Lesson 3 Tile Rectangles

    • Let’s count square tiles.

Warm-up Which One Doesn’t Belong: Tiles

Which one doesn’t belong?

  1. Rectangle partitioned into 4 rows of 6 of the same size squares, with every other square shaded.
  2. A partially tiled rectangle.
  3. Diagram. Rectangle partitioned into 4 rows of 6 of the same size squares.
  4. Rectangle. 6 rows of 4 square tiles. Tiles have gaps and overlaps. 

Activity 1 Time to Tile

Your teacher will give you square tiles and a handout showing rectangles and squares.

Problem 1

Describe or show how to use the square tiles to measure the area of each rectangle. You can place square tiles on the handout where squares are already shown. You can also move the tiles, if needed.

  1. A square with 4 of the same size square tiles in it.
  2. 3 square tiles inside a rectangle.
  3. 7 square tiles inside a rectangle.
  4. A partially tiled rectangle.

Problem 2

Describe how to use square tiles to find the area of any rectangle.

Activity 2 Card Sort: Rectangles

Problem 1

What do you notice? What do you wonder?

Rectangle made of inch tiles.
Shaded area diagram. Length, 4. Width, 3.
Area diagram. Length, 4. Width, 3.

Problem 2

Draw a rectangle with an area of 8 square units on the grid.

Diagram. Rectangle partitioned into 6 rows of 10 same size squares.

Problem 3

Your teacher will give you a set of cards that show rectangles. Sort the cards into categories of your choosing. Be prepared to explain your categories.

Rectangle with square units.
Diagram. Rectangle partitioned into 2 rows of 8 of the same size squares.
Diagram. Rectangle partitioned into 8 rows of 3 of the same size squares.
Area diagram. Length, 4. Width, 4. 
Diagram. Rectangle partitioned into one column of 12 of the same size squares.
Diagram. Rectangle partitioned into 12 rows of 2 of the same size squares.

Problem 4

Create a rectangle that would fit in each group.

Diagram. Rectangle partitioned into 20 rows of 20 of the same size squares.

Practice Problem

Problem 1

  1. Find the area of each rectangle.

    Grid with 3 rectangles labeled A, B, and C.

  2. Can rectangles with different shapes have the same area? Explain your reasoning.