## Friday, October 11, 2013

### Assembling Arrays and Finding Factors #2

4th graders have been learning many strategies for solving multiplication problems. They are also learning ways to represent multiplication problems using models.

One of the models they have learned to use is called an ARRAY. An ARRAY is a model consisting of equal rows and columns.

The video below shows how students can use ARRAYS to help them find the FACTORS of a number. Please note: this is NOT an efficient strategy for finding FACTORS in a number as large as 36. I just had them do this task in groups to see if they could successfully use the strategy.

Here, students use different materials in class to Assemble Arrays and Find Factors of the number 16.

First, they make 1 row of the number they are working with.

1 row of 16 = 1 x 16
The FACTORS in this ARRAY are 1, 16.

These students used maps to assemble their ARRAYS.

Here, they made 2 rows of 8 = 2 x 8.
The FACTORS of this ARRAY are 2, 8.

The students below used other materials to show the next possible ARRAY: 4 rows of 4.

4 rows of 4 = 4 x 4.
The FACTORS of this ARRAY are 4, 4 (or just 4).

The first 2 photos above (and the ARRAYS in them) can be rotated to show different dimensions. Although the total is the same, the arrangement is different.

This shows 8 rows of 2 = 8 x 2
The FACTORS are still 8 and 2, but the arrangement is different.

This shows 16 rows of 1 = 16 x 1
The FACTORS are still 16 and 1, but the arrangement is different.

Based on the work the students did, they found that these combinations are used
in multiplication to make 16:
1 x 16
2 x 8
4 x 4
8 x 2
16 x 1

The FACTORS of 16 are: 1, 2, 4, 8, 16.