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Year group guide

Year 5 maths: what your child learns (age 9 to 10)

Year 5 is for children aged 9 to 10, roughly the same as Grade 4 in the US. It's the third year of Key Stage 2. Numbers grow to a million, written methods get longer, and fractions, decimals and percentages start to join up into one big idea.

What Year 5 children are working on

Year 5 is a busy year. Children learn long multiplication and short division, meet prime numbers, square numbers and cube numbers, and work with fractions bigger than one. Percentages appear for the first time, alongside decimals with up to three decimal places.

In geometry, angles are measured in degrees with a protractor, and children find areas of rectangles in square centimetres. Much of what's learned this year is tested in the Key Stage 2 SATs in Year 6, so it's a good year to keep times tables sharp.

The Year 5 maths curriculum

This follows the National Curriculum in England. Each heading links to a full guide to that topic.

Number and place value

• Read, write, order and compare numbers to at least 1,000,000, and say what each digit is worth.
• Count forwards and backwards in powers of 10 (10s, 100s, 1,000s, 10,000s and 100,000s) from any number.
• Use negative numbers in context, such as temperatures: from −3 °C to 4 °C is a rise of 7 degrees.
• Round any number up to 1,000,000 to the nearest 10, 100, 1,000, 10,000 and 100,000: 247,385 rounds to 250,000 to the nearest 10,000.
• Read Roman numerals to 1,000 (M) and years written in Roman numerals: MMXXVI is 2026.

Addition and subtraction

• Add and subtract whole numbers with more than four digits, using the column method.
• Add and subtract mentally with bigger numbers: 12,462 − 2,300 = 10,162.
• Use rounding to check answers, and solve multi-step problems.

Multiplication and division

• Find multiples, factors, factor pairs and common factors: the common factors of 12 and 18 are 1, 2, 3 and 6.
• Know what prime numbers, prime factors and composite numbers are, check whether a number up to 100 is prime, and recall the primes up to 19: 2, 3, 5, 7, 11, 13, 17 and 19.
• Multiply numbers with up to four digits by a one-digit or two-digit number, including long multiplication: 24 × 36 = 864.
• Divide numbers with up to four digits by a one-digit number using short division, and deal with remainders sensibly: 437 ÷ 4 = 109 remainder 1.
• Multiply and divide whole numbers and decimals by 10, 100 and 1,000: 3.7 × 100 = 370.
• Know square numbers and cube numbers and the signs ² and ³: 5² = 5 × 5 = 25 and 2³ = 2 × 2 × 2 = 8.
• Understand the equals sign as "is the same as", and solve problems with all four operations, scaling and simple rates.

Fractions

• Compare and order fractions whose denominators are multiples of the same number: ⅔ = ⁴⁄₆, so ⁵⁄₆ is bigger than ⅔.
• Find equivalent fractions, including tenths and hundredths: ³⁄₁₀ = ³⁰⁄₁₀₀.
• Change between mixed numbers and improper fractions: ⅖ + ⅘ = ⁶⁄₅ = 1⅕.
• Add and subtract fractions with the same denominator, and where one denominator is a multiple of the other: ⅓ + ⅙ = ²⁄₆ + ⅙ = ³⁄₆ = ½.
• Multiply fractions and mixed numbers by whole numbers: ¾ × 3 = ⁹⁄₄ = 2¼.

Decimals and percentages

• Write decimals as fractions: 0.71 = ⁷¹⁄₁₀₀.
• Understand thousandths: 0.375 is 3 tenths, 7 hundredths and 5 thousandths.
• Round decimals with two decimal places to the nearest whole number and to one decimal place: 3.47 rounds to 3, or to 3.5.
• Read, write, order and compare numbers with up to three decimal places.
• Understand that per cent (%) means "out of 100", and write percentages as fractions and decimals: 37% = ³⁷⁄₁₀₀ = 0.37.
• Know the percentage and decimal equivalents of ½, ¼, ⅕, ⅖ and ⅘ (50%, 25%, 20%, 40% and 80%), and of fractions whose denominator is a multiple of 10 or 25, like ³⁄₂₅ = 12%.

Measurement

• Convert between metric units: 2.5 kg = 2,500 g.
• Know rough equivalents between metric and imperial units: an inch is about 2.5 cm, a kilogram is about 2.2 pounds, and a pint is a little more than half a litre.
• Find the perimeter of shapes made from rectangles, in cm and m.
• Calculate the area of rectangles in square centimetres (cm²) and square metres (m²): a rectangle 6 cm by 4 cm has an area of 24 cm². Estimate the area of irregular shapes.
• Estimate volume and capacity, for example by building cuboids from 1 cm³ cubes.
• Solve problems converting units of time, and use all four operations with measures and money, using decimals.

Geometry: properties of shapes

• Recognise 3D shapes, including cubes and other cuboids, from 2D drawings.
• Know that angles are measured in degrees (°). Estimate and compare acute (less than 90°), obtuse (between 90° and 180°) and reflex (more than 180°) angles.
• Draw and measure angles with a protractor.
• Know that angles at a point make a whole turn (360°), and angles on a straight line make a half turn (180°): if one angle on a straight line is 130°, the other is 50°.
• Use the properties of rectangles to find missing lengths and angles.
• Tell the difference between regular polygons (all sides and angles equal) and irregular ones.

Geometry: position and direction

• Describe and draw the position of a shape after a reflection (a flip in a mirror line) or a translation (a slide), and know the shape itself hasn't changed.

Statistics

• Solve problems using information in line graphs.
• Complete, read and use tables, including timetables: a bus that leaves at 10:45 and arrives at 11:20 takes 35 minutes.

By the end of Year 5, most children can…

• read, write, order and round numbers up to 1,000,000
• add and subtract large numbers with the column method
• use long multiplication, such as 24 × 36 = 864
• use short division with remainders, such as 437 ÷ 4 = 109 r 1
• find factors, multiples and prime numbers, and know square and cube numbers
• change between mixed numbers and improper fractions, and add fractions such as ⅓ + ⅙
• read and order decimals with up to three decimal places
• write percentages as fractions and decimals, and know that ¼ = 25% = 0.25
• work out the area of a rectangle in cm²
• measure and draw angles in degrees, and know angles on a straight line add up to 180°
• read line graphs and timetables

Key vocabulary

Tests in Year 5

There are no national maths tests in Year 5. Your child's school will use its own assessments to see how they're getting on. The Key Stage 2 SATs come in May of Year 6 and cover everything from Year 3 to Year 6, so a solid Year 5 makes Year 6 much calmer.

How to help at home

• Keep the times tables quick. Long multiplication, short division, factors and fractions all lean on them.
• Spot percentages. Sale signs, phone batteries and food labels are full of them. "It says 25% off. What fraction is that?"
• Measure the room. Work out the area of a bedroom floor in m², or the perimeter of the garden.
• Read timetables. Plan a trip using a real bus or train timetable: when do we need to leave, and how long will it take?
• Hunt for angles. How many degrees does the minute hand turn in 15 minutes? (A quarter turn, 90°.)
• Ask about primes. House numbers, ages and car registration numbers: is it prime?

Free Year 5 maths worksheets

Print these for practice at home or in class. Each one has an answer sheet on the second page.

Rounding numbersYear 4, Year 5 · Round to the nearest 10, 100 and 1,000Download PDF

Multiplication gridYear 3, Year 4, Year 5, Year 6 · Fill in the 12 × 12 gridDownload PDF

Short multiplicationYear 4, Year 5 · Three-digit by one-digit numbersDownload PDF

Equivalent fractionsYear 4, Year 5 · Find the missing numberDownload PDF

Tenths and hundredthsYear 4, Year 5 · Fractions as decimalsDownload PDF

Percentages of amountsYear 5, Year 6 · 10%, 25%, 50% and moreDownload PDF

Perimeter and areaYear 4, Year 5 · Rectangles on a centimetre gridDownload PDF

Missing number problemsYear 3, Year 4, Year 5, Year 6 · Find the number in the boxDownload PDF

Quick answers

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