Step-by-step Maths Level 3: Checking, missing numbers and word problems
Part of the Step-by-step Maths Level 3 subtracting within 1000 chapter. Chapter overview · whole chapter on one page
Checking, missing numbers and word problems
Addition undoes subtraction. To check a subtraction, add the answer back to the number taken away. You should get the number you started with.
To find a missing number, think about the addition that matches it.
Key ideas
- Check: answer + the number taken away = the start.
- Missing number: think of the matching addition.
- Words like left, eaten and gives mean take away.
Method. Use addition to work out the missing number, then check it with subtraction.
- Think of the take away as a missing number. The number taken away is the missing part.432 - ? = 245
- Use addition to find it. Taking away the missing number leaves 245, so 245 + ? = 432.245 + ? = 432
- Work out the missing number. Subtract the answer from the start.432 - 245 = 187
- Write the missing number. Check: the number taken away is this.187
Check. Check: 432 - 187 = 245.
Watch out. Check the missing number by putting it back in the question.
Method. Use addition to work out the missing number, then check it with subtraction.
- Think about what we started with. The starting number is the one we took from.? - 215 = 425
- Add back the number taken away. Adding 215 back to 425 gives the starting number.425 + 215 = 640
- Write the missing number. This is the number we started with.640
Check. Check: 640 - 215 = 425.
Watch out. Check the missing number by putting it back in the question.
Method. Find the operation, then work out what is left.
- Find the operation. Words like left, gives and empty mean take away.340 - 178
- Work out the answer. Use column subtraction, and exchange if needed.340 - 178 = 162
- Write the answer. This is the number left.162
Check. Check: 162 + 178 = 340.
Watch out. Words like left, gone and gives away mean take away.
Watch out
Watch out. When a number is missing from the start, add the answer and the number taken away. Do not subtract them.
Exam tip
Grown-up tip. Ask the child to put the answer back into the question to see if it fits.
Exercise 5D Practice: checks, missing numbers and problems
Non-calculatorMethod. Use addition to work out the missing number, then check it with subtraction.
- Think about what we started with. The starting number is the one we took from.? - 113 = 348
- Add back the number taken away. Adding 113 back to 348 gives the starting number.348 + 113 = 461
- Write the missing number. This is the number we started with.461
Check. Check: 461 - 113 = 348.
Watch out. Check the missing number by putting it back in the question.
Method. Use addition to work out the missing number, then check it with subtraction.
- Think about what we started with. The starting number is the one we took from.? - 209 = 234
- Add back the number taken away. Adding 209 back to 234 gives the starting number.234 + 209 = 443
- Write the missing number. This is the number we started with.443
Check. Check: 443 - 209 = 234.
Watch out. Check the missing number by putting it back in the question.
Method. Use addition to work out the missing number, then check it with subtraction.
- Think about what we started with. The starting number is the one we took from.? - 145 = 412
- Add back the number taken away. Adding 145 back to 412 gives the starting number.412 + 145 = 557
- Write the missing number. This is the number we started with.557
Check. Check: 557 - 145 = 412.
Watch out. Check the missing number by putting it back in the question.
Method. Use addition to work out the missing number, then check it with subtraction.
- Think about what we started with. The starting number is the one we took from.? - 65 = 99
- Add back the number taken away. Adding 65 back to 99 gives the starting number.99 + 65 = 164
- Write the missing number. This is the number we started with.164
Check. Check: 164 - 65 = 99.
Watch out. Check the missing number by putting it back in the question.
Method. Use addition to work out the missing number, then check it with subtraction.
- Think of the take away as a missing number. The number taken away is the missing part.837 - ? = 665
- Use addition to find it. Taking away the missing number leaves 665, so 665 + ? = 837.665 + ? = 837
- Work out the missing number. Subtract the answer from the start.837 - 665 = 172
- Write the missing number. Check: the number taken away is this.172
Check. Check: 837 - 172 = 665.
Watch out. Check the missing number by putting it back in the question.
Method. Use addition to work out the missing number, then check it with subtraction.
- Think of the take away as a missing number. The number taken away is the missing part.631 - ? = 554
- Use addition to find it. Taking away the missing number leaves 554, so 554 + ? = 631.554 + ? = 631
- Work out the missing number. Subtract the answer from the start.631 - 554 = 77
- Write the missing number. Check: the number taken away is this.77
Check. Check: 631 - 77 = 554.
Watch out. Check the missing number by putting it back in the question.
Method. Use addition to work out the missing number, then check it with subtraction.
- Think about what we started with. The starting number is the one we took from.? - 95 = 742
- Add back the number taken away. Adding 95 back to 742 gives the starting number.742 + 95 = 837
- Write the missing number. This is the number we started with.837
Check. Check: 837 - 95 = 742.
Watch out. Check the missing number by putting it back in the question.
Method. Use addition to work out the missing number, then check it with subtraction.
- Think about what we started with. The starting number is the one we took from.? - 157 = 57
- Add back the number taken away. Adding 157 back to 57 gives the starting number.57 + 157 = 214
- Write the missing number. This is the number we started with.214
Check. Check: 214 - 157 = 57.
Watch out. Check the missing number by putting it back in the question.
Method. Find the operation, then work out what is left.
- Find the operation. Words like left, gives and empty mean take away.576 - 395
- Work out the answer. Use column subtraction, and exchange if needed.576 - 395 = 181
- Write the answer. This is the number left.181
Check. Check: 181 + 395 = 576.
Watch out. Words like left, gone and gives away mean take away.
Method. Find the operation, then work out what is left.
- Find the operation. Words like left, gives and empty mean take away.590 - 333
- Work out the answer. Use column subtraction, and exchange if needed.590 - 333 = 257
- Write the answer. This is the number left.257
Check. Check: 257 + 333 = 590.
Watch out. Words like left, gone and gives away mean take away.
Method. Find the operation, then work out what is left.
- Find the operation. Words like left, gives and empty mean take away.705 - 479
- Work out the answer. Use column subtraction, and exchange if needed.705 - 479 = 226
- Write the answer. This is the number left.226
Check. Check: 226 + 479 = 705.
Watch out. Words like left, gone and gives away mean take away.
Method. Find the operation, then work out what is left.
- Find the operation. Words like left, gives and empty mean take away.376 - 94
- Work out the answer. Use column subtraction, and exchange if needed.376 - 94 = 282
- Write the answer. This is the number left.282
Check. Check: 282 + 94 = 376.
Watch out. Words like left, gone and gives away mean take away.
Method. Subtract the ones first. If the top digit is too small, exchange from the next column, then subtract.
- Write the numbers in columns. Keep the ones under the ones and the tens under the tens.408 over 222
- Exchange 1 hundred for 10 tens. The tens on top are fewer than the tens below (2 tens), so we need more tens.4 hundreds become 3 hundreds, and 0 tens become 10 tens
- Subtract the ones. 8 - 2 = 6.8 - 2 = 6
- Subtract the tens. 10 - 2 = 8.10 - 2 = 8
- Subtract the hundreds. 3 - 2 = 1.3 - 2 = 1
- Write the answer. Read the columns from left to right.186
Check. Check: 186 + 222 = 408.
Watch out. When a column is too small, exchange one from the column to its left. Ten ones make one ten, ten tens make one hundred.
Method. Add the take away back to the answer. It should give the number we started with.
- Start with the answer, 186. We check by adding back.186
- Add 222. Adding undoes the take away.186 + 222 = 408
- Write the answer. We are back at the start.408
Check. 408 - 222 = 186, so the check works.
Watch out. If the check gives the wrong number, look again at the exchanges.
Method. Subtract the ones first. If the top digit is too small, exchange from the next column, then subtract.
- Write the numbers in columns. Keep the ones under the ones and the tens under the tens.106 over 50
- Exchange 1 hundred for 10 tens. The tens on top are fewer than the tens below (5 tens), so we need more tens.1 hundreds become 0 hundreds, and 0 tens become 10 tens
- Subtract the ones. 6 - 0 = 6.6 - 0 = 6
- Subtract the tens. 10 - 5 = 5.10 - 5 = 5
- Subtract the hundreds. 0 - 0 = 0.0 - 0 = 0
- Write the answer. Read the columns from left to right.56
Check. Check: 56 + 50 = 106.
Watch out. When a column is too small, exchange one from the column to its left. Ten ones make one ten, ten tens make one hundred.
Method. Add the take away back to the answer. It should give the number we started with.
- Start with the answer, 56. We check by adding back.56
- Add 50. Adding undoes the take away.56 + 50 = 106
- Write the answer. We are back at the start.106
Check. 106 - 50 = 56, so the check works.
Watch out. If the check gives the wrong number, look again at the exchanges.
Method. Subtract the ones first. If the top digit is too small, exchange from the next column, then subtract.
- Write the numbers in columns. Keep the ones under the ones and the tens under the tens.360 over 352
- Exchange 1 ten for 10 ones. The ones on top (0) are fewer than the ones below (2), so we need more ones.6 tens become 5 tens, and the ones go from 0 to 10
- Subtract the ones. 10 - 2 = 8.10 - 2 = 8
- Subtract the tens. 5 - 5 = 0.5 - 5 = 0
- Subtract the hundreds. 3 - 3 = 0.3 - 3 = 0
- Write the answer. Read the columns from left to right.8
Check. Check: 8 + 352 = 360.
Watch out. Exchange a ten for ten ones when the ones on top are too small. Then take away.
Method. Add the take away back to the answer. It should give the number we started with.
- Start with the answer, 8. We check by adding back.8
- Add 352. Adding undoes the take away.8 + 352 = 360
- Write the answer. We are back at the start.360
Check. 360 - 352 = 8, so the check works.
Watch out. If the check gives the wrong number, look again at the exchanges.
Method. Subtract the ones first. If the top digit is too small, exchange from the next column, then subtract.
- Write the numbers in columns. Keep the ones under the ones and the tens under the tens.504 over 311
- Exchange 1 hundred for 10 tens. The tens on top are fewer than the tens below (1 tens), so we need more tens.5 hundreds become 4 hundreds, and 0 tens become 10 tens
- Subtract the ones. 4 - 1 = 3.4 - 1 = 3
- Subtract the tens. 10 - 1 = 9.10 - 1 = 9
- Subtract the hundreds. 4 - 3 = 1.4 - 3 = 1
- Write the answer. Read the columns from left to right.193
Check. Check: 193 + 311 = 504.
Watch out. When a column is too small, exchange one from the column to its left. Ten ones make one ten, ten tens make one hundred.
Method. Add the take away back to the answer. It should give the number we started with.
- Start with the answer, 193. We check by adding back.193
- Add 311. Adding undoes the take away.193 + 311 = 504
- Write the answer. We are back at the start.504
Check. 504 - 311 = 193, so the check works.
Watch out. If the check gives the wrong number, look again at the exchanges.