Step-by-step Maths Level 4: Estimating, checking and missing numbers
Part of the Step-by-step Maths Level 4 column addition and subtraction chapter. Chapter overview · whole chapter on one page
Estimating, checking and missing numbers
Estimate first: round each number to the nearest thousand, then add or subtract. Your exact answer should be close to the estimate.
Check an addition by subtracting. Check a subtraction by adding. For a missing number, use the inverse operation.
Key ideas
- Estimate by rounding to the nearest 1000.
- Check with the inverse: subtract to check an addition.
- For a missing number, do the opposite operation.
Method. Round each number, then add the rounded numbers. This gives an estimate close to the answer.
- Round 4826 to the nearest 1000. Look at the hundreds, tens and ones: 826 is more than 500.4826 rounds to 5000
- Round 2375 to the nearest 1000. Look at 375: it is less than 500.2375 rounds to 2000
- Add the rounded numbers. This gives the estimate.5000 + 2000 = 7000
- Write the estimate. The exact total, 7201, is close to this.7000
Check. Check: the exact answer 4826 + 2375 = 7201 is close to 7000.
Watch out. An estimate should be about the size of the exact answer.
Method. Use the inverse operation to find the missing number.
- Find what must be added. The gap is the difference between the total and the known number.5000 - 3456 = 1544
- Check the sum. Put the missing number back in the sum.3456 + 1544 = 5000
- Write the missing number. It fills the gap.1544
Check. Check: 3456 + 1544 = 5000.
Watch out. Subtract the known number from the total to find the gap.
Method. Use the inverse operation to find the missing number.
- Add the number that was taken away. Adding undoes the take away.2000 + 2378 = 4378
- Check the subtraction. Taking away the known number should give the answer.4378 - 2378 = 2000
- Write the missing number. It fills the gap.4378
Check. Check: 4378 - 2378 = 2000.
Watch out. Adding undoes subtracting.
Watch out
Watch out. The missing number in 3456 + ___ = 5000 is 1544, not 8456. Find the gap by subtracting.
Exam tip
Grown-up tip. Ask: “Is your answer close to the estimate? Does the check work?”
Exercise 3E Practice: estimating, checking and missing numbers
Non-calculatorMethod. Use the inverse operation to find the missing number.
- Add the number that was taken away. Adding undoes the take away.6139 + 1974 = 8113
- Write the missing number. Check it: taking away gives the answer.8113
Check. Check: 8113 - 1974 = 6139.
Watch out. Addition and subtraction undo each other. Use the operation that undoes the one in the question.
Method. Use the inverse operation to find the missing number.
- Add the number that was taken away. Adding undoes the take away.4327 + 4874 = 9201
- Write the missing number. Check it: taking away gives the answer.9201
Check. Check: 9201 - 4874 = 4327.
Watch out. Addition and subtraction undo each other. Use the operation that undoes the one in the question.
Method. Round each number, then add the rounded numbers. This gives an estimate close to the answer.
- Round 1698 to the nearest 1000. Look at the hundreds, tens and ones.1698 rounds to 2000
- Round 5815 to the nearest 1000. Look at the hundreds, tens and ones.5815 rounds to 6000
- Add the rounded numbers. This gives the estimate.2000 + 6000 = 8000
- Write the estimate. The exact total is close to this.8000
Check. Check: the exact answer 7513 is close to 8000.
Watch out. An estimate tells you the answer should be about this size. Check the exact answer is close.
Method. Subtract one number from the total. If the check is right, you get the other number.
- Use the inverse. Subtracting the second number should give back the first.9274 - 3776
- Work out the difference. If the sum is right, this matches the first number.9274 - 3776 = 5498
- Write the check. The check is correct because it gives the first number.9274 - 3776 = 5498
Check. Check: 5498 + 3776 = 9274, so the subtraction works both ways.
Watch out. A subtraction can check an addition. Use the inverse operation to check your answer.
Method. Use the inverse operation to find the missing number.
- Find what must be added. The missing number is the difference between the total and the known number.8775 - 4634 = 4141
- Write the missing number. Check it fills the gap.4141
Check. Check: 4634 + 4141 = 8775.
Watch out. Addition and subtraction undo each other. Use the operation that undoes the one in the question.
Method. Round each number, then add the rounded numbers. This gives an estimate close to the answer.
- Round 3728 to the nearest 1000. Look at the hundreds, tens and ones.3728 rounds to 4000
- Round 4385 to the nearest 1000. Look at the hundreds, tens and ones.4385 rounds to 4000
- Add the rounded numbers. This gives the estimate.4000 + 4000 = 8000
- Write the estimate. The exact total is close to this.8000
Check. Check: the exact answer 8113 is close to 8000.
Watch out. An estimate tells you the answer should be about this size. Check the exact answer is close.
Method. Round each number, then add the rounded numbers. This gives an estimate close to the answer.
- Round 8529 to the nearest 1000. Look at the hundreds, tens and ones.8529 rounds to 9000
- Round 1397 to the nearest 1000. Look at the hundreds, tens and ones.1397 rounds to 1000
- Add the rounded numbers. This gives the estimate.9000 + 1000 = 10000
- Write the estimate. The exact total is close to this.10000
Check. Check: the exact answer 9926 is close to 10000.
Watch out. An estimate tells you the answer should be about this size. Check the exact answer is close.
Method. Subtract one number from the total. If the check is right, you get the other number.
- Use the inverse. Subtracting the second number should give back the first.6065 - 2013
- Work out the difference. If the sum is right, this matches the first number.6065 - 2013 = 4052
- Write the check. The check is correct because it gives the first number.6065 - 2013 = 4052
Check. Check: 4052 + 2013 = 6065, so the subtraction works both ways.
Watch out. A subtraction can check an addition. Use the inverse operation to check your answer.
Method. Use the inverse operation to find the missing number.
- Find the missing number. Subtract the known number from the total.8025 - 2161 = 5864
- Write the missing number. Check it fills the gap.5864
Check. Check: 5864 + 2161 = 8025.
Watch out. Addition and subtraction undo each other. Use the operation that undoes the one in the question.
Method. Round each number, then add the rounded numbers. This gives an estimate close to the answer.
- Round 7716 to the nearest 1000. Look at the hundreds, tens and ones.7716 rounds to 8000
- Round 1250 to the nearest 1000. Look at the hundreds, tens and ones.1250 rounds to 1000
- Add the rounded numbers. This gives the estimate.8000 + 1000 = 9000
- Write the estimate. The exact total is close to this.9000
Check. Check: the exact answer 8966 is close to 9000.
Watch out. An estimate tells you the answer should be about this size. Check the exact answer is close.
Method. Round each number, then add the rounded numbers. This gives an estimate close to the answer.
- Round 7520 to the nearest 1000. Look at the hundreds, tens and ones.7520 rounds to 8000
- Round 1861 to the nearest 1000. Look at the hundreds, tens and ones.1861 rounds to 2000
- Add the rounded numbers. This gives the estimate.8000 + 2000 = 10000
- Write the estimate. The exact total is close to this.10000
Check. Check: the exact answer 9381 is close to 10000.
Watch out. An estimate tells you the answer should be about this size. Check the exact answer is close.
Method. Use the inverse operation to find the missing number.
- Add the number that was taken away. Adding undoes the take away.2214 + 6531 = 8745
- Write the missing number. Check it: taking away gives the answer.8745
Check. Check: 8745 - 6531 = 2214.
Watch out. Addition and subtraction undo each other. Use the operation that undoes the one in the question.
Method. Round each number, then add the rounded numbers. This gives an estimate close to the answer.
- Round 6919 to the nearest 1000. Look at the hundreds, tens and ones.6919 rounds to 7000
- Round 1219 to the nearest 1000. Look at the hundreds, tens and ones.1219 rounds to 1000
- Add the rounded numbers. This gives the estimate.7000 + 1000 = 8000
- Write the estimate. The exact total is close to this.8000
Check. Check: the exact answer 8138 is close to 8000.
Watch out. An estimate tells you the answer should be about this size. Check the exact answer is close.
Method. Round each number, then add the rounded numbers. This gives an estimate close to the answer.
- Round 8848 to the nearest 1000. Look at the hundreds, tens and ones.8848 rounds to 9000
- Round 1029 to the nearest 1000. Look at the hundreds, tens and ones.1029 rounds to 1000
- Add the rounded numbers. This gives the estimate.9000 + 1000 = 10000
- Write the estimate. The exact total is close to this.10000
Check. Check: the exact answer 9877 is close to 10000.
Watch out. An estimate tells you the answer should be about this size. Check the exact answer is close.
Method. Round each number, then add the rounded numbers. This gives an estimate close to the answer.
- Round 2814 to the nearest 1000. Look at the hundreds, tens and ones.2814 rounds to 3000
- Round 2870 to the nearest 1000. Look at the hundreds, tens and ones.2870 rounds to 3000
- Add the rounded numbers. This gives the estimate.3000 + 3000 = 6000
- Write the estimate. The exact total is close to this.6000
Check. Check: the exact answer 5684 is close to 6000.
Watch out. An estimate tells you the answer should be about this size. Check the exact answer is close.
Method. Use the inverse operation to find the missing number.
- Find the missing number. Subtract the known number from the total.9615 - 3915 = 5700
- Write the missing number. Check it fills the gap.5700
Check. Check: 5700 + 3915 = 9615.
Watch out. Addition and subtraction undo each other. Use the operation that undoes the one in the question.