Free Year 6 maths practice questions

Year 6 maths in Australia pulls together everything from primary school and adds trickier ideas — negative numbers, percentages, area and volume, and multi-step word problems. This page gives you free, original practice for every Year 6 strand, with worked examples and answers, plus a printable PDF you can use at the kitchen table. Everything here is free.

Number and place value (including integers)

Year 6 extends numbers below zero — negative numbers (integers) on a number line — and looks at factors, multiples, prime, composite and square numbers. Children also work with very large numbers and the order of operations.

Try this: The temperature is 4 °C at midday and drops by 7 °C overnight. What is the overnight temperature? Answer: −3 °C.

Fractions, decimals and percentages

This is the heart of Year 6: comparing and ordering fractions, adding and subtracting fractions, converting between fractions, decimals and percentages, and finding a percentage of an amount.

Try this: A jacket costs $80 and is reduced by 25%. What is the sale price? Answer: 25% of $80 is $20, so the sale price is $60.

Ratio and rates (an introduction)

Year 6 introduces simple ratios and rates — sharing in a given ratio and working with "per" quantities like speed or price per item. This builds the thinking used heavily in high school.

Try this: Share 18 lollies between two children in the ratio 2 : 1. How many does each get? Answer: 3 equal parts, so 12 and 6.

Measurement — area, perimeter, volume and time

Students calculate the perimeter and area of rectangles, the volume of rectangular prisms, convert between units (mm, cm, m; mL, L; g, kg), and read 24-hour and analogue time, including timetables.

Try this: A rectangle is 8 cm long and 5 cm wide. What is its area? Answer: 8 × 5 = 40 cm².

Geometry — angles and 2D/3D shapes

Year 6 covers measuring and estimating angles, the properties of 2D shapes, the faces, edges and vertices of 3D objects, and using coordinates on the Cartesian plane (all four quadrants).

Try this: Two angles on a straight line are 110° and x. What is x? Answer: angles on a straight line add to 180°, so x = 70°.

Data and chance

Children read and build column graphs, dot plots and tables, find the mean (average) of a small data set, and describe the chance of events using fractions, decimals and percentages.

Try this: Find the mean of 6, 9, 3 and 10. Answer: (6 + 9 + 3 + 10) ÷ 4 = 28 ÷ 4 = 7.

Word problems and problem solving

By Year 6, the big shift is multi-step problems — questions that need two or three steps and a bit of planning. Strategies like working backwards, drawing a diagram and estimating to check an answer all matter.

Try this: A class of 24 students goes on an excursion. Tickets are $9 each and the bus costs $60 in total. What is the total cost? Answer: 24 × $9 = $216, plus $60 = $276.

Practise online, free

Prefer to practise on screen with instant feedback? Kids Learning Hub has free, original Year 6 maths built into interactive levels, so your child gets a tick or a helpful hint straight away and you can see how they are going.

Start free Year 6 maths practice

How to help at home

You do not need to be a maths teacher. The most useful thing is little and often — ten minutes a few times a week, with no pressure.

• Use real life. Work out discounts while shopping, split a bill, double a recipe, or read a bus timetable together.
• Let them explain. Asking "how did you get that?" builds the reasoning Year 6 is really testing.
• Keep mistakes normal. A wrong answer is just the next thing to learn — stay calm and curious.

For the official content for each year level, you can check the Australian Curriculum (state syllabuses such as NSW build on it).

Frequently asked questions