Section A: Practice Problems Concepts of Area Measurement

Section Summary


In this section, we learned that area is the amount of space covered by a shape.

We saw that we can count squares to measure area. When we tile a shape, we need to make sure that the squares are covering the whole shape without gaps or overlaps.

Area diagram. Length, 6. Width, 4. 
Rectangle. 3 rows of 6 unit tiles. Tiles have gaps and overlaps.

Area is measured in square units. The area of the tiled rectangle here is 24 square units.

Problem 1 (Pre-Unit)

  1. Partition the rectangle into 4 equal rows and 5 equal columns.

    A rectangle.
  2. How many small squares are there in the rectangle?

Problem 2 (Pre-Unit)

Is the number of dots in each image even or odd? Explain how you know.

    Group of dots.
    9 dots arranged 3 by 3.
    A group of dots.

Problem 3 (Pre-Unit)

How many dots are in each array? Explain or show your reasoning.

    Array. 3 rows of 5 dots.
    18 dots, arranged in 9 by 2 rectangle.
    12 dots, arranged in 3 by 4 rectangle.

Problem 4 (Pre-Unit)

A centimeter ruler with 2 line segments labeled A and B.

Use the centimeter ruler to find the lengths of the two line segments A and B. Explain your reasoning.

Problem 5 (Lesson 1)

Which shape is the largest? Which shape is the smallest? Explain your reasoning. You may trace and cut out the shapes if it is helpful.

3 shapes labeled A, B, and C.

Problem 6 (Lesson 2)

Lin, Han, and Elena made letters from squares. Put the letters in order from least area to greatest area. Explain your reasoning.

Letters L, H, E. L, 8 squares. E, 11 squares. H, 12 squares.

Problem 7 (Lesson 3)

  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.

Problem 8 (Lesson 4)

Find the area of the rectangle. Explain or show your reasoning.

Diagram. Rectangle partitioned into 5 rows of 8 of the same size squares.

Problem 9 (Exploration)

Which shape has greater area, a green triangle pattern block or a tan rhombus pattern block? Explain your reasoning.

A triangle and a rhombus.

Problem 10 (Exploration)

Here are two rectangles.

Diagram. Rectangle partitioned into 6 rows of 8 of the same size squares.
a square gridded with same size squares.
  1. What is the area of the larger rectangle?

  2. What is the area of 3 smaller rectangles?

  3. Can you cover the first rectangle with 3 of the smaller rectangles without cutting them up? Explain or show your reasoning.

Problem 11 (Exploration)

  1. How many different rectangles can you make with 36 square tiles? Describe or draw the rectangles.

  2. How are the rectangles the same? How are they different?