# Toothpick Squares

Finding patterns

*Directions*

Consider that each small square is one toothpick long on each side and the larger squares are made from these 1x1 squares.

Explore the three squares that get progressively larger.

*Focus Questions:*

## What is the perimeter pattern?

- Square number 3 on the right (3 x 3) is constructed with a perimeter of 12 toothpicks. If the pattern were continued, how many toothpicks would be used to construct the perimeter of square #4?
- Write a rule you could use to determine how many toothpicks would be used in the perimeter for any larger square in the pattern.

## What is the number of squares in the increasing squares pattern?

- Square number 3 has nine small (1x1) squares. How many small squares would be needed to make the larger squares: #4, #5, #6 in the pattern?
- Write a rule you could use to determine how many small squares would be in any square in the pattern (for example: square #n).
- Can a toothpick square be made with exactly 40 small squares? Support your conclusion.
- Can a toothpick square be made with exactly 144 small square? Support your conclusion.

## What is the total number of toothpicks in the increasing squares pattern?

- Square #1 includes a total of 4 toothpicks
- Square #2 includes 12 toothpicks.
- Square #3 includes a total of how many toothpicks?
- Square #4...?
- Can you determine the total toothpicks for square #7, #10, #__ ?
- Write a rule to use to determine the number of toothpicks in square #n.

*Hint*: Collect the data asked with the questions, organize it in sequential order, look for a pattern.

*Discussion:*

*Mind boggler*: Toothpick functions

*Enjoy!*