Area of Shaded Regions

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Objective

SWBAT calculate the area of a region shaded between two polygons.

Big Idea

Students use a previous strategy to help them find area of shaded regions.

Do Now

10 minutes

Students will use their prior knowledge of finding the area of an irregular polygon to complete the Do Now problems.  

After 10 minutes, we will discuss the problems.  For problem 1, most students will have chosen to divide the irregular polygon into a triangle and trapezoid.  Students should make sure that they are using the formulas correctly to find the area of the shapes.  A common mistake is students forget to add the bases when finding the area of a trapezoid. 

For problem 2, students may feel comfortable with either method.  I will choose 3 students to share their work and answers with the class.  The first student will have chosen to horizontally divide the shape into 2 rectangles.  The second student will have vertically divided the shape into 2 rectangles.  The third student will have formed a larger rectangle.

Mini Lesson

15 minutes

For this lesson, students will develop a strategy for finding the area of shaded regions.  Through a series of questions that I will ask students, they will develop steps that will be useful for finding the area.

Each student will receive an Area of Shaded Region worksheet . 

Example 1

What polygons are in this diagram?

Students should recognize that there is a rectangle and square.

Can we find the area of the rectangle? What is the length and width?

We will look at the rectangle to verify that we have the necessary lengths and widths. The length is 9 ft and the width is 7 ft.  Students should apply the formula to find the area.

Can we find the area of the square?

Students should apply the formula.

We now have the area of both polygons, how can we find the area of the region between the two areas?

Students should see that we need to subtract the areas for this method.  They may recognize this as a strategy similar one discussed in a previous lesson,  Finding the Area of Irregular Polygons, Method 2.

At this point, students have developed a strategy for finding the area of shaded regions.  I will formalize these steps for them.

Steps

1.  Find area of whole figure.

2.  Find area of unshaded figure(s).

3.  Subtract unshaded area from whole figure.

4.  Label answer with units2.

 

We will continue and work through examples 2 and 3 together as a class.

Independent Practice

10 minutes

Each student will receive an Area of Shaded Region Independent Practice.  They will complete the three problems using their notes and steps that they developed.  I will emphasize how important it is to label and organize their work.  Students will work independently, but may ask questions of their group.

As students work, I will focus on the lower level math students who have shown difficulty in applying the area formulas.  These students have previously created flashcards that I will encourage them to use.

After 10 minutes, students will discuss and compare their work with their group.  If there are any differences, students should discuss their steps to determine where and why they differ in answers.  Through this process, students should develop a deeper understanding of the concept.

If there are any remaining questions or misconceptions, we will discuss them as a class.

Lesson Summary

5 minutes

For the lesson review we will discuss and review the steps.  I will ask the class a series of questions to assess their understanding of the concept.

 

Is it possible to have more than 2 shapes that create a shaded region?

Are the dimensions of the polygons always directly given?

How can you find the missing dimensions?

What operation do we use to find the area of the shaded region?  Why do we subtract and not add the areas?