In this lesson, the teacher will guide students in discovering different ways of finding the area of a trapezoid. This lesson will show students that there is more than one correct way of finding area of a figure. Students will discover that they can find the area by using the formula and by dividing the trapezoid into other shapes, such as rectangles and triangles, and adding their areas to find the area of a trapezoid. Students will use problem-solving skills throughout the lesson.
Lesson: Different Ways of Finding Area of a Trapezoid (8.5)
New Jersey Core Curriculum Content Standards
4.2E Measuring Geometric Objects
1. Develop and apply strategies for finding area of a trapezoid
2. Develop and apply strategies for finding area by combining triangles
and rectangles
Focus: Connections
Learning Objectives
· Given any trapezoid, students will correctly calculate its area using the formula.
· Given any trapezoid, students will correctly find the area by dividing the trapezoid into other shapes, finding the areas, and adding them together.
Lesson Strategy
Students will be given Different Ways of Finding Area of a Trapezoid (1) worksheet. They will be asked to find the areas of the trapezoids in questions 1 and 2 by using the formula that was discovered the previous class period. After, the teacher will ask students if there is another way we could find the area of a trapezoid. The teacher will guide students in discovering that a trapezoid can be dividing into other shapes that they know how to find the areas of, such as triangles, rectangles, and squares. The teacher will have an example of a trapezoid on an overhead and ask students how it can be divided it into other shapes. As a class, the students will help the teacher find the area of the trapezoid. After, the teacher will instruct students to find the area of the trapezoids using this method for questions 3 and 4 on Different Ways of Finding Area of a Trapezoid (1) worksheet. Finally, students will work on some textbook problems with a partner to practice finding missing measures of trapezoids as well as finding areas of different shapes. At the end of class, students will be instructed to do a journal entry. They will be given a homework assignment and instructed to study for a quiz the following day (on finding areas of parallelograms and trapezoids).
This lesson accommodates auditory learners because they benefit by the classroom discussion. Also, the visual learners will like the lesson because there are drawings of trapezoids for them to refer to.
Adaptations: The worksheet is intended to be done individually. However, if students struggle, the teacher may decide to have students work with a partner so that they can help each other. Also, the teacher may need to review with students how to find the area of shapes such as triangles, rectangles, and squares if students forget.
Materials
· Pencils
· Textbooks
· Rulers
· Worksheets: Different Ways of Finding Area of a Trapezoid (1, 2)
· Transparency with an example of a trapezoid
Preparation
The teacher must prepare worksheets Different Ways of Finding Area of a Trapezoid (1, 2). In addition, the teacher must prepare a transparency with an example of a trapezoid with the height and bases labeled. The teacher should also decide in advance which textbook problems he/she wants the students to complete as well as a journal entry question. The teacher should know which pairs of students will be working together on the textbook problems.
The students must have pencils and their textbooks. Copies of the textbooks are kept in class so students do not have to worry about forgetting them. Students should also have their homework from the previous class, and it will be collected.
Procedure
Before
· Collect homework from previous class period
· Tell students that we are going to continue to work with trapezoids and finding areas
· Hand out Different Ways of Finding Area of a Trapezoid (1) worksheet
- Instruct students to complete questions 1 and 2 individually
- When students are finished, ask for volunteers to share answers
- Answer any questions students may have
· Show students a transparency with an example of a trapezoid
- Ask students: Is there another way to find the area of this trapezoid other than using the formula?
- Guide students to discover that the trapezoid can be divided into a triangle and a rectangle
- Ask students about the triangle: What is the base? What is the height? What is the area?
- Ask students about the rectangle: What is the length? What is the width? What is the area?
- Ask students: How do we find the area of the trapezoid? (Add the area of the triangle to the area of the rectangle)
Activity
· Instruct students to complete questions 3 and 4 on Different Ways of Finding Area of a Trapezoid (1) worksheet individually
- After students are finished, have students volunteer to share their methods of finding the area (other than using the formula)
- Answer any questions
· Instruct students to complete problems 17-20 on page 399 of their textbook
- If students struggle, ask the class for ideas on how to begin solving the problems
- Have students work with a partner
Summary and Reinforcement
· Have students complete Journal Entry E
- Journal Entry:
Draw a trapezoid that (a) Has two right angles (b) Has two sides of equal length
- Give students a ruler to help them
· Assign homework: Different Ways of Finding Area of a Trapezoid (2) worksheet
· Remind students to study for the quiz the following day
- Quiz is on area of a parallelogram and area of a trapezoid
Assessment
While students are working individually and with a partner on solving problems, the teacher should work around and observe students. Also, the teacher will be able to look at students’ journal entries to determine if they understand properties of trapezoids and if they are able to draw them meeting different criteria. Also, students will be given a homework assignment that will be reviewed the next day before the quiz.
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