ___
If a = 2 and b = −4, evaluate 3a − b². ___
Simplify: 5x − 3y + 2x + 7y. ___
Simplify: 3(2x − 4) + 5x. ___
Simplify: 4(x + 3) − 2(x − 1). ___
Expand and simplify: (2x + 3)(x − 1). Extension for strong students.
Factor: 6x + 9. ___
Factor: 12a − 8b. ___

Answers: 1) 43 2) −10 3) 7x + 4y 4) 11x − 12 5) 2x + 14 6) 2x² + x − 3 7) 3(2x + 3) 8) 4(3a − 2b)

Solving Equations

Practice Set 6 — Multi-Step Equations

3x + 7 = 22 → x = ___
5n − 8 = 27 → n = ___
2(x + 4) = 18 → x = ___
4x − 3 = 2x + 9 → x = ___
3(2n − 1) = 5n + 4 → n = ___
x/3 + 5 = 11 → x = ___
(2x + 6)/4 = 5 → x = ___
2(3x − 4) = 4(x + 1) → x = ___
A number is doubled and then 7 is subtracted. The result is 19. What is the number? ___
Three consecutive integers add up to 54. What are they? ___

Answers: 1) 5 2) 7 3) 5 4) 6 5) 7 6) 18 7) 7 8) 6 9) 13 10) 17, 18, 19

Grade 8 Math Worksheets: Linear Relations

Practice Set 7 — Linear Relations

Complete the table of values for y = 2x + 3:

x	−2	−1	0	1	2
y	___	___	___	___	___

What is the slope of the line through (2, 5) and (6, 13)? ___
What is the y-intercept of y = 3x − 4? ___
Write the equation of a line with slope 2 and y-intercept −5. ___
Does the point (3, 7) lie on the line y = 2x + 1? ___
What is the x-intercept of y = 2x − 8? ___
Two lines: y = 3x + 1 and y = 3x − 4. Are they parallel, perpendicular, or neither? ___
A plumber charges $50 plus $30 per hour. Write an equation for the total cost C after h hours. ___

Answers: 1) −1, 1, 3, 5, 7 2) 2 3) −4 4) y = 2x − 5 5) Yes (2×3 + 1 = 7) 6) x = 4 7) Parallel (same slope) 8) C = 30h + 50

Grade 8 Math Worksheets: Geometry Practice Problems

The Pythagorean Theorem

Practice Set 8 — Pythagorean Theorem

Use c² = a² + b² where c is the hypotenuse.

A right triangle has legs of 6 cm and 8 cm. Find the hypotenuse. ___
A right triangle has a hypotenuse of 13 cm and one leg of 5 cm. Find the other leg. ___
Is a triangle with sides 9, 40, and 41 a right triangle? ___
A ladder 10 m long leans against a wall. The base is 6 m from the wall. How high up the wall does it reach? ___
A rectangular park is 24 m long and 7 m wide. How long is the diagonal path? ___
Find the distance between points (1, 2) and (4, 6). ___
A right triangle has legs x and (x + 1), and hypotenuse (x + 2). Find x. ___
A television screen is 40 cm wide and 30 cm tall. What is the diagonal measurement? ___

Answers: 1) 10 cm 2) 12 cm 3) Yes (9² + 40² = 81 + 1600 = 1681 = 41²) 4) 8 m 5) 25 m 6) 5 7) 3 8) 50 cm

Surface Area and Volume

Practice Set 9 — Surface Area and Volume

Use π ≈ 3.14

Find the volume of a cylinder with radius 4 cm and height 10 cm. ___
Find the surface area of a rectangular prism: 5 cm × 3 cm × 2 cm. ___
Find the volume of a cone with radius 3 cm and height 8 cm. (V = 1/3 πr²h) ___
Find the surface area of a cylinder with radius 5 cm and height 12 cm. ___
A sphere has radius 6 cm. Find its volume. (V = 4/3 πr³) ___
A rectangular prism has volume 120 cm³, length 5 cm, and width 4 cm. Find the height. ___
Find the volume of a triangular prism with base area 15 cm² and height 8 cm. ___
A can has a diameter of 10 cm and height of 15 cm. How much liquid does it hold? ___

Answers: 1) 502.4 cm³ 2) 62 cm² 3) 75.36 cm³ 4) 534.07 cm² 5) 904.32 cm³ 6) 6 cm 7) 120 cm³ 8) 1,177.5 cm³

Grade 8 Math Worksheets: Data and Probability Practice Problems

Practice Set 10 — Probability and Data

A bag has 3 red, 5 blue, and 2 green marbles. What is the probability of picking a blue marble? ___
A die is rolled. What is the probability of getting an even number? ___
Two coins are flipped. List all possible outcomes. How many are there? ___
A spinner has 4 equal sections: red, blue, green, yellow. What is the probability of landing on red or blue? ___
In 80 coin flips, heads came up 38 times. What is the experimental probability of heads? ___
How does this compare to the theoretical probability? ___
A scatter plot shows as hours studying increase, test scores increase. Is this a positive or negative correlation? ___
Data set: 4, 7, 2, 9, 3, 8, 1, 6. Find the median. ___

Answers: 1) 5/10 = 1/2 2) 1/2 3) HH, HT, TH, TT — 4 outcomes 4) 1/2 5) 38/80 = 19/40 6) Slightly below theoretical probability of 1/2 7) Positive 8) 5.5 (ordered: 1,2,3,4,6,7,8,9 — average of 4 and 6)

Why Grade 8 Is the Last Chance Before High School

If there is one message this guide should leave every Grade 8 parent with, it is this: gaps in Grade 8 mathematics do not close on their own when high school starts. They compound.

The Ontario Grade 9 mathematics course (MTH1W) builds directly on Grade 8 content. Specifically:

Grade 8 algebra feeds directly into MTH1W’s linear relations and equations units — the two units most students find hardest in Grade 9
Grade 8 linear relations is the exact prerequisite for slope, y-intercept, and equation of a line in Grade 9
Grade 8 Pythagorean theorem recurs in Grade 9 and 10 geometry
Grade 8 integers and fractions are assumed as automatic in every strand of Grade 9 mathematics

A student with Grade 8 gaps will not have a fresh start in September. They will have the same gaps, now being asked to apply them in more complex contexts, at a faster pace, with less individual teacher support.

The summer before Grade 9 is the single best preparation window available. Six to eight weeks of targeted work — addressing the specific Grade 8 strands that are weakest — produces a meaningfully different September than doing nothing. For what that preparation looks like in practice, see our Grade 9 math September preparation guide.

Signs Your Grade 8 Child Has Gaps That Need Addressing Before Grade 9

Algebra is procedural, not understood. A student who can follow the steps of equation solving but cannot explain what “solving for x” means — that they are finding the value that makes the equation true — has a procedure without understanding. This will surface immediately in Grade 9 when equations become more complex.

Linear relations feel arbitrary. Students who can fill in a table of values but cannot explain why the slope is constant, or what the y-intercept represents in context, do not have genuine understanding of linear relations. They have a calculation procedure. Grade 9 requires the conceptual understanding.

The Pythagorean theorem is a formula, not a concept. A student who knows c² = a² + b² but cannot recognise which side is the hypotenuse in a non-standard diagram, or cannot apply the theorem in a word problem, has memorised a formula without understanding it. This is a specific and common Grade 8 gap.

Word problems are avoided or rushed. Grade 9 mathematics is significantly more applied than Grade 8. Students who have avoided word problems, or who rush through them and make consistent errors, are not prepared for the problem types that MTH1W regularly includes.

EQAO Grade 9 preparation feels overwhelming. Most Ontario Grade 9 students sit the EQAO mathematics assessment. A student who feels overwhelmed by the idea of this assessment, or whose Grade 8 teacher has expressed concern, is showing a clear signal that support is needed. For guidance on what the assessment involves, see our EQAO Grade 9 complete guide.

How Think Academy Helps Grade 8 Students

Think Academy Canada works with Grade 8 students across Ontario to build the algebraic fluency, geometric reasoning, and problem-solving skills that Grade 9 mathematics demands.

Our Grade 8 programme is diagnostic-led: every student starts with a targeted assessment that identifies specifically which strands are secure and which have gaps. The programme then addresses those gaps directly — not through generic Grade 8 curriculum review, but through targeted work on the concepts most consequential for the Grade 9 transition.

For students using the summer before Grade 9, we offer a focused transition programme specifically designed to close Grade 8 gaps and build Grade 9 readiness before September. The students who begin Grade 9 with this preparation consistently outperform those who rely on catching up during the school year.

The free diagnostic assessment is 20 minutes, produces a written feedback report, and requires no commitment. It is the most useful thing a Grade 8 parent can do before September.

Frequently Asked Questions

What maths should a Grade 8 student know before starting Grade 9? Grade 8 students entering Grade 9 should be fluent in: integer operations (including negative exponents), multi-step equation solving, basic linear relations (tables of values, slope, y-intercept), the Pythagorean theorem and its applications, surface area and volume of basic 3D shapes, and operations with fractions including multiplication and division.

My child got 75% in Grade 8 math — are they ready for Grade 9? Possibly, but a course mark alone is not the most reliable indicator. A 75% averaged across multiple strands can mask genuine weakness in one strand — and if that strand is algebra or linear relations, it will surface immediately in MTH1W. A strand-level diagnostic is more informative than an overall mark.

How hard is the jump from Grade 8 to Grade 9 math? Significant — and consistently underestimated by students and parents. The pace is faster, the content is more abstract, the assessment structure is more demanding, and there is less hand-holding. Students who arrive prepared find the jump manageable. Students who arrive with gaps find it genuinely difficult within the first month.

Are these Grade 8 math worksheets aligned to EQAO? These worksheets are aligned to the Ontario Grade 8 mathematics curriculum. The EQAO assesses Ontario students at Grade 3, Grade 6, and Grade 9. Grade 8 content directly feeds into the Grade 9 EQAO assessment. See our EQAO Grade 9 complete guide for more on that assessment.

My child is strong in Grade 8 — what should they do next? For mathematically strong Grade 8 students, two paths are worth considering: mathematics competitions (the Gauss Contest and AMC 8 are both appropriate) and early enrichment in Grade 9 content. For more on enrichment options, see our math enrichment guide.

Grade 8 is the last chance to prepare. Don’t leave it to September.

Grade 8 Math Worksheets: Practice Problems with Answers