Question

1. the triangles below show 3 groups of four.

a. redraw the triangles as an array that shows 3 rows of four.

b. compare the drawing to your array. how are they the same? how are they different?

Explanation:

Part a

Step 1: Understand the total number of triangles

We have 3 groups of 4 triangles. So the total number of triangles is \(3\times4 = 12\).

Step 2: Draw the array

To draw an array with 3 rows of 4, we will draw 3 horizontal rows, and in each row, we will place 4 triangles. So the array will look like:

Row 1: \(\triangle\triangle\triangle\triangle\)

Row 2: \(\triangle\triangle\triangle\triangle\)

Row 3: \(\triangle\triangle\triangle\triangle\)

Part b

• Same: Both the original drawing (3 groups of 4) and the array (3 rows of 4) have a total of \(3\times4=12\) triangles. The total number of triangles is the same in both representations.
• Different: In the original drawing, the triangles are grouped as 3 separate groups (clusters) of 4 triangles each. In the array, the triangles are arranged in 3 horizontal rows with 4 triangles in each row, which is a more organized, rectangular arrangement compared to the clustered groups in the original drawing.

Answer:

s:
a. The array with 3 rows of 4 triangles is drawn as 3 horizontal rows, each containing 4 triangles (as shown above).

b. Same: Both have a total of 12 triangles. Different: Original has 3 clusters of 4, array has 3 rows of 4 (arranged in a rectangular pattern vs. clustered groups).