Grade 8 Math practice

25 Grade 8 math lessons, including exponent rules, true or false: exponent laws, scientific notation, order scientific notation, square roots, rational or irrational? and more. Each one has a short video where Pip explains the idea, a worked example, and endless new practice questions with step-by-step help when a child gets stuck.

Step 1: Exponent rules

With the same base: multiplying adds exponents, dividing subtracts them, and a power of a power multiplies them.

Example: 4^11 ÷ 4^6 = 4^ ?

Tip: 2³ × 2⁴ = 2⁷ because that is 7 twos multiplied together.

Step 2: True or false: exponent laws

Multiplying powers with the same base: add exponents. Dividing: subtract. Power of a power: multiply.

Example: Is this true or false? 4⁷ ÷ 4³ = 4¹⁰

Tip: 2³ × 2⁴ = 2⁷.

Step 3: Scientific notation

Scientific notation writes big numbers as a number times a power of 10.

Example: 5.4 × 10^3

Tip: The exponent tells you how many places the decimal point moves.

Step 4: Order scientific notation

In scientific notation, a bigger power of 10 means a bigger number.

Example: Put these in order, smallest first.

Tip: Compare the powers of 10 first.

Step 5: Square roots

A square root asks: which number times itself gives this number?

Example: √36

Tip: Learn the perfect squares: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100.

Step 6: Rational or irrational?

Rational numbers can be written as fractions. Irrational ones (like π and √2) go on forever without repeating.

Example: Sort each number.

Tip: √ of a perfect square is rational: √16 = 4.

Step 7: Estimate square roots

If a number is not a perfect square, its square root is between two whole numbers. √50 is between 7 and 8 because 49 < 50 < 64.

Example: ? < √51 < 8

Tip: Find the perfect squares just below and just above the number.

Step 8: Where is the square root?

√30 is between √25 = 5 and √36 = 6, and closer to 5.

Example: Tap the whole number closest to √41.

Tip: Find the perfect squares on each side.

Step 9: Cube roots

The cube root of a number is what you multiply by itself three times to get it: ∛27 = 3 because 3 × 3 × 3 = 27.

Example: ∛343

Tip: Know the first cubes: 1, 8, 27, 64, 125, 216, 343, 512, 729, 1000.

Step 10: Evaluate expressions

To evaluate, swap the letter for its number, then follow the order of operations.

Example: If x = 2, what is the value? 5 x ^2 − 8

Tip: Exponents come before multiplying, and multiplying comes before subtracting.

Step 11: Variables on both sides

Move all the x terms to one side and the numbers to the other, then solve.

Example: 8x + 10 = 3x + 50

Tip: Subtract the smaller x term from both sides first.

Step 12: Solve and type

Undo each operation: subtract first, then divide.

Example: Solve for x. Type the number. 6x + 10 = 22

Tip: Do the same thing to both sides.

Step 13: Evaluate linear functions

In y = mx + b, put the x value in, multiply by m, then add b.

Example: If y = 5x − 4, what is y when x = −1?

Tip: Watch the signs when x or m is negative.

Step 14: Points on the line

A point is on a line if its x and y make the equation true.

Example: Choose every point on the line y = 2x + 2.

Tip: Put x into the equation and see if you get y.

Step 15: Slope between two points

Slope = rise ÷ run: how much y changes for each step in x.

Example: What is the slope of the line through these points? (4, 4) and (8, 24)

Tip: Subtract in the same order on top and bottom.

Step 16: Build the slope

Slope = rise ÷ run = (y₂ − y₁) ÷ (x₂ − x₁).

Example: Build the slope of the line through (3, −2) and (5, 2).

Tip: Subtract the y values, then the x values, then divide.

Step 17: Slope and y-intercept

In y = mx + b, m is the slope (how steep) and b is the y-intercept (where the line crosses the y-axis).

Example: What is the y-intercept of y = −3x + 4?

Tip: The number with x is the slope. The number on its own is the y-intercept.

Step 18: Match the lines

In y = mx + b, m is the slope and b is where the line crosses the y-axis.

Example: Match each line to its slope.

Tip: The number with x is the slope.

Step 19: Tap the y-intercept

In y = mx + b, the number b is the y-intercept: where the line crosses the y-axis.

Example: Tap the y-intercept.

Tip: It is the number on its own, without x.

Step 20: Solve a system by substitution

If you know what y equals, put that into the other equation to find x.

Example: Solve for x. y = 3x and x + y = 4

Tip: Replace y with its expression, combine like terms, then solve.

Step 21: Pythagorean theorem

In a right triangle, a² + b² = c², where c is the longest side (the hypotenuse).

Example: Find the length of side c. 5 12 c = ?

Tip: Some famous triangles: 3-4-5, 5-12-13 and 8-15-17.

Step 22: Translations and reflections

A translation slides a point. A reflection flips it over an axis: over the x-axis, y changes sign.

Example: Reflect (−8, 0) over the x-axis. What is the new y-coordinate?

Tip: Slide: add the moves. Flip over the x-axis: change the sign of y. Over the y-axis: change the sign of x.

Step 23: Volume of cylinders

Volume of a cylinder = area of the circle base × height = 3.14 × r × r × h.

Example: A cylinder has radius 4 cm and height 9 cm. What is its volume in cm³? (Use 3.14 for π.)

Tip: Find the base area first, then multiply by the height.

Step 24: Count the outcomes

To count outcomes of two events, multiply: a coin (2) and a die (6) have 2 × 6 = 12 outcomes.

Example: You flip a coin and roll a die. How many outcomes are possible?

Tip: Make a table or a tree diagram to see every outcome.

Step 25: Outcomes of two coins

Two coins have 4 outcomes: HH, HT, TH, TT.

Example: Two coins are flipped. The 4 squares are HH, HT, TH, TT. Shade the outcomes with exactly one head.

Tip: List every outcome before counting.

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