Question

Jill’s teacher asked her to construct a rectangular prism from unit cubes. She has built the structure about. In order for Jill to complete her assignment, how many unit cubes will Jill need to add to the below structure? Explain how you were able to figure out how many more cubes will be needed. Is there a different way to solve this situation?

Answer 1

Answer:

• 36 cubes
• There are several forms to figure it out: see two different ways explained below.

Explanation:

The first way to figure out how many more cubes Jill will need to add to complete the structure until forming a rectangular prism  is to add the cubes from column to colum,

The first column is complete: it has four rows each with 4 cubes.

The second column (the one next to the right of the first column) has three rows. Then Jill has to add one more row. This is 4 cubes.

The third column has two rows. Then, Jill will need to add two rows with 4 cubes each, for a total of 8 cubes. So far, the count is 4 + 8 = 12 cubes.

The fourth and fifth columns have just one row. Then, Jill will need 3 rows for each column, making it 2 × 3 × 4 = 24 cubes.

The total final count is 12 + 24 = 36 cubes. ← answer

There are different ways to figure out the number of cubes needed to complete the rectangular prism. This is another one:

How many cubes shall the complete pyramid have? : 4 × 4 × 5 = 80 (length × width × height).

How many cubes does the shown incomplete structure have?: 4×4 + 3×4 + 2×4 + 4 + 4 = 16 + 12 + 8 + 4 + 4 = 44.

Difference: 80 - 44 = 36 cubes. ← answer