Decimals and fractions
Year 6 · 6 questions
Line up decimal points, shift digits by powers of 10 and add unlike fractions.
For parents: By the end of Year 6, your child should be able to add and subtract decimals, multiply and divide decimals by 10, 100 and 1000, and add fractions with related denominators.
AC9M6N04apply knowledge of place value to add and subtract decimals, using digital tools where appropriate; use estimation and rounding to check the reasonableness of answersAC9M6N05solve problems involving addition and subtraction of fractions using knowledge of equivalent fractionsAC9M6N06multiply and divide decimals by multiples of powers of 10 without a calculator, applying knowledge of place value and proficiency with multiplication facts; using estimation and rounding to check the reasonableness of answers
Sample question and its hints
Jess ran 3.75 km on Saturday and 2.6 km on Sunday. How far did she run altogether?
- You need the total distance for both days, so add the two distances together.
- Line up the decimal points. Write 2.6 as 2.60 so both numbers have two decimal places, then add column by column.
- 1.25 + 3.5: write 3.5 as 3.50, then 1.25 + 3.50 = 4.75. Now try yours.
Area, metric units and angles
Year 6 · 6 questions
Veggie patches, bags of flour and crossing roads: area, units and angles.
For parents: By the end of Year 6, your child should be able to convert between metric units, use length times width for the area of a rectangle, and work with angles on a line and at a point.
AC9M6M01convert between common metric units of length, mass and capacity; choose and use decimal representations of metric measurements relevant to the context of a problemAC9M6M02establish the formula for the area of a rectangle and use it to solve practical problemsAC9M6M04identify the relationships between angles on a straight line, angles at a point and vertically opposite angles; use these to determine unknown angles, communicating reasoning
Sample question and its hints
A rectangular veggie patch is 12 m long and 6 m wide. What is its area?
- Area is how many square metres it takes to cover the whole patch.
- Picture rows of 1 m squares: how many squares fit along the length, and how many rows fit across?
- A patch 5 m by 3 m holds 3 rows of 5 squares, so its area is 5 × 3 = 15 m². Now try yours.
Primes, squares and number patterns
Year 6 · 6 questions
Hunt for primes, spot square numbers and crack pattern rules.
For parents: By the end of Year 6, your child should be able to tell prime, composite and square numbers apart, follow pattern rules, and solve equations that use brackets.
AC9M6N02identify and describe the properties of prime, composite and square numbers and use these properties to solve problems and simplify calculationsAC9M6A01recognise and use rules that generate visually growing patterns and number patterns involving rational numbersAC9M6A02find unknown values in numerical equations involving brackets and combinations of arithmetic operations, using the properties of numbers and operations
Sample question and its hints
Tap all the prime numbers.
Choices: 2 · 9 · 17 · 21 · 29 · 1
- A prime number has exactly two factors: 1 and itself. Which of these numbers can be split into equal groups another way?
- For each number, try dividing by 2, 3, 5 and 7. If one of them divides evenly (and isn’t the number itself), it is composite.
- Is 15 prime? 15 = 3 × 5, so its factors are 1, 3, 5 and 15. It is composite. Now try yours.
Data displays and chance
Year 6 · 6 questions
Read the data, rate the chance and spot a sneaky graph.
For parents: By the end of Year 6, your child should be able to compare data displays, question a misleading graph, and describe chance as a number from 0 to 1 or a percentage.
AC9M6ST01interpret and compare data sets for ordinal and nominal categorical, discrete and continuous numerical variables using comparative displays or visualisations and digital tools; compare distributions in terms of mode, range and shapeAC9M6ST02identify statistically informed arguments presented in traditional and digital media; discuss and critique methods, data representations and conclusionsAC9M6P01recognise that probabilities lie on numerical scales of 0 – 1 or 0% – 100% and use estimation to assign probabilities that events occur in a given context, using common fractions, percentages and decimalsAC9M6P02conduct repeated chance experiments and run simulations with an increasing number of trials using digital tools; compare observations with expected results and discuss the effect on variation of increasing the number of trials
Sample question and its hints
You roll a normal six-sided die. Which describes the chance of rolling a number less than 7?
Choices: Impossible (0) · Even chance (0.5) · Certain (1) · Unlikely (about 0.2)
- Probabilities go from 0 (impossible) to 1 (certain). What numbers are on a die?
- Count how many of the faces show a number less than 7, out of 6 faces.
- Rolling a number bigger than 10 on a die: no face works, so it is impossible, 0. Now try yours.
Fractions
For Years 3–6 · 6 questions
Share pizzas, lamingtons and kangaroos into equal parts.
For parents: Across Years 3 to 6, your child learns to name unit fractions, find equivalent fractions, and compare and order fractions.
AC9M3N02recognise and represent unit fractions includingAC9M4N03find equivalent representations of fractions using related denominators and make connections between fractions and decimal notationAC9M5N03compare and order fractions with the same and related denominators including mixed numerals, applying knowledge of factors and multiples; represent these fractions on a number line
Sample question and its hints
What fraction of the pizza is left?
- How many equal slices made the whole pizza? That number goes on the bottom of the fraction.
- Now count the slices that are still there. That number goes on top. Drawing the pizza can help.
- If a pizza has 4 slices and 2 are eaten, 2 of the 4 slices are left, so 2/4 is left. Now try yours.
Integers and negative numbers
For Years 6–8 · 6 questions
Temperatures below zero, number lines, and adding, subtracting and multiplying integers.
For parents: Across Years 6 to 8, your child learns to place negative numbers on a number line, and add, subtract and multiply positive and negative numbers.
AC9M6N01recognise situations, including financial contexts, that use integers; locate and represent integers on a number line and as coordinates on the Cartesian planeAC9M7N07compare, order and solve problems involving addition and subtraction of integersAC9M8N04use the 4 operations with integers and with rational numbers, choosing and using efficient strategies and digital tools where appropriate
Sample question and its hints
Which number is the smallest?
Choices: −2 · 0 · −8 · 3
- Smallest means furthest to the left on a number line.
- Draw a number line from −10 to 5 and mark each number. Which one is furthest left?
- Between −5 and −1, −5 is smaller because it is further below zero. Now try yours.