# 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!