B. Number · Operations: Adding, Subtracting and Equal GroupsEstimating Sums and Differences
B2.3 A1About 30 minutes
Learning goals- I can find the closest ten to a number.
- I can estimate a sum or difference using friendly numbers.
- I can tell if an answer makes sense.
- I can say whether an answer will be more or less than a number without solving it exactly.
Words to know
estimate
A smart guess that is close to the exact answer. We say "about".
exact
The real, perfect answer.
closest ten
The ten that a number is nearest to on a number line. 28 is closest to 30.
reasonable
Makes sense. A reasonable answer is close to your estimate.
about
Close to, but maybe not exactly. "About 30" means near 30.
Let's start with a question
You are going to a family picnic. Grandma asks, "About how many people are coming?" You do not need the exact number. You can say "about 30".
An estimate is a smart guess that is close to the real answer. We estimate all the time: about how long until lunch, about how many crackers are in the bag, about how far to the park.
Why estimate in math?
- Sometimes close is good enough.
- An estimate helps you check if your exact answer makes sense. If you estimate about 40 and get 85, something went wrong!
Find the closest ten
Tens like 10, 20, 30, 40 and 50 are friendly numbers. To estimate, we often change a number to its closest ten.
Look at 28 on the number line. It is between 20 and 30. It is only 2 away from 30, but 8 away from 20. So 28 is closest to 30.
A quick way to find the closest ten
Look at the ones digit.
- Ones digit 1, 2, 3 or 4: go back to the ten. 34 is about 30.
- Ones digit 6, 7, 8 or 9: go up to the next ten. 36 is about 40.
- Ones digit 5: it is right in the middle! 35 is the same distance from 30 and 40. Pick either one and say why. Many people choose to go up (40).
Worked exampleExample 1: Estimate a sum
About how much is 19 + 22?
- 19 is closest to 20.
- 22 is closest to 20.
- 20 + 20 = 40.
- The exact answer is 19 + 22 = 41. 41 is very close to 40!
Worked exampleExample 2: Estimate a difference
About how much is 48 − 21?
- 48 is closest to 50.
- 21 is closest to 20.
- 50 − 20 = 30.
- The exact answer is 48 − 21 = 27, which is close to 30.
More or less?
Sometimes you just need to know if an answer is more or less than a number.
Is 21 + 12 more or less than 30?
21 is a bit more than 20. 12 is a bit more than 10. 20 + 10 = 30. Both numbers are bigger than the friendly numbers, so the sum must be more than 30. (Exactly: 33.)
Worked exampleExample 3: Will I have enough?
Jayden wants to buy a book for $17 and a puzzle for $14. He has $40. Does he have enough money?
- Estimate: 17 is about 20. 14 is less than 20.
- 20 + 20 = 40. Both prices are less than 20, so the total must be less than $40.
- Exact total: 17 + 14 = 31.
Yes, he has enough. The total is $31, which is less than $40.
Worked exampleExample 4: Does the answer make sense?
Pria says 26 + 13 = 59. Use an estimate to check.
- 26 is about 30. 13 is about 10.
- 30 + 10 = 40. So the answer should be about 40.
- 59 is much too big! It does not make sense.
- Exact: 26 + 10 = 36, then 36 + 3 = 39.
Pria's answer is not reasonable. 26 + 13 = 39, which is close to the estimate of 40.
| Question | Estimate | Exact | Close? |
|---|
| 21 + 18 | 20 + 20 = 40 | 39 | Yes |
| 32 + 11 | 30 + 10 = 40 | 43 | Yes |
| 47 − 19 | 50 − 20 = 30 | 28 | Yes |
| 39 − 12 | 40 − 10 = 30 | 27 | Yes |
Estimate first!
A great habit: estimate before you solve. Then compare your exact answer to your estimate. If they are far apart, check your work. This is how mathematicians catch their own mistakes.
Just for funGrandma: "About how many people are coming to the picnic?" You: "About 40." Grandma: "And about how many cookies will they eat?" You: "About... all of them."
Hands-on activityGrocery store estimates
You need: a flyer from a grocery store, or 6 small items from the kitchen with price stickers you make (whole dollars from $1 to $25).
- Pick two items. Write their prices, like $12 and $19.
- Estimate the total using closest tens: 10 + 20 = about $30.
- Now find the exact total (12 + 19 = $31). Use counters or a number line if you need to.
- Was your estimate close?
- Play "Under $50": choose items, and estimate if the total is under $50 before you add.
Math talk: "How did your estimate help you check your answer?"
Your turn
1What is the closest ten to 37?
40. 37 is 3 away from 40 and 7 away from 30.
2What is the closest ten to 12?
10. 12 is only 2 away from 10.
About 50. 21 is about 20, 29 is about 30, and 20 + 30 = 50. (Exact: 50.)
About 30. 38 is about 40, 9 is about 10, and 40 − 10 = 30. (Exact: 29.)
5Is 12 + 13 more or less than 30?
Less. Both numbers are close to 10, and 10 + 10 = 20. Even 15 + 15 would only be 30. (Exact: 25.)
6Sam says 31 + 18 = 29. Does that make sense?
No. 31 alone is already more than 29! Adding more should give a bigger number. Estimate: 30 + 20 = 50. (Exact: 49.)
More practice: warm-up
1What is the closest ten to 19?
2What is the closest ten to 41?
About 40. 10 + 30 = 40. (Exact: 38.)
4Which is an estimate: "about 20" or "exactly 19"?
"About 20" is an estimate.
About 30. 50 − 20 = 30. (Exact: 29.)
More practice: on your own
1Estimate 23 + 18. Then find the exact answer.
Estimate: 20 + 20 = 40. Exact: 23 + 18 = 41. 23 + 10 = 33, then 33 + 8 = 41.
2Estimate 42 − 17. Then find the exact answer.
Estimate: 40 − 20 = 20. Exact: 42 − 17 = 25. 42 − 10 = 32, then 32 − 7 = 25.
3Will 19 + 19 be more or less than 40? Explain.
Less. 20 + 20 = 40, and each 19 is 1 less than 20. So 19 + 19 = 38, which is less than 40.
4A class collected 27 cans on Monday and 21 cans on Tuesday for the food bank. About how many cans is that?
About 50 cans. 27 is about 30 and 21 is about 20. 30 + 20 = 50. (Exact: 48.)
5Lucas says 44 − 21 = 13. Use an estimate to check.
Estimate: 40 − 20 = 20. 13 is far from 20, so check again. Exact: 44 − 20 = 24, then 24 − 1 = 23. Lucas was wrong.
Challenge
1You have $30. Can you buy a toque for $16 and mitts for $13? Explain without finding the exact total first.
Yes. 16 + 14 would be 30 (16 + 4 = 20, plus 10). 13 is less than 14, so the total is less than $30. Exact: 16 + 13 = $29.
2Write an addition question where both numbers are between 10 and 30 and the estimate is about 40.
Many answers. Example: 21 + 19 (20 + 20 = 40; exact 40) or 18 + 22 (exact 40) or 29 + 12 (30 + 10 = 40; exact 41).
3The number 35 is right in the middle of 30 and 40. Ava estimates 35 + 14 as 40 + 10 = 50. Ben estimates it as 30 + 10 = 40. The exact answer is 49. Whose estimate is closer?
Ava's. 49 is only 1 away from 50, but 9 away from 40. Both made fair choices for 35, but Ava's estimate is closer this time.
Quiz
1. What is the closest ten to 26?
2. Which is the best estimate for 31 + 18?
3. Which is the best estimate for 39 − 21?
4. Is 14 + 12 more or less than 40?
5. Mo says 22 + 27 = 89. Why does this not make sense?
6. Which sentence uses an estimate?
Big idea: Estimation is part of B2.3 (mental math, including estimation, with sums to 50). The goal is a quick, sensible answer and the habit of asking "Does my answer make sense?" This connects to the mathematical processes in strand A (reasoning, reflecting).
Common mistakes:
- Thinking an estimate must be exact. Reassure your child: any sensible estimate is good. If they work out the exact answer first and call it an estimate, ask them to use tens instead.
- Choosing the wrong ten (28 is about 20). Draw a short number line from 20 to 30 and ask which end 28 is closer to.
- Numbers ending in 5. Either ten is fine if the child explains. Rounding rules are not required in Grade 2.
- Not using the estimate to check. Make "estimate, solve, compare" a routine.
How to help: Estimate during shopping ("Is it more or less than $20?"), cooking and car trips. Ask "About how many?" before counting.