This strategy is used when regrouping is required. One of the addends is broken up into its expanded form and added in parts to the other addend.
For example:
57 + 38
can be calculated this way:
57 + 330 = 87
87 + 8 = 95
This strategy involves adding the frontend digits  the hundreds, then the tens and then the ones.
For example:
124 + 235
100 + 200 = 300
20 + 30 = 50
4 + 5 = 9
300 + 50 + 9 = 359
This method involves adding from the left and then grouping the numbers in order to adjust the estimate.
For example:
2667 + 5239
2000 + 5000 = 7000
600 + 200 = 800
No, make that 900
As 39 + 67 is about 100
7000 + 900 = 7900
Compatible numbers are number pairs that go together to make “friendly” numbers. That is, numbers that are easy to work with.
For example:
25 + 78
Easier:
25 + 75 + 3 = 103
Knowledge of the compatible numbers that are used for mental calculations is used for estimation.
For example:
76 + 45 + 19 + 26 + 52
Estimating these numbers:
76 + 26 is about 100
45 + 52 is about 100
Add 19
Estimate answer, about 219
A variation of the compatible number strategy, this method involves taking one or more from one addend and adding it to the other. For example, 68 + 57 becomes 70 + 55 (add 2 to 68 and take 2 from 57).
68 + 57
Becomes
70 + 55 = 125
[Add 68 + 2 and 57  2]
Clustering involves grouping addends and determining the average.
For example:
when estimating 53 + 47 + 48 + 58 +52, notice that the addends cluster around 50. The estimate would be 250 (5 x 50)
When estimating
53 + 47 + 57 + 52 + 48
The addends cluster around 50
5 x 50 = 250
In the early grades, students learn the number of pairs that total ten – 1 and 9, 2 and 8, 3 and 7, and so on. These can be extended to such combinations as 10 and 90, 300 and 700, etc.
1 and 9
2 and 8
3 and 7
4 and 6
5 and 5
6 and 4
7 and 3
8 and 2
9 and 1
Using the compensation strategy, you substitute a compatible number for one of the numbers so that you can more easily compute mentally. For example, in doing the calculation 47 + 29 one might think (47 + 30) – 1.
47 + 29
[47 + 30]  1 = 76
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