Grade 6 Math practice

25 Grade 6 math lessons, including greatest common factor, divide by a fraction, divide decimals by whole numbers, equal ratios, equivalent ratios, shade a ratio 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: Greatest common factor

The greatest common factor is the biggest number that divides both numbers evenly.

Example: GCF of 24 and 40

Tip: List the factors of each number and find the biggest one they share.

Step 2: Divide by a fraction

Dividing by 1/4 asks "how many quarters fit?" There are 4 quarters in 1, so 3 ÷ 1/4 = 12.

Example: 6 ÷ 1/4

Tip: Dividing by 1/d is the same as multiplying by d.

Step 3: Divide decimals by whole numbers

Divide as if there were no decimal point, then put the point back.

Example: 14.8 ÷ 4

Tip: 4.8 ÷ 4: think 48 tenths ÷ 4 = 12 tenths = 1.2.

Step 4: Equal ratios

Equal ratios grow by the same amount on both sides, like doubling a recipe.

Example: 2 : 7 = 4 : ?

Tip: If 2 cups of flour need 3 eggs, 4 cups need 6 eggs.

Step 5: Equivalent ratios

Equivalent ratios multiply both parts by the same number: 2 : 3 = 4 : 6.

Example: Is each ratio equivalent to 2 : 5?

Tip: Divide both parts by the same number to simplify.

Step 6: Shade a ratio

A ratio compares two parts: shaded : unshaded.

Example: Shade squares so shaded : unshaded is 2 : 1.

Tip: Shade the first number, leave the second unshaded.

Step 7: Unit rates

A unit rate is the amount for exactly one: price per item, kilometres per hour.

Example: 5 balls cost $45. How many dollars does 1 ball cost?

Tip: Divide the total by the number of items.

Step 8: Best price per item

A unit price is the cost for one: $6 for 3 is $2 each.

Example: 3 muffins cost $8.25. How much is one muffin? (like $1.50)

Tip: Divide the total cost by how many.

Step 9: Percent of a number

Percent means "out of 100". 25% is 25 out of every 100.

Example: 75% of 100

Tip: 10% is easy: divide by 10. Build other percents from it.

Step 10: Match the percent

To find 25% of 40, think of 25% as one quarter: 40 ÷ 4 = 10.

Example: Match each to its answer.

Tip: 10% is easy: move the decimal one place left.

Step 11: Compare integers

On a number line, numbers to the right are greater. −2 is greater than −7.

Example: 7 ? −5

Tip: With negatives, the number closer to zero is greater.

Step 12: Order integers

Negative numbers are less than 0. −8 is less than −3.

Example: Put the integers in order, least first.

Tip: The further left on the number line, the smaller.

Step 13: Add integers

On a number line, adding a positive moves right and adding a negative moves left.

Example: 4 + (−1)

Tip: Draw a quick number line. It works every time.

Step 14: Integers on a number line

Positive numbers are right of 0 and negative numbers are left of 0.

Example: Tap −8 on the number line.

Tip: Count jumps from 0.

Step 15: Subtract integers

Subtracting a number is the same as adding its opposite.

Example: −1 − 5

Tip: Keep, change, change: keep the first number, change − to +, change the sign of the second.

Step 16: True or false: integers

On the number line, numbers to the right are greater.

Example: Is this true or false? −1

Tip: −2 is greater than −5 because it is closer to 0.

Step 17: Exponents

An exponent says how many times to multiply a number by itself.

Example: 5^3

Tip: 2³ means 2 × 2 × 2, not 2 × 3.

Step 18: Build the power

An exponent says how many times to multiply: 2⁵ = 2 × 2 × 2 × 2 × 2.

Example: Build the value of 5².

Tip: Multiply step by step.

Step 19: One-step equations

An equation is a balance. Do the opposite operation to get x by itself.

Example: 4 x = 36

Tip: Always check by putting your answer back in.

Step 20: Same solution

Different equations can have the same solution.

Example: Choose every equation where x = 7 is the solution.

Tip: Put the number in for x and check.

Step 21: Area of triangles

A triangle is half of a rectangle, so its area is base × height ÷ 2.

Example: What is the area in square cm? base 9 cm height 12 cm

Tip: The height is straight up from the base, not along a slanted side.

Step 22: Surface area of boxes

Surface area is the total area of all the faces. A box has 3 pairs of matching faces.

Example: A box is 2 cm long, 4 cm wide and 5 cm tall. What is its surface area in cm²?

Tip: Find the area of the top, front and side, add them, then double.

Step 23: Find the average

The average (mean) shares the total equally: add everything, then divide by how many there are.

Example: What is the average? 5, 5, 6, 20

Tip: The average is always between the smallest and biggest numbers.

Step 24: Median and range

The median is the middle number when the data is in order. The range is the biggest minus the smallest.

Example: Find the median. 8, 18, 11, 16, 24

Tip: Always put the numbers in order first.

Step 25: Find the mode

The mode is the value that appears most often.

Example: Tap one of the numbers that is the mode.

Tip: Count how many times each number shows up.

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