Year 5 Maths practice, done properly
Year 5 Maths practice doesn’t need to feel like a mystery. This page gives you 600 Australian Curriculum Maths questions for Year 5 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 5 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 5 Maths covers
Number, algebra, measurement, geometry, statistics and probability, matched to the Year 5 Australian Curriculum scope:
Year 5 Maths explained, topic by topic
Every Year 5 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
Place value tells us the value of a digit based on its position within a number. As we move from right to left in a whole number, each column becomes 10 times larger than the previous one. In Year 5, we work with large numbers up to hundreds of thousands or millions. To read and manage these numbers easily, we group digits into families of three using commas or spaces as placeholders (for example, millions, thousands, and ones).
- Ones column: Tells us how many single units we have (0 to 9).
- Tens column: Worth 10 times the ones column.
- Hundreds column: Worth 10 times the tens column (or 100 times the ones column).
- Thousands column: Worth 10 times the hundreds column.
- Ten-Thousands column: Worth 10 times the thousands column.
- Hundred-Thousands column: Worth 10 times the ten-thousands column.
Why it matters: Population figures, house prices and the distances between Australian towns are all written in the hundreds of thousands or millions, and reading them correctly is what makes a news headline mean something.
- Losing track of the place-value columns in a large number and misreading it. Break the digits into groups of three from the right (1 | 234 | 567) before you name the number, so the thousands and millions are obvious.
- Rounding to the wrong place. Underline the digit in the place you are rounding to, then look only at the single digit immediately to its right — everything further right is irrelevant to the decision.
2. Number Properties (Primes, Composites, Squares, Factors)
Numbers have unique personalities based on how they can be broken down or built up.
- Factors: Whole numbers that multiply together to make another number. For example,
the factors of 6 are 1, 2, 3, and 6.
- Multiples: The numbers you get when you multiply a number by other whole numbers
(like its skip-counting track). The multiples of 5 are 5, 10, 15, 20, and so on.
- Prime Numbers: Numbers greater than 1 that have exactly two factors: 1 and
themselves. Examples include 2, 3, 5, 7, and 11.
- Composite Numbers: Numbers that have more than two factors. Examples include 4,
6, 8, 9, and 10.
- Square Numbers: The result of multiplying a whole number by itself. For example, 3 x 3
= 9, so 9 is a square number.
Why it matters: Arranging chairs in equal rows for a school assembly is a factor problem — the numbers that divide evenly into the total are exactly the row sizes that will work.
- Calling 1 a prime number. A prime has exactly two different factors, itself and 1, and 1 only has one factor — so 1 is neither prime nor composite. The smallest prime is 2.
- Confusing factors with multiples. Factors divide into a number (the factors of 12 are 1, 2, 3, 4, 6, 12) while multiples come out of it when you count up in that number (12, 24, 36). Factors are never bigger than the number itself.
3. The Four Operations (+, -, x, /)
The four mathematical operations allow us to manipulate numbers to solve real problems. In Year 5, we look at formal column methods for addition and subtraction, and standard models for multi-digit multiplication and short division.
- Addition (+): Combining groups. We line up columns by place value and carry (regroup)
over to the left when a column sum exceeds 9.
- Subtraction (-): Finding differences or taking away. We line up columns by place value
and borrow (regroup) from the left column when the top digit is smaller than the bottom digit.
- Multiplication (x): Repeated addition. We multiply digits column by column, using a
zero placeholder when multiplying by the tens digit.
- Division (/): Sharing or grouping into equal parts. We calculate from left to right, carrying
any leftovers (remainders) over to the next digit.
Why it matters: Working out the total cost of a family shop, then splitting it between households, uses all four operations in a single everyday calculation.
- Working left to right regardless of the operation. Multiplication and division are done before addition and subtraction, so 3 + 4 x 5 is 23, not 35.
- Forgetting to keep place-value columns lined up in a written algorithm. A single digit written one column across turns a sensible answer into one ten times too big.
4. Patterns and Algebra
Patterns are sequences of numbers or shapes that follow a consistent mathematical rule. Algebra involves identifying that hidden rule and using it to find missing numbers or predict what comes next.
- Number Sequences: A list of numbers that grows or shrinks by a specific step rule. For
example, in the sequence 3, 7, 11, 15, the rule is "+4 each time".
- Geometric Sequences: Sequences that change by multiplying or dividing by a number
each time. For example, in 2, 6, 18, 54, the rule is "multiply by 3 each time".
- Missing Number Equations: Using inverse operations to find an unknown value. For
example, if a mystery box plus 5 equals 12 (Box + 5 = 12), we work backward to find that the box must be 7 ($12 - 5 = 7$).
Why it matters: Working out the cost of hiring something with a call-out fee plus an hourly rate is exactly a number rule — a fixed amount plus a repeated one.
- Describing a pattern from only its first two terms. Check your rule against the third and fourth terms too — 2, 4, ... could be adding 2 or doubling, and only the next term settles it.
- Reading a rule like 3n + 2 as 'three, then n plus two'. The number in front of the letter means multiply, so for n = 5 it is 3 x 5 + 2 = 17.
5. Fractions (Comparing, Adding, Subtracting)
A fraction represents a part of a whole unit or group. It is written as a top number (numerator) over a bottom number (denominator).
- Numerator: Tells us how many parts we are counting or looking at.
- Denominator: Tells us the total number of equal pieces the whole unit has been cut into.
- Like Denominators: When fractions have the exact same bottom number, they are
using the same size pieces. We can add or subtract them easily by combining the numerators and keeping the denominator exactly the same.
- Comparing Fractions: If denominators are the same, the fraction with the larger
numerator is bigger. If denominators are different, we scale them to a common format to compare their sizes accurately.
Why it matters: Halving or doubling a recipe means adding and comparing fractions of a cup, and getting it wrong is the difference between a cake and a puddle.
- Adding the denominators as well as the numerators. One quarter plus one quarter is two quarters, not two eighths — the denominator names the size of the piece and does not change when you add pieces of that same size.
- Comparing fractions by their numbers alone. One third is larger than one quarter even though 3 is smaller than 4, because the more pieces you cut a whole into, the smaller each piece becomes.
6. Equivalent Fractions and Simplifying
Equivalent fractions are different fractions that name the exact same amount or value. For example, eating 1/2 of a pizza is the same as eating 2/4 of it. We create equivalent fractions by multiplying or dividing both the top number (numerator) and the bottom number (denominator) by the same whole number. Simplifying a fraction means reducing it to its smallest possible numbers without changing its value. To simplify a fraction to its lowest terms, we find the highest common factor (HCF) that divides evenly into both the numerator and the denominator, and then divide them both by that number. If the only number that can divide both parts is 1, the fraction is already in its simplest form.
Why it matters: Sale signs use equivalent fractions constantly: '50% off', 'half price' and '1/2 off' are three ways of writing the same discount.
- Multiplying or dividing only the top or only the bottom. Whatever you do to the numerator you must do to the denominator, or you have changed the value rather than renamed it.
- Stopping before the fraction is fully simplified. After dividing 8/12 by 2 you have 4/6, which still shares a factor of 2 — keep going until the only number that divides both is 1.
7. Improper Fractions and Mixed Numbers
Fractions can be written in two different formats when they represent an amount greater than one whole: improper fractions and mixed numbers. An improper fraction is a fraction where the top number (numerator) is equal to or larger than the bottom number (denominator), such as 7/3. This shows the total number of equal parts you have altogether. A mixed number combines a whole number and a proper fraction together, such as 2 and 1/3. This shows how many completely full items you have, along with any leftover fractional parts. Both formats represent the exact same value, and we can convert back and forth between them easily.
Why it matters: A recipe calling for 7/2 cups is easier to measure once you see it as 3 1/2 cups — the same amount, in the form a measuring jug can actually show you.
- Adding the whole number to the numerator when converting. For 2 3/4, multiply the whole number by the denominator first (2 x 4 = 8), then add the numerator, giving 11/4 — not 5/4.
- Leaving an improper fraction in a final answer when the question asked for a mixed number, or the reverse. Reread what form the question wants before you write the answer.
8. Decimals (Place Value, Comparing, Conversions)
Decimals are another way to write fractions that represent parts of a whole. They use a decimal point to separate whole numbers on the left from fractional values on the right. Just like whole number columns, decimal places have specific names and decrease by dividing by 10 each time you move right:
- Tenths column (first place after the decimal point): Represents pieces of a whole cut
into 10 equal parts (1/10 or 0.1).
- Hundredths column (second place after the decimal point): Represents pieces of a
whole cut into 100 equal parts (1/100 or 0.01).
Why it matters: Petrol prices, race times and supermarket weights are all decimals, and comparing them correctly is how you tell a genuine saving from a rounding trick.
- Assuming a longer decimal is a larger one. 0.4 is greater than 0.39, because the tenths column is compared first — line the numbers up by their decimal points, not by how many digits they have.
- Dropping the decimal point when adding amounts of different lengths. Write 12 as 12.00 and 3.5 as 3.50 first, so every column has a digit and nothing shifts.
9. Measurement (Units, Conversions, Time)
Measurement allows us to quantify the world around us. In Year 5, we look at metric units for length, mass (weight), and capacity (fluid volume), as well as conversions between units and reading 24-hour time schedules.
- Length: Measured in millimetres (mm), centimetres (cm), metres (m), and kilometres
(km).
- Mass: Measured in grams (g) and kilograms (kg).
- Capacity: Measured in millilitres (mL) and litres (L).
- Metric Conversions: The metric system works on scales of 10, 100, or 1,000. Going
from a larger unit to a smaller unit means multiplying (moving decimal right). Going from a smaller unit to a larger unit means dividing (moving decimal left).
- Time: Includes 12-hour AM/PM formats and 24-hour time (where hours run from 00:00
to 23:59 with no AM/PM attached).
Why it matters: Reading a recipe in grams, a bottle in millilitres and a trip in kilometres all needs unit conversion — the metric system is built so the conversions are always powers of ten.
- Multiplying when you should divide during a conversion. Going from a small unit to a larger one (grams to kilograms) means dividing, so the number gets smaller while the amount stays the same.
- Treating time as decimal. 2.5 hours is 2 hours 30 minutes, not 2 hours 50 minutes, because an hour has 60 minutes rather than 100.
10. Geometry and Perimeter/Area
Geometry is the study of shapes, lines, angles, and spatial spaces.
- Angles: Formed where two lines meet. Classified as Acute (less than 90 degrees),
Right (exactly 90 degrees, like a square corner), Obtuse (between 90 and 180 degrees), and Straight (exactly 180 degrees).
- Polygons: Flat 2D shapes with straight lines. Named by side count: Triangle (3),
Quadrilateral (4), Pentagon (5), Hexagon (6), Octagon (8).
- Perimeter: The total distance around the outside edge of a flat shape. Found by adding
all the side lengths together.
- Area: The total flat space inside a 2D shape. For rectangles, found by multiplying length
by width (Area = length x width).
Why it matters: Fencing a paddock is a perimeter problem while turfing it is an area problem, which is why the fencing is sold by the metre and the turf by the square metre.
- Swapping perimeter and area. Perimeter is the distance all the way around and is measured in centimetres or metres; area is the space covered and is measured in square units such as cm squared.
- Using the slanted side of a shape as its height. For triangles and parallelograms the height must be perpendicular to the base — measured straight up from it, not along the sloping edge.
11. Money and Financial Mathematics
Money problems in Year 5 combine decimals, multiplication and percentages. Unit pricing tells you the true cost of an item by dividing the price by the quantity, so two different-sized packets can be compared fairly. Discounts are percentages of the original price: finding 10% means dividing by 10, and other percentages can be built from that. Always finish a discount question by subtracting the saving from the original price, because the question usually asks what you pay, not what you save.
Why it matters: Supermarket shelf labels in Australia show a unit price (per 100 g or per litre) precisely so shoppers can compare value at a glance — you are doing the same maths the label does.
- Comparing two packet prices without converting to the same unit first. A bigger packet with a bigger price tag is not automatically worse value — only the price per unit settles it.
- Stopping after calculating the discount. If a $60 item is 25% off, the $15 you worked out is the saving; the answer to 'what do you pay' is $60 - $15 = $45.
12. Chance, Probability and Averages
Probability describes how likely something is, on a scale from 0 (impossible) to 1 (certain), and it can be written as a fraction, a decimal or a percentage. For equally likely outcomes, the probability is the number of favourable outcomes divided by the total number of outcomes. Because every possible outcome together must total 1, the chance of something NOT happening is 1 minus the chance that it does. The mean (often called the average) is found by adding all the values and dividing by how many values there are.
Why it matters: A weather forecast saying '70% chance of rain' is exactly this idea, and a cricket batting average is a mean — the total runs divided by the number of innings.
- Writing a probability as a count instead of a fraction of the total. With 3 red marbles out of 10, the probability is 3/10 — an answer of '3' is not a probability at all, and no probability can ever be larger than 1.
- Forgetting to divide when finding a mean, or dividing by the wrong number. Always divide the total by how many values you added, not by the largest value.
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 5 Maths practice free?
Yes. Test 1 for Year 5 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 5 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 5 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 5 students (typically 10-11 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.