## Perimeter of Tiles

## Opening

# Perimeter of Tiles

Each square tile has side length *x*.

- Write an expression for the perimeter of the rectangle that is made up of the 5 tiles.

Each square tile has side length *x*.

- Write an expression for the perimeter of the rectangle that is made up of the 5 tiles.

Write equivalent expressions that represent the perimeters and areas of geometric figures.

Write an expression for the perimeter of the rectangle that is 100 tiles long.

- Think about how you found the perimeter of the rectangle that was 5 tiles long.
- Use the same reasoning to write an expression for the perimeter of the rectangle that is 100 tiles long.

The image shows four expressions that Sophie, Jack, Kevin, and Marcus wrote for the perimeter of the rectangle that is 100 tiles long.

- Which three expressions are correct?
- Are the three correct expressions equivalent? Explain.
- What is an expression for the perimeter that has only one term?

- Are any of the four expressions equivalent to the expression you wrote?
- Think about how you might use properties of operations (associative, commutative, and distributive) to identify equivalent expressions.
- Look for an expression with only one term. Can you write it in a simpler way?

Each student’s statement below describes a different way of thinking about how to express the perimeter of the rectangle that is 100 tiles long.

Read how these students approached the problem in order to write an expression.

Kevin: I added the lengths of the sides of the rectangle.

Jack: I added the length and width and then multiplied by 2.

Sophie: I saw that the first and last squares had 3 sides as part of the perimeter, but all of the other squares had only 2 sides in the perimeter.

- Match each correct expression from the image with each of the three students’ statements.

Look at the figure.

- Write an expression for the perimeter.
- Write an expression for the area.

- What values do you add to find the perimeter?
- What is the length of the bottom of the figure?
- How do you find the area of a figure?
- How could you use subtraction to find the area?

- Choose from Sophie’s, Jack’s, Marcus’s, or Kevin’s solutions to the problem of 100 tiles.
- Compare and contrast your solution with the solution you chose.

An equilateral triangle and a square both have the same perimeter:

12*x* + 24

- Find the length of a side of the equilateral triangle and the length of a side of the square.

Think about how to use the distributive property and common factors.

Take notes about your classmates’ strategies for writing equations for the perimeter and area of geometric figures.

As your classmates present, ask questions such as:

- How did you connect your expression to the figure?
- How did you know that two expressions were equivalent?
- How did you match the approaches of the three students to the expressions for the perimeter of the rectangle made up of 100 tiles?
- What formulas did you use to find the perimeter and area of a figure?

Write a summary about equivalent expressions.

Check your summary:

- Do you explain what
*equivalent expressions*means? - Do you discuss how properties of operations can be used to identify equivalent expressions?

Write a reflection about the ideas discussed in class today. Use the sentence starter below if you find it to be helpful.

**Properties of operations are used to create equivalent expressions because …**