Estimating Sums and Differences Worksheets

Estimating with rounding means finding a quick, close answer to a sum or difference by rounding the numbers first, such as 47 + 38 as 50 + 40. The three PDFs on this page have 2-digit sums, 2-digit differences and 3-digit problems, and every sheet has an answer key. They follow standards 3.OA.D.8 and 4.OA.A.3 of the Common Core standards for grade 3 operations and algebraic thinking, and the notes below show how to estimate, how far off an estimate can be, and how to use it to check an answer.

Why estimate?

An estimate is a quick, close answer. It is how we check that an exact answer makes sense: if 47 + 38 is about 90, an answer of 715 must be wrong. The Common Core standards ask children to judge whether answers are reasonable using estimation (3.OA.D.8 and 4.OA.A.3).

How these worksheets work

1. Round each number to the nearest ten or hundred.
2. Add or subtract the rounded numbers: that is the estimate.
3. Work out the exact answer.
4. Compare. A close estimate means the exact answer is probably right.

Rounding both numbers can push the estimate away from the exact answer, especially in subtraction. Talking about why 72 − 46 is estimated as 70 − 50 = 20 when the exact answer is 26 is a great discussion.

Estimating with rounding worksheets: what is in the set

There are 3 estimating with rounding worksheets on this page, and every one has an answer key except for any cut-out games. One sheet estimates sums, one estimates differences, and one uses 3-digit numbers rounded to the nearest 100.

Estimating sums worksheets: round, then add

The estimating sums worksheets use three steps: round each number, add the rounded numbers, and then compare with the exact sum. An estimate is a quick, close answer, and it is how people check that an exact answer makes sense. Wikipedia’s article on estimation describes how estimates are used in science and daily life. This table shows eight problems, four sums and four differences, with the estimate and the exact answer:

The estimate is always within 10 of the exact answer for 2-digit numbers, since each rounding changes a number by at most 5. A child who gets an answer far from the estimate has made a mistake in one of the two calculations, and should do both again.

Estimating differences worksheets: why subtraction is trickier

The estimating differences worksheets use the same steps, but subtraction needs more care. Rounding one number up and the other down can move the difference by up to 10. For 72 − 46, the estimate is 70 − 50 = 20, but the exact answer is 26, since 72 went down by 2 and 46 went up by 4. Talking about why the estimate is lower than the exact answer is a good discussion for a class. The diagram above shows the two side by side.

The same problem as an addition would round the other way: if the question was 72 + 46, the estimate would be 70 + 50 = 120, and the exact answer is 118. In a subtraction, the rounding of the second number works against the first. The subtraction worksheets pages have the exact subtraction that the estimate checks.

Estimation using rounding: how far off can an estimate be?

When children use estimation using rounding, they can ask how good the estimate is. For a sum of two 2-digit numbers, rounded to the nearest ten, the error is the sum of two rounding changes, each between −4 and +5. This table counts the 8,100 sums of two 2-digit numbers from 10 to 99 by the size and direction of the error:

Most estimates are close, and the biggest error is 10. About 55% of the estimates are too high, and 36% are too low. The estimates are a little more often high than low, because the halfway numbers round up. The diagram above shows the distribution.

Rounding to estimate: higher, lower or the same?

Rounding to estimate gives an answer that is higher than the exact sum when both numbers round up, and lower when both round down. When one rounds up and the other down, the two changes partly cancel. This table shows four sums:

Knowing this helps children to say whether an estimate is an overestimate or an underestimate, which is useful when they decide whether they have enough money or time. If both numbers round up and the estimate is still below what you can spend, there is enough.

Estimate and check worksheets: using the estimate to catch mistakes

The estimate and check worksheets ask children to estimate first, calculate second, and compare. The estimate catches big mistakes, such as writing two numbers side by side, but small ones can slip through, such as forgetting a carry. This table shows six wrong answers, and whether the estimate would catch each:

A forgotten carry or borrow changes the answer by exactly 10, which is as big as the biggest error of an estimate, so the estimate often misses it. For those mistakes, the check is the opposite operation. The 2-digit subtraction with regrouping page practices the borrowing, and the addition worksheets pages practice the carrying.

Estimating 3-digit numbers: rounding to the nearest 100

With 3-digit numbers, children round to the nearest hundred to estimate. The errors are bigger, as each rounding can change a number by up to 50. This table shows six problems:

The estimate is within 100 of the exact answer in each row. The rounding to the nearest 100 page has the rounding, and the rounding large numbers page extends it to bigger numbers. The standard 3.OA.D.8 asks children to assess the reasonableness of answers using estimation strategies including rounding.

Other ways to estimate

Rounding both numbers is not the only way to estimate. Children should also know a few others, which they can use to decide what is best for a problem. This table compares four:

The worksheets on this page use rounding, since that is the way that is easiest to teach and to check. The two-step word problems page uses estimation to check two-step problems.

Common mistakes with estimating with rounding

The most common mistake is to cut off the ones instead of rounding. This table shows five mistakes, what went wrong and the fix:

Estimating with rounding word problems

Estimates answer “about how many” questions. Ask children to round, calculate, and then say the answer with the word about:

Games and activities for estimating with rounding

Children learn estimating with rounding best when they play with it. These games use things that are found at home or in a classroom:

• Estimate first: estimate each answer before using a calculator, and see who is closest
• Over or under: say whether the estimate of a sum will be higher or lower than the exact answer
• Estimation race: give a problem and have children estimate in ten seconds
• Shopping estimate: estimate the total of three items from a catalog
• Catch the mistake: give a worked sum with a wrong answer, and ask children to catch it with an estimate
• Estimation bingo: a bingo card with estimates, and calling cards with problems

Extra support and extra challenge with estimating with rounding

For children who need more support: make sure that rounding to the nearest 10 is secure. Use a number line for each number, and write the rounded number beside it. Do the sums before the differences. Say the word “about” each time. Compare the estimate with the exact answer, and use the answer key to check both.

For children who need more challenge: ask for two numbers that give an estimate of 100 when rounded to the nearest ten, for a subtraction whose estimate is bigger than the exact answer, and for the biggest possible error in an estimate of a difference. Try to make up a problem where an estimate would not catch a mistake.

How to tell that a child is ready to move on from estimating with rounding

Before moving on from estimating with rounding, check that the child can do all four of these things:

1. The child rounds both numbers to the nearest 10 or 100.
2. The child adds or subtracts the rounded numbers.
3. The child compares the estimate with the exact answer.
4. The child says whether an answer is reasonable.

When all four are true, move on to the two-step word problems page, or the rounding large numbers page.

A 20-minute lesson on estimating with rounding

A short lesson is the best way to introduce estimating with rounding. This 20-minute plan can be used in a classroom, at a tutoring session or at home, and it uses the worksheets at the end:

Where estimating with rounding fits across the grades

No skill stands alone. This table shows what children learn before and after estimating with rounding, with the standard that goes with each step:

This page puts rounding to use. The whole sequence is on the rounding worksheets page.

Helping at home with estimating with rounding

Parents do not need to be experts to help with estimating with rounding. These suggestions work well, and each takes only a few minutes:

• Estimate the total at the store by rounding each price.
• Ask “about how many?” instead of “exactly how many?”.
• Compare the estimate with the real total on the receipt.
• Ask whether the estimate is higher or lower than the exact answer.
• Check the answers with the answer key, and ask the child to explain one.

How to check progress in estimating with rounding

A teacher or parent can check progress in estimating with rounding with the answer key and a few questions. This table shows three common situations, what they mean and what to do next:

A five-day plan for estimating with rounding

Most children need about a week of short sessions for estimating with rounding. This plan follows the order of the worksheets on this page:

When the plan for estimating with rounding is complete, move on to the two-step word problems page. The whole sequence is on the rounding worksheets page.