Year 6 Maths practice, done properly
Year 6 Maths practice doesn’t need to feel like a mystery. This page gives you 600 Australian Curriculum Maths questions for Year 6 students, organised into 15 tests that build from an easy confidence-starter through to genuine extension-level challenge questions. Every test covers the core Year 6 Australian Curriculum topics — place value, mental strategies, fractions, measurement, shape, data and more — with every single answer option explained, so a wrong guess still teaches the concept behind it. The top tiers are calibrated against real past papers from competitive primary exams, so this is also strong preparation for NAPLAN and for the OC and Selective placement tests.
What Year 6 Maths covers
Number, algebra, measurement, geometry, statistics and probability, matched to the Year 6 Australian Curriculum scope:
Year 6 Maths explained, topic by topic
Every Year 6 Maths topic below is explained in plain language, with the mistakes children most often make. This is the same teaching inside the site, free to read.
1. Place Value and Large Numbers
Concept explanation: Students explore place value up to millions, focusing on how a digit's position determines its total value. Each position to the left increases by a factor of 10. Year 6 students must successfully read, write, partition, and order numbers up to 10,000,000. They apply this knowledge to compare large populations, stellar distances, and data sets. Understanding place value prevents fundamental errors when adding, subtracting, or estimating with multi-digit integers. It also builds the foundation for understanding decimals, where moving positions to the right decreases value by a factor of 10.
Why it matters: Census counts use large numbers to track national populations. For instance, comparing the populations of major global cities requires an accurate understanding of millions and hundred-thousands to allocate public infrastructure budgets fairly.
- Misidentifying columns due to zero placeholders. For example, writing 40,000 instead of 4,000 for the digit 4 in 5,004,120 because it is the fourth digit from the left. Students must always count columns starting from the rightmost ones column.
- Confusing the terms value and face value. The face value of 8 in 9,800,000 is simply 8, but its place value is eight hundred thousand.
2. Fractions, Decimals and Percentages
Concept explanation: Students learn to convert between fractions, decimals, and percentages to compare and order values effectively. These three forms represent parts of a whole. A percentage is a fraction out of 100, while a decimal uses place value columns like tenths and hundredths. Year 6 students simplify fractions, use division to turn fractions into decimals, and multiply decimals by 100 to find percentages. Mastery of these connections allows students to solve real-world problems involving retail discounts, probability metrics, and accurate scientific measurements.
Why it matters: Stores often display sales using different formats, such as 25 percent off, half price, or 0.2 off the regular retail amount. Shoppers must quickly convert these values to determine which deal offers the biggest savings.
- Thinking that a longer decimal is automatically larger. For example, believing that 0.125 is larger than 0.4 because 125 is larger than 4. Students must compare the tenths column first, where 4 tenths is larger than 1 tenth.
- Forgetting to change the denominator when adding fractions. Writing 1/4 + 1/4 = 2/8 is incorrect; only the numerators are added when denominators match, giving 2/4.
3. Operations and Order of Operations
Concept explanation: Students apply the rules of BODMAS or BIDMAS to solve equations containing multiple operations. This order dictates that Brackets are solved first, followed by Orders or Indices, then Division and Multiplication (from left to right), and finally Addition and Subtraction (from left to right). Without a strict order of operations, mathematical expressions would yield inconsistent results. Year 6 students use this structure to handle multi-step calculations accurately, combining addition, subtraction, multiplication, and division within a single problem to evaluate expressions properly.
Why it matters: Software programmers write algorithmic code using order of operations to ensure video games calculate scores, health points, and currency values accurately without software bugs corrupting player data.
- Working strictly from left to right regardless of the operators. For example, solving 5 + 2 x 3 by doing 5 + 2 = 7, then 7 x 3 = 21. The correct method requires multiplying 2 x 3 first to get 6, then adding 5 to get 11.
- Believing addition must always happen before subtraction because A comes before S in BODMAS. These two operations have equal priority and must be done in order from left to right.
4. Patterns, Algebra and Number Sentences
Concept explanation: Students identify geometric and numerical patterns, describe them using rules, and use inverse operations to solve unknown variables in number sentences. Algebra involves using symbols or letters to represent missing numbers. Year 6 students learn that an equation is like a balanced scale; whatever operation is done to one side must be done to the other to keep it equal. They work backward to isolate the unknown, applying addition to undo subtraction and multiplication to undo division, allowing them to solve missing number puzzles systematically.
Why it matters: Engineers use algebraic formulas to calculate the exact amount of weight a bridge support can hold, using variables to represent changing traffic levels and wind speeds safely.
- Forgetting to apply operations to both sides of the equals sign when balancing an equation. For example, adding 5 to the left side to cancel a subtraction but failing to add 5 to the right side.
- Assuming a pattern is always based on addition, overlooking rules based on multiplication or squaring.
5. Measurement, Units and Conversions
Concept explanation: Students learn to choose appropriate units and convert between standard metric measurements for length, mass, and capacity. The metric system relies on powers of 10. For length, students convert between millimetres, centimetres, metres, and kilometres. For mass, they move between grams and kilograms, and for capacity, between millilitres and litres. Year 6 students must know whether to multiply or divide when changing units. Moving from a larger unit to a smaller unit requires multiplication, whereas moving from a smaller unit to a larger unit requires division.
Why it matters: International trade relies completely on standardized metric conversions. Shipping companies must convert cargo weight from grams to kilograms and tonnes to avoid overloading container ships and airplanes.
- Multiplying instead of dividing when converting a small unit to a large unit. For example, stating that 500 metres is equal to 500,000 kilometres instead of 0.5 kilometres.
- Forgetting that length conversions use different factors, such as 10 millimeters in a centimetre and 100 centimetres in a metre, rather than always using 1,000.
6. Geometry, Shapes, Perimeter and Area
Concept explanation: Students study the properties of two-dimensional shapes and three-dimensional objects, calculating perimeter, area, and volume. Perimeter is the total distance around the outside of a shape, found by adding its side lengths. Area measures the surface inside a shape, calculated for rectangles by multiplying length by width. Year 6 students classify triangles based on sides and angles, and find the properties of prisms and pyramids. They understand that area is expressed in square units, which represents the number of grid squares a shape covers.
Why it matters: Landscapers use perimeter to figure out how many metres of fencing are needed to secure a backyard, and they use area to determine how many rolls of grass turf are required to cover the lawn completely.
- Confusing the formulas for perimeter and area, such as multiplying the sides when asked for perimeter, or adding the sides when asked for area.
- Forgetting to include the correct units, like writing centimetres instead of square centimetres for area calculations.
7. Position, Direction, Angles and Transformations
Concept explanation: Students locate points on grids, identify paths using directional compass points, measure angles, and execute shape transformations. Angles are measured in degrees using a protractor, categorised as acute (less than 90 degrees), right (exactly 90 degrees), obtuse (between 90 and 180 degrees), or reflex (greater than 180 degrees). Transformations describe how shapes move: translation slides a shape, reflection flips it across a line, and rotation turns it around a fixed point. Year 6 students combine these ideas to analyse navigation maps and structural symmetries.
Why it matters: Air traffic controllers rely on exact angle degrees and directional coordinates to guide airplanes safely along flight paths, preventing collisions during approaches to busy airport runways.
- Reading the wrong scale on a protractor, such as measuring an obtuse angle as 60 degrees instead of 120 degrees. Students must check if the angle is wider or narrower than a right angle first.
- Reversing coordinate pairs by reading the vertical y-axis before the horizontal x-axis, forgetting the rule to go along the hall before up the stairs.
8. Data, Graphs, Statistics and Probability
Concept explanation: Students gather data, represent it using graphs, and analyse it using statistics like mean, median, mode, and range. The mean is the average, found by adding scores and dividing by the total number of items. The median is the middle value when numbers are sorted in order. Probability measures the likelihood of an event occurring, ranging from 0 (impossible) to 1 (certain), often expressed as fractions or percentages. Year 6 students interpret column graphs, line graphs, and pie charts to draw accurate conclusions from raw experimental data.
Why it matters: Weather scientists analyse years of temperature data graphs to track global climate shifts, using mean values to predict seasonal rain volumes for agricultural planning.
- Forgetting to arrange numbers in order before finding the median, simply picking the middle number of the un-sorted list.
- Dividing by the wrong number when calculating the mean, such as always dividing by 2 instead of dividing by the actual count of data points.
9. Problem Solving, Logic and Reasoning
Concept explanation: Students develop strategies to decode word problems, eliminate impossible options, and use logical deductions. Problem solving requires pulling essential numerical facts out of text narratives while ignoring irrelevant filler words. Year 6 students use tools like drawing tables, working backward from an end goal, or testing small numbers to find patterns. Logic reasoning forces students to connect clues systematically, checking that their mathematical conclusions satisfy all constraints outlined in the question.
Why it matters: Computer scientists write logic paths for automated security systems, ensuring doors only unlock when multiple conditions like correct passwords and valid security badges are met at the same time.
- Jumping straight into arithmetic operations using whatever numbers appear first in the text without reading the actual question constraint carefully.
- Making assumptions that are not supported by the logic clues, such as assuming two people are the same age because they are both older than a third person.
10. Mixed Visual and Operational Word Problems
Concept explanation: Students solve multi-step word problems that combine numerical calculations with visual or spatial arrangements, such as grids, calendars, schedules, or architectural blueprints. These problems test a student's ability to process multiple data formats simultaneously. Year 6 students learn to extract geometric data from text descriptions and combine it with financial or time constraints, showing flexible thinking across maths domains to solve realistic compound challenges.
Why it matters: Event planners use combined operational planning to arrange seating grids within conference halls, matching the physical area constraints of the building with ticket sales and catering timeline schedules.
- Missing hidden steps in visual word problems, such as calculating the area of only one side of a wall when a painting project requires painting both sides.
- Forgetting that time cycles change at 60 minutes rather than 100, leading to incorrect calculations when subtracting minutes across hourly boundaries.
11. Time, 24-Hour Time and Timetables
24-hour time runs from 00:00 to 23:59, so afternoon and evening times are written by adding 12 to the hour: 7:45 pm becomes 19:45. Times before midday keep their hour but are written with four digits, so 8:05 am is 08:05. Elapsed time is worked out by counting on in chunks — minutes to the next whole hour, then whole hours — rather than subtracting like ordinary numbers, because an hour is 60 minutes, not 100. Timetables put many of these journeys in one table, and reading across a row while checking the column headings carefully is what makes them easy.
Why it matters: Train, bus and ferry timetables across Australia are published in 24-hour time, and so are flight departures — reading them correctly is the difference between catching a service and watching it leave.
- Treating time as an ordinary decimal. 1.5 hours is 1 hour 30 minutes, not 1 hour 50 minutes, because there are 60 minutes in an hour — subtracting 09:45 from 10:30 as '85' is the same error.
- Adding 12 to a morning time. 9:15 am is simply 09:15 in 24-hour time; only pm times have 12 added, and 12:30 am is written 00:30.
12. Money, Percentages and Financial Mathematics
Year 6 money problems are percentage problems wearing a dollar sign. A discount is a percentage taken off the original price, and what you pay is the price minus that discount. In Australia, GST is a Goods and Services Tax of 10% added to most purchases, so it is found by dividing the pre-tax price by 10. Profit is what is left after costs are subtracted from the money taken, and a loss is the same calculation ending below zero. The safest habit is to identify the original amount the percentage refers to before doing any arithmetic.
Why it matters: Every Australian receipt shows the GST included in the total, and sale signs in shopping centres are percentage problems — knowing how to check them yourself means you can tell a real bargain from a loud sticker.
- Confusing '15% off' with 'pay 15%'. A 15% discount on $80 means you pay $68, not $12 — the percentage names the saving, not the price.
- Applying a second percentage to the wrong amount. If an item is discounted and then GST is added, the GST is calculated on the discounted price, not on the original ticket price.
Try real questions — easy and hard
Tests are graded from an easy confidence-builder (Test 1, free to try in full) up to genuine extension-level challenge questions by Test 15. Here's one of each:
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Frequently asked questions
Is this Year 6 Maths practice free?
Yes. Test 1 for Year 6 Maths is completely free — no credit card and no account required to try it. Tests 2–15 are part of the paid subscription, which unlocks every year level and subject.
How many Year 6 Maths questions are there?
600 questions across 15 tests, graded from an easy confidence-builder through to extension-level challenge tests. Every question has all 4 answer options explained, not just the correct one.
Is this aligned with the Australian Curriculum?
Yes. Questions are written to match the Year 6 Australian Curriculum scope, and pitched a step above it, so a confident child is stretched rather than repeating classwork.
What age or year level is this for?
This is built for Year 6 students (typically 11-12 year olds) following the Australian Curriculum, in every state and territory.
Do wrong answers get explained too?
Yes — every single option (right and wrong) has its own explanation, so a wrong guess still teaches the underlying concept instead of just marking it incorrect.