Adding and subtracting large numbers: what children learn
Year 5 pupils add and subtract whole numbers with more than four digits, including using formal written methods, and use rounding to check answers.
In this game children work out additions and subtractions with five- and six-digit numbers. The method is the same as for smaller numbers; the challenge is keeping every digit in the right column.
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 whole numbers with more than 4 digits, including using formal written methods (columnar addition and subtraction)”. 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.
How to play
Answer 10 questions before the clock runs out. Tap an answer, or press 1 to 4. Each game has 10 multiple-choice questions and a 180-second timer. A wrong answer shows the correct one before moving on. You earn up to three stars depending on your score.
Step by step
- Line up from the ones. Write the numbers so that ones, tens, hundreds and so on are in columns.
- Work right to left. Carry or exchange as you go, just as with smaller numbers.
- Use the commas. The comma separates thousands. It helps you line up the digits.
- Estimate to check. Round each number and check that your answer is close.
Worked examples
Example 1: 70,711 + 44,496
Working: Estimate: 71,000 + 44,000 = 115,000. Add in columns from the ones.
Answer: 115,207
Example 2: 693,299 − 66,540
Working: Estimate: 693,000 − 67,000 = 626,000. Subtract in columns from the ones.
Answer: 626,759
Example 3: 842,634 − 55,642
Working: Estimate: 843,000 − 56,000 = 787,000. Subtract in columns from the ones.
Answer: 786,992
Common mistakes and how to fix them
- Lining up a five-digit number under a six-digit number from the left. Line up from the ones. Use squared paper.
- Missing an exchange in a long subtraction. Check each column before moving on.
- Not checking with an estimate. Round to the nearest thousand and compare.
Activities to try at home
- Add the populations of two towns or cities.
- Find the difference between two car mileages.
- Check large calculations with a calculator after doing them on paper.
Ideas for the classroom
- Pupils estimate first and only calculate exactly when the estimate is in a given range.
- Give calculations with deliberate errors for pupils to find.
- Use real data, such as stadium capacities, for word problems.
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
How big are the numbers in Year 5?
Year 5 pupils read and write numbers up to 1,000,000 and add and subtract numbers with more than four digits.
When should children use a mental method instead?
When the numbers are round or close to round, such as 45,000 − 2,000.
Can it be played with a keyboard?
Yes. Press 1, 2, 3 or 4 to choose an answer.