SME
Grade 3 Math · Problem type
Estimate differences
Use this for “612 children, 287 at lunch. About how many are in class?”
Diagram
512 rounds to 510.
287 rounds to 290.
Estimate: 510 − 290 = 220.
First rounded: 510
Second rounded: 290
Estimate: 220
How far off the estimate is: 5
This is an example. Type your own values to start a new problem.
First number
example
Second number
example
First rounded
worked out (not typed)
Second rounded
worked out (not typed)
Estimate
worked out (not typed)
Difference
worked out (not typed)
How far off the estimate is
worked out (not typed)
Formulas
512 rounds to 510
First number rounds to first rounded
287 rounds to 290
Second number rounds to second rounded
510 − 290 = 220
First rounded − second rounded = estimate
512 − 287 = 225
First number − second number = difference
The estimate 220 is 5 away from the difference 225
Difference − estimate = how far off the estimate is (or the other way round)
Assumptions
•
Round each number to the nearest ten, then subtract the rounded numbers.
•
The estimate is close to the real difference. Use it to check the answer.
Step-by-step
WE KNOW
First number: 512
Second number: 287
FIND
first rounded, second rounded, estimate, difference, how far off the estimate is
Step 1 · Find first rounded
512 rounds to ?
First number rounds to first rounded
Round the first number to the nearer ten. 5 ones or more rounds up.
512 is between 510 and 520.
2 ones is less than 5: round down to 510.
First rounded = 510
Step 2 · Find second rounded
287 rounds to ?
Second number rounds to second rounded
Round the second number to the nearer ten. 5 ones or more rounds up.
287 is between 280 and 290.
7 ones is 5 or more: round up to 290.
Second rounded = 290
Step 3 · Find estimate
510 − 290 = ?
First rounded − second rounded = estimate
Take the second rounded away from the first rounded.
4
11
5
1
0
−
2
9
0
2
2
0
Estimate = 220
Step 4 · Find difference
512 − 287 = ?
First number − second number = difference
Take the second number away from the first number.
4
10
12
5
1
2
−
2
8
7
2
2
5
Difference = 225
Step 5 · Find how far off the estimate is
The estimate 220 is ? away from the difference 225
Difference − estimate = how far off the estimate is (or the other way round)
Take the smaller from the bigger. A small distance means the estimate is close.
How far off the estimate is = 225 − 220
Exact: 512 − 287 = 225
225 − 220 = 5
How far off the estimate is = 5
Check
Put the numbers back in. Both sides should match.
512 rounds to 510 ✓
287 rounds to 290 ✓
510 − 290 = 220 ✓
512 − 287 = 225 ✓
The estimate 220 is 5 away from the difference 225 ✓
Topic check
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