Step-by-step Maths Level 5: Estimating and checking
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
Estimating and checking
An estimate tells you roughly how big the answer should be. Round each number first, then calculate with the rounded numbers.
To check a sum, subtract one number from the total. To check a difference, add the number you took away back on.
Key ideas
- Round first, then calculate, to estimate.
- The exact answer should be close to the estimate.
- Check a sum by subtraction; check a difference by addition.
Method. Round each number first, then calculate with the rounded numbers.
- Round the first number. Look at the thousands digit: 5 or more rounds up.482,000 is about 480,000
- Round the second number. Use the same rule.310,000 is about 310,000
- Add the rounded numbers. This is the estimate.480,000 + 310,000 = 790,000
- Write the estimate. The exact answer should be close to this.790,000
Check. The exact answer is 792,000, which is close to 790,000.
Watch out. Estimate with the rounded numbers, then work out the exact answer with the column method.
Method. Check by using the inverse: subtract for a sum, or add back for a difference.
- Take one number away from the answer. If the sum is correct, taking one number away gives the other.700,001 - 582,463 = 117,538
- Compare with the other number. Is 117,538 the same as 117,538?Same
- Write Yes or No. Yes if the check works; No if it does not.Yes
Check. The correct answer is 700,001.
Watch out. A check that does not work means the answer is wrong. Find the mistake in the columns.
Method. Round each number first, then calculate with the rounded numbers.
- Round the first number. Look at the thousands digit: 5 or more rounds up.738,000 is about 740,000
- Round the second number. Use the same rule.205,000 is about 210,000
- Subtract the rounded numbers. This is the estimate.740,000 - 210,000 = 530,000
- Write the estimate. The exact answer should be close to this.530,000
Check. The exact answer is 533,000, which is close to 530,000.
Watch out. Estimate with the rounded numbers, then work out the exact answer with the column method.
Watch out
Watch out. An estimate is not the exact answer. Use the estimate to check that your answer is about the right size.
Exam tip
Grown-up tip. Ask the child: “Is the answer about the right size?” before they check it exactly.
Exercise 2D Practice: estimating and checking
Non-calculatorMethod. Check by using the inverse: subtract for a sum, or add back for a difference.
- Take one number away from the answer. If the sum is correct, taking one number away gives the other.688,072 - 569,853 = 118,219
- Compare with the other number. Is 118,219 the same as 118,219?Same
- Write Yes or No. Yes if the check works; No if it does not.Yes
Check. The correct answer is 688,072.
Watch out. A check that does not work means the answer is wrong. Find the mistake in the columns.
Method. Round each number first, then calculate with the rounded numbers.
- Round the first number. Look at the thousands digit: 5 or more rounds up.236,844 is about 240,000
- Round the second number. Use the same rule.314,998 is about 310,000
- Add the rounded numbers. This is the estimate.240,000 + 310,000 = 550,000
- Write the estimate. The exact answer should be close to this.550,000
Check. The exact answer is 551,842, which is close to 550,000.
Watch out. Estimate with the rounded numbers, then work out the exact answer with the column method.
Method. Check by using the inverse: subtract for a sum, or add back for a difference.
- Take one number away from the answer. If the sum is correct, taking one number away gives the other.994,651 - 854,966 = 139,685
- Compare with the other number. Is 139,685 the same as 139,685?Same
- Write Yes or No. Yes if the check works; No if it does not.Yes
Check. The correct answer is 994,651.
Watch out. A check that does not work means the answer is wrong. Find the mistake in the columns.
Method. Check by using the inverse: subtract for a sum, or add back for a difference.
- Take one number away from the answer. If the sum is correct, taking one number away gives the other.946,272 - 869,345 = 76,927
- Compare with the other number. Is 76,927 the same as 75,927?Not the same
- Write Yes or No. Yes if the check works; No if it does not.No
Check. The correct answer is 945,272.
Watch out. A check that does not work means the answer is wrong. Find the mistake in the columns.
Method. Round each number first, then calculate with the rounded numbers.
- Round the first number. Look at the thousands digit: 5 or more rounds up.448,428 is about 450,000
- Round the second number. Use the same rule.326,766 is about 330,000
- Add the rounded numbers. This is the estimate.450,000 + 330,000 = 780,000
- Write the estimate. The exact answer should be close to this.780,000
Check. The exact answer is 775,194, which is close to 780,000.
Watch out. Estimate with the rounded numbers, then work out the exact answer with the column method.
Method. Round each number first, then calculate with the rounded numbers.
- Round the first number. Look at the thousands digit: 5 or more rounds up.459,919 is about 460,000
- Round the second number. Use the same rule.25,866 is about 30,000
- Add the rounded numbers. This is the estimate.460,000 + 30,000 = 490,000
- Write the estimate. The exact answer should be close to this.490,000
Check. The exact answer is 485,785, which is close to 490,000.
Watch out. Estimate with the rounded numbers, then work out the exact answer with the column method.
Method. Check by using the inverse: subtract for a sum, or add back for a difference.
- Take one number away from the answer. If the sum is correct, taking one number away gives the other.304,704 - 228,141 = 76,563
- Compare with the other number. Is 76,563 the same as 76,573?Not the same
- Write Yes or No. Yes if the check works; No if it does not.No
Check. The correct answer is 304,714.
Watch out. A check that does not work means the answer is wrong. Find the mistake in the columns.
Method. Check by using the inverse: subtract for a sum, or add back for a difference.
- Take one number away from the answer. If the sum is correct, taking one number away gives the other.715,368 - 303,532 = 411,836
- Compare with the other number. Is 411,836 the same as 401,836?Not the same
- Write Yes or No. Yes if the check works; No if it does not.No
Check. The correct answer is 705,368.
Watch out. A check that does not work means the answer is wrong. Find the mistake in the columns.
Method. Check by using the inverse: subtract for a sum, or add back for a difference.
- Take one number away from the answer. If the sum is correct, taking one number away gives the other.930,992 - 834,723 = 96,269
- Compare with the other number. Is 96,269 the same as 106,269?Not the same
- Write Yes or No. Yes if the check works; No if it does not.No
Check. The correct answer is 940,992.
Watch out. A check that does not work means the answer is wrong. Find the mistake in the columns.
Method. Check by using the inverse: subtract for a sum, or add back for a difference.
- Take one number away from the answer. If the sum is correct, taking one number away gives the other.926,248 - 781,794 = 144,454
- Compare with the other number. Is 144,454 the same as 134,454?Not the same
- Write Yes or No. Yes if the check works; No if it does not.No
Check. The correct answer is 916,248.
Watch out. A check that does not work means the answer is wrong. Find the mistake in the columns.
Method. Check by using the inverse: subtract for a sum, or add back for a difference.
- Take one number away from the answer. If the sum is correct, taking one number away gives the other.869,153 - 266,137 = 603,016
- Compare with the other number. Is 603,016 the same as 603,016?Same
- Write Yes or No. Yes if the check works; No if it does not.Yes
Check. The correct answer is 869,153.
Watch out. A check that does not work means the answer is wrong. Find the mistake in the columns.
Method. Check by using the inverse: subtract for a sum, or add back for a difference.
- Take one number away from the answer. If the sum is correct, taking one number away gives the other.581,188 - 135,649 = 445,539
- Compare with the other number. Is 445,539 the same as 455,539?Not the same
- Write Yes or No. Yes if the check works; No if it does not.No
Check. The correct answer is 591,188.
Watch out. A check that does not work means the answer is wrong. Find the mistake in the columns.
Method. Check by using the inverse: subtract for a sum, or add back for a difference.
- Take one number away from the answer. If the sum is correct, taking one number away gives the other.867,377 - 345,902 = 521,475
- Compare with the other number. Is 521,475 the same as 521,475?Same
- Write Yes or No. Yes if the check works; No if it does not.Yes
Check. The correct answer is 867,377.
Watch out. A check that does not work means the answer is wrong. Find the mistake in the columns.
Method. Check by using the inverse: subtract for a sum, or add back for a difference.
- Take one number away from the answer. If the sum is correct, taking one number away gives the other.740,005 - 191,459 = 548,546
- Compare with the other number. Is 548,546 the same as 548,546?Same
- Write Yes or No. Yes if the check works; No if it does not.Yes
Check. The correct answer is 740,005.
Watch out. A check that does not work means the answer is wrong. Find the mistake in the columns.
Method. Round each number first, then calculate with the rounded numbers.
- Round the first number. Look at the thousands digit: 5 or more rounds up.392,244 is about 390,000
- Round the second number. Use the same rule.37,060 is about 40,000
- Subtract the rounded numbers. This is the estimate.390,000 - 40,000 = 350,000
- Write the estimate. The exact answer should be close to this.350,000
Check. The exact answer is 355,184, which is close to 350,000.
Watch out. Estimate with the rounded numbers, then work out the exact answer with the column method.
Method. Round each number first, then calculate with the rounded numbers.
- Round the first number. Look at the thousands digit: 5 or more rounds up.363,966 is about 360,000
- Round the second number. Use the same rule.191,116 is about 190,000
- Add the rounded numbers. This is the estimate.360,000 + 190,000 = 550,000
- Write the estimate. The exact answer should be close to this.550,000
Check. The exact answer is 555,082, which is close to 550,000.
Watch out. Estimate with the rounded numbers, then work out the exact answer with the column method.