Lesson 4

Helipads for Antopolis

Est. Class Sessions: 2

Developing the Lesson

Part 1: Comparing Rectangles

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Provide chenille stems cut into 24 1-inch pieces rather than a single piece of wire or string. Students can re-arrange the pieces more easily around the different shapes they make.

Provide each group of 2–3 students with one piece of wire or string 24 inches long. Ask each student group to measure the wire, and then make a rectangle with it. If string is used, students will need to tape their rectangle to a piece of Square-Inch Grid Paper. If string or wire is not available, ask student groups to draw a rectangle with a perimeter of 24 inches on a sheet of Square-Inch Grid Paper.

Before comparing rectangles, ask the following questions about each group's rectangle. Students can use their rulers and the Square-Inch Grid Paper to find the answers.

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  • Is the perimeter 24 inches? How do you know? (Yes. I know because I started with 24-inch-long wire and used all of it.)
  • What is the length and what is the width of your rectangle? (Answers will vary.)
  • What is the area of your rectangle? How did you find the area? (Possible response: 32 sq. in. I know because I have 4 rows of 8 tiles, so 4 × 8 = 32.)

Students using string or twist ties will most likely have rectangles with side lengths that are not whole numbers. Have these students estimate the area to the nearest square inch.

Have each group compare their rectangle to the rectangles of neighboring groups and discuss:

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  • Which rectangle has the largest area and which has the smallest area?

Ask volunteers from two of the groups to compare their rectangles in front of the class. Ask the class to vote on which of the rectangles has the largest area. Ask a few of the students why they thought the rectangle they voted for was the larger one. Now ask if there is a group whose rectangle has a larger area than either of the two rectangles on display. Have a volunteer from the group bring their rectangle to the front and compare it. The class can vote again on which one has the largest area. Again, ask a few students for a reason they thought one was larger than the other.

Students should realize that even though the perimeter of each rectangle is 24 inches, the rectangles have different shapes and areas.

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Squares and Rectangles in Everyday Language and in Mathematics.

A rectangle is defined as a four-sided figure with four right angles. If all four sides of a rectangle are the same length, then it is a square. A square is a special kind of rectangle.

In talking about vocabulary with students, distinguish mathematical language from everyday language. Some everyday terms are also used in mathematics and given a precise definition that differs significantly from the meaning that may be familiar to students. This can be confusing. For example, in everyday English, square and rectangles sometimes are considered to be two different shapes. Both have four sides and four right angles, but the square is the one with four equal sides and the rectangle is the one whose length differs from its width. When students hear that a square is a rectangle because it satisfies the definition of a rectangle, they may distrust the mathematical definition because it differs from their prior understanding. Confusion can be avoided by addressing the issue and discussing the distinction between mathematical and everyday usage of words.

When creating and comparing the rectangles, some students may not know that a square is a rectangle. Knowing that a square is a rectangle is necessary to solve the problem that will be explored later in this lesson. Ask students to define a rectangle and then to explain whether a square fits that definition. The Content Note discusses the definitions of a rectangle and a square.

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