The first three figures of a tile pattern are shown.

Question

Three figures.Short description, Three figures.,Long description,
Figure 1 has 1 tile in the center with 1 tile on each side. Altogether, there are 5 tiles in the figure.
Figure 2 has a 2 by 2 tile square in the center with 2 tiles on each side. Altogether, there are 12 tiles in the figure.
Figure 3 has a 3 by 3 tile square in the center with 3 tiles on each side. Altogether, there are 21 tiles in the figure.

Question
The expression p squared plus 4 p finds the number of tiles in the pattern for figure number p.



Move options to the blanks to explain why the expression represents the number of tiles in figure p.

Response area with 5 blank spaces
The pattern is made up of a
Blank space 1 empty
by
Blank space 2 empty
square plus an additional
Blank space 4 empty
tiles added to each side.


The total number of tiles is given by the number of tiles in the square,
Blank space 7 empty
, plus the number of additional tiles,
Blank space 6 empty
.

Answer options with 3 options.

Answer 1

Certainly! Here is how you can fill in the blanks to explain why the expression \( p^2 + 4p \) represents the number of tiles in figure \( p \):

The pattern is made up of a Blank space 1: p by Blank space 2: p square plus an additional Blank space 4: 4p tiles added to each side.

The total number of tiles is given by the number of tiles in the square, Blank space 7: p^2, plus the number of additional tiles, Blank space 6: 4p.

So, the response should be filled in as follows:

• Blank space 1: p
• Blank space 2: p
• Blank space 4: 4p
• Blank space 7: p^2
• Blank space 6: 4p