# Invented Strategies for

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```					                    Invented Strategies for Multiplication & Division

Students invented strategies are very similar to the traditional algorithm. The big
difference is how the students think about the numbers. They always begin with the large
or left-had numbers.

18 x 6

6 groups of 18 = 18 +18 + 18 + 18 + 18 + 18 = 108 using an array
OR
Repeated Addition Double 18 is 36, so 36 + 36 + 36 = 108

18

6
6 x 10                                    6x8

6 x 10 = 60      and     6 x 8 = 48
60 + 48 = 108

OR

Using Multiplication Clusters to solve multiplication problems
6 x 10 = 60     If a student needs a simpler problem     6 x 10 = 60
6 x 8 = 48      they may do this instead                    6 x 4 = 24
so, 6 x 18 = 60 + 48 which is 108                                   6 x 4 = 24
so, 6 x 18 = 60 + 24 + 24 which is 108
92 / 4

Sharing

453 / 6
Person 1        Person 2     Person 3      Person 4        Person 5     Person 6
50             50           50            50              50           50
10             10           10            10              10           10
10             10           10            10              10           10
5              5            5             5               5            5
1/2             1/2         1/2           1/2             1/2          1/2
Each person has 75 ½
So, 453 divided by 6 = 75 ½

Inverse Operation
156 / 4

I know that 4 x 25 = 100 (so 100/4 = 25)
4 x 10 = 40
4 x 4 = 16, and 40 + 16 =56 (so 56/4 = 14)

If I add the numbers (25 + 10 + 4 = 39) which I had originally multiplied by 4, then I
know that 156 / 4 = 39

```
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 views: 21 posted: 2/24/2012 language: English pages: 2
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