Mental addition and subtraction

Mental addition and subtraction: what children learn

Year 5 pupils add and subtract numbers mentally with increasingly large numbers.

In this game children match calculations such as 12,500 + 3,000 and 23,999 + 6,001 to their answers. They are chosen so that a mental method, not a written one, is the best choice.

This topic covers the Year 5 statutory requirement in the National Curriculum in England (Number – addition and subtraction): pupils should be taught to “add and subtract numbers mentally with increasingly large numbers”. Year 5 pupils are usually aged 9–10.

For families following US standards, the closest Common Core standard is 4.NBT.B.4, which is taught in Grade 4. Mental strategies with large numbers build on 4.NBT.B.4.

How to play

Pick a card on the left, then the card on the right that matches it. Each game has 6 pairs. Wrong matches are counted as mistakes, and you get three stars for a game with no mistakes.

Step by step

1. Look for round numbers. 12,500 + 3,000 changes only the thousands digit: 15,500.
2. Make a number round. 23,999 + 6,001: move 1 from 6,001 to 23,999 to make 24,000 + 6,000.
3. Bridge through a multiple. 9,950 + 50: 50 more makes the next thousand, 10,000.
4. Subtract the round part. 61,200 − 1,200 = 60,000.

Worked examples

Common mistakes and how to fix them

• Reaching for a written method for every calculation. Look at the numbers first. Are any of them round?
• Changing the wrong digit. Say the place value of each digit: 3,000 means 3 thousands.
• Losing track when bridging. Write down the step you reached, such as 10,000.

Activities to try at home

• Ask quick mental questions in the car: 45,000 − 2,000?
• Use prices to practise: what is £9,950 + £50?
• Challenge each other to find the quickest way to work out a calculation.

Ideas for the classroom

• Pupils sort calculations into 'mental' and 'written' and explain why.
• Use a number line to show bridging through a multiple of 1,000.
• Pupils compare strategies for the same calculation.

Free printable game and worksheet

The free printable starts with a game sheet, such as a colour-by-answer picture, an answer maze or a secret-code joke, followed by a worksheet. Both use the same checked questions as the online game, and the answers are on the last page. Print it, or save it as a PDF from your browser’s print menu.

Open the free printable game and worksheet

Frequently asked questions

Related topics

• Adding and subtracting large numbers (Year 5 maths) – Add and subtract 5- and 6-digit numbers with the column method. A free Year 5 maths game.
• Rounding numbers to 1,000,000 (Year 5 maths) – Round numbers up to 1,000,000 to the nearest 10, 100, 1,000, 10,000 or 100,000. Free Year 5 maths game.
• Multiplying and dividing by 10, 100 and 1,000 (Year 5 maths) – Multiply and divide whole numbers and decimals by 10, 100 and 1,000. Free Year 5 maths game.
• Column methods with 4 digits (Year 4 maths) – Add and subtract 4-digit numbers with the column method. A free Year 4 maths game.
• Missing numbers and inverse operations (Year 4 maths) – Use the inverse to find the missing number in □ + 2,350 = 5,000. A free Year 4 maths game.
• Column addition and subtraction (Year 3 maths) – Add and subtract 3-digit numbers with the column method, exchanging when you need to. A free Year 3 maths game.

Back to Year 5 maths