Area of Composite Shapes

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Objective

SWBAT find the area of a parallelogram by using the formula, find the area of a trapezoid and composite shapes by decomposing them into triangles, rectangles, and/or squares.

Big Idea

Students take their knowledge about area of rectangles, squares and triangles and apply it to parallelograms, trapezoids, and composite shapes.

Do Now

5 minutes

See the Do Now video in the Strategy Folder for more details on how I start my class.  I chose these problems to serve as a quick review of finding perimeter and area of rectangles and triangles.  A common mistake is for students to find the area of the triangle by multiplying the base times height.  Another common mistake is confusing the hypotenuse as either the base or height when calculating area.  I look for these mistakes and may present one as my answer if I see multiple students making one of these mistakes while I circulate during the do now.

Perimeter vs. Area Review

5 minutes

This lesson has students working on calculating area so I created these two problems to make sure students are still practicing differentiating between when to calculate perimeter and when to calculate area.  I have students work on these problems in pairs.  I circulate and look the common mistakes mentioned in the do now problems.  I ask students: What are you calculating?  Why?

Problem

10 minutes

Explore

5 minutes

Students work on breaking the composite shapes into shapes they can use to find area.  Most students will break this shape into 2 right triangles and a rectangle.  Some students may create triangles that are not right triangles and a rectangle.  They will struggle to calculate the area because the grid will not allow them to accurately calculate the area.  I will choose a student to share their work and strategy with the class.

Class Notes

5 minutes

We quickly review the strategy of breaking composite shapes that we know.  There is more than one way to do this with many composite shapes.  I emphasize to students that they need to find a way that is efficient and works with the measurements that are given.  Sometimes they will have to do detective work to figure out missing measurements.

Some students look at the composite shape and immediately say, “I can’t find the area of the triangle because I don’t know the length of the base of the triangle”.  I ask this student what they know about the relationship about the sides of a rectangle.  I am looking for students to tell me that opposite sides of the rectangle are equal.  With that knowledge they can then figure out the base of the triangle is 8 meters.

Practice

15 minutes

Students work independently on the practice pages.  When they complete a page, they get up and check their work with the key that I have posted around the room.  See the Posting a Key video in my Strategy Folder for more details. 

I circulate and address student questions.  I look for what students will do on #3 on page 7.  A common mistake is that students use 12 cm as the base of the triangle.  Here students have to compare the length of the rectangle (4 cm) to the measurement of 12 cm to figure out that the base of the triangle is 8 cm.  If many students struggle with this I will stop students from working and address this problem as a class. Students will have to use this skill of figuring out missing measurements for the problems on page 8.

If students successfully complete their work on the practice they can move onto the challenge questions.

Closure

5 minutes

I have a student review our objectives for the lesson.  Then I ask students how they found the area of #3 on page 8. I want a student to show exactly how they broke up the shape to the right into a triangle and rectangle as well as how they figured out the measurements of the base and height of the triangle.  I ask students what their strategy is for finding the area of composite shapes.  

Instead of giving a ticket to go I will collect students’ packets so that I can analyze students’ work and strategies.