Geometric Expressions

Geometric Expressions

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.

Math Mission

Opening

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

Perimeter of 100 Tiles

Work Time

Perimeter of 100 Tiles

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

Hint:

  • 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.

Student Work

Work Time

Student Work

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?

Hint:

  • 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?

Match Approach and Expression

Work Time

Match Approach and Expression

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.

Area and Perimeter

Work Time

Area and Perimeter

Look at the figure.

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

Hint:

  • 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?

Prepare a Presentation

Work Time

Prepare a Presentation

  • 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.

Challenge Problem

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

12x + 24

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

Hint:

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

Make Connections

Performance Task

Ways of Thinking: Make Connections

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

Hint:

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?

Equivalent Expressions

Formative Assessment

Summary of the Math: Equivalent Expressions

Write a summary about equivalent expressions.

Hint:

Check your summary:

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

Reflect On Your Work

Work Time

Reflection

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 …