Step-by-step Maths Level 5: Missing numbers and two-step problems
Part of the Step-by-step Maths Level 5 adding and subtracting whole numbers to a million chapter. Chapter overview · whole chapter on one page
Missing numbers and two-step problems
To find a missing number in a sum, subtract the known number from the total. To find a missing number in a difference, add.
In a two-step problem, work out the first step, then use the answer to work out the second step.
Key ideas
- Subtract to find a missing addend.
- Add to find a missing number in a difference.
- Do one step at a time, and check the answer fits the story.
Method. Use the inverse operation to find the missing number.
- Think about the total. The missing number is what is left when we take the known number away.300,000 - 248,000
- Subtract to find the missing number. Use the column method.300,000 - 248,000 = 52,000
- Check by adding. The missing number and the known number must make the total.248,000 + 52,000 = 300,000
- Write the missing number. This is the number in the box.52,000
Check. Check: put 52,000 into the sum and it works.
Watch out. To find a missing number in a sum, subtract. To find it in a difference, add.
Method. Work out the answer in the order the story happens, one step at a time.
- Work out the people left after some moved away. Take away the people who moved away.384,500 - 17,250 = 367,250
- Add the people who moved in. Add the new people to the number left.367,250 + 9,800 = 377,050
- Write the answer. Check the answer makes sense in the story.377,050
Check. Check: the answer should fit the story; the numbers left are less than the start unless people or things came in.
Watch out. Read the whole problem first. Decide the operation for each step before you calculate.
Method. Work out the answer in the order the story happens, one step at a time.
- Find the total picked. Add the two months together.412,000 + 287,500 = 699,500
- Take away the apples sold. Subtract the apples that were sold.699,500 - 150,000 = 549,500
- Write the answer. Check the answer makes sense in the story.549,500
Check. Check: the answer should fit the story; the numbers left are less than the start unless people or things came in.
Watch out. Read the whole problem first. Decide the operation for each step before you calculate.
Watch out
Watch out. In a two-step problem, the second step uses the answer of the first step, not the original number.
Exam tip
Grown-up tip. Ask the child to say the first step, and what it tells us, before they write any numbers.
Exercise 2E Practice: missing numbers and problems
Non-calculatorMethod. Work out the answer in the order the story happens, one step at a time.
- Find the total picked. Add the two months together.194,973 + 222,088 = 417,061
- Take away the apples sold. Subtract the apples that were sold.417,061 - 154,665 = 262,396
- Write the answer. Check the answer makes sense in the story.262,396
Check. Check: the answer should fit the story; the numbers left are less than the start unless people or things came in.
Watch out. Read the whole problem first. Decide the operation for each step before you calculate.
Method. Use the inverse operation to find the missing number.
- Think about the total. The missing number is what is left when we take the known number away.802,502 - 384,343
- Subtract to find the missing number. Use the column method.802,502 - 384,343 = 418,159
- Check by adding. The missing number and the known number must make the total.384,343 + 418,159 = 802,502
- Write the missing number. This is the number in the box.418,159
Check. Check: put 418,159 into the sum and it works.
Watch out. To find a missing number in a sum, subtract. To find it in a difference, add.
Method. Use the inverse operation to find the missing number.
- Think about the total. The missing number is what is left when we take the known number away.495,682 - 257,682
- Subtract to find the missing number. Use the column method.495,682 - 257,682 = 238,000
- Check by adding. The missing number and the known number must make the total.257,682 + 238,000 = 495,682
- Write the missing number. This is the number in the box.238,000
Check. Check: put 238,000 into the sum and it works.
Watch out. To find a missing number in a sum, subtract. To find it in a difference, add.
Method. Use the inverse operation to find the missing number.
- Add the number taken away to the answer. Adding undoes subtracting.83,088 + 37,426
- Work out the sum. Use the column method.83,088 + 37,426 = 120,514
- Check by subtracting. The answer must go back to the missing number.120,514 - 37,426 = 83,088
- Write the missing number. This is the number in the box.120,514
Check. Check: put 120,514 into the sum and it works.
Watch out. To find a missing number in a sum, subtract. To find it in a difference, add.
Method. Use the inverse operation to find the missing number.
- Think about the total. The missing number is what is left when we take the known number away.217,543 - 11,097
- Subtract to find the missing number. Use the column method.217,543 - 11,097 = 206,446
- Check by adding. The missing number and the known number must make the total.11,097 + 206,446 = 217,543
- Write the missing number. This is the number in the box.206,446
Check. Check: put 206,446 into the sum and it works.
Watch out. To find a missing number in a sum, subtract. To find it in a difference, add.
Method. Use the inverse operation to find the missing number.
- Think about the total. The missing number is what is left when we take the known number away.638,511 - 175,694
- Subtract to find the missing number. Use the column method.638,511 - 175,694 = 462,817
- Check by adding. The missing number and the known number must make the total.175,694 + 462,817 = 638,511
- Write the missing number. This is the number in the box.462,817
Check. Check: put 462,817 into the sum and it works.
Watch out. To find a missing number in a sum, subtract. To find it in a difference, add.
Method. Use the inverse operation to find the missing number.
- Think about the total. The missing number is what is left when we take the known number away.504,279 - 55,917
- Subtract to find the missing number. Use the column method.504,279 - 55,917 = 448,362
- Check by adding. The missing number and the known number must make the total.55,917 + 448,362 = 504,279
- Write the missing number. This is the number in the box.448,362
Check. Check: put 448,362 into the sum and it works.
Watch out. To find a missing number in a sum, subtract. To find it in a difference, add.
Method. Use the inverse operation to find the missing number.
- Add the number taken away to the answer. Adding undoes subtracting.249,478 + 110,200
- Work out the sum. Use the column method.249,478 + 110,200 = 359,678
- Check by subtracting. The answer must go back to the missing number.359,678 - 110,200 = 249,478
- Write the missing number. This is the number in the box.359,678
Check. Check: put 359,678 into the sum and it works.
Watch out. To find a missing number in a sum, subtract. To find it in a difference, add.
Method. Use the inverse operation to find the missing number.
- Think about the total. The missing number is what is left when we take the known number away.508,306 - 102,018
- Subtract to find the missing number. Use the column method.508,306 - 102,018 = 406,288
- Check by adding. The missing number and the known number must make the total.102,018 + 406,288 = 508,306
- Write the missing number. This is the number in the box.406,288
Check. Check: put 406,288 into the sum and it works.
Watch out. To find a missing number in a sum, subtract. To find it in a difference, add.
Method. Use the inverse operation to find the missing number.
- Think about the total. The missing number is what is left when we take the known number away.778,095 - 427,966
- Subtract to find the missing number. Use the column method.778,095 - 427,966 = 350,129
- Check by adding. The missing number and the known number must make the total.427,966 + 350,129 = 778,095
- Write the missing number. This is the number in the box.350,129
Check. Check: put 350,129 into the sum and it works.
Watch out. To find a missing number in a sum, subtract. To find it in a difference, add.
Method. Use the inverse operation to find the missing number.
- Add the number taken away to the answer. Adding undoes subtracting.340,542 + 281,988
- Work out the sum. Use the column method.340,542 + 281,988 = 622,530
- Check by subtracting. The answer must go back to the missing number.622,530 - 281,988 = 340,542
- Write the missing number. This is the number in the box.622,530
Check. Check: put 622,530 into the sum and it works.
Watch out. To find a missing number in a sum, subtract. To find it in a difference, add.
Method. Use the inverse operation to find the missing number.
- Add the number taken away to the answer. Adding undoes subtracting.346,409 + 78,701
- Work out the sum. Use the column method.346,409 + 78,701 = 425,110
- Check by subtracting. The answer must go back to the missing number.425,110 - 78,701 = 346,409
- Write the missing number. This is the number in the box.425,110
Check. Check: put 425,110 into the sum and it works.
Watch out. To find a missing number in a sum, subtract. To find it in a difference, add.
Method. Use the inverse operation to find the missing number.
- Think about the total. The missing number is what is left when we take the known number away.748,123 - 255,684
- Subtract to find the missing number. Use the column method.748,123 - 255,684 = 492,439
- Check by adding. The missing number and the known number must make the total.255,684 + 492,439 = 748,123
- Write the missing number. This is the number in the box.492,439
Check. Check: put 492,439 into the sum and it works.
Watch out. To find a missing number in a sum, subtract. To find it in a difference, add.
Method. Work out the answer in the order the story happens, one step at a time.
- Work out the people left after some moved away. Take away the people who moved away.499,278 - 193,221 = 306,057
- Add the people who moved in. Add the new people to the number left.306,057 + 81,406 = 387,463
- Write the answer. Check the answer makes sense in the story.387,463
Check. Check: the answer should fit the story; the numbers left are less than the start unless people or things came in.
Watch out. Read the whole problem first. Decide the operation for each step before you calculate.
Method. Use the inverse operation to find the missing number.
- Add the number taken away to the answer. Adding undoes subtracting.476,717 + 45,129
- Work out the sum. Use the column method.476,717 + 45,129 = 521,846
- Check by subtracting. The answer must go back to the missing number.521,846 - 45,129 = 476,717
- Write the missing number. This is the number in the box.521,846
Check. Check: put 521,846 into the sum and it works.
Watch out. To find a missing number in a sum, subtract. To find it in a difference, add.
Method. Use the inverse operation to find the missing number.
- Think about the total. The missing number is what is left when we take the known number away.486,234 - 141,505
- Subtract to find the missing number. Use the column method.486,234 - 141,505 = 344,729
- Check by adding. The missing number and the known number must make the total.141,505 + 344,729 = 486,234
- Write the missing number. This is the number in the box.344,729
Check. Check: put 344,729 into the sum and it works.
Watch out. To find a missing number in a sum, subtract. To find it in a difference, add.