Lesson 3

Area of Composite Shapes Using a Grid

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SWBAT find the area of composite shapes (on a grid) by finding the sum of the areas of its component shapes using area formulas

Big Idea

Students find the area of shapes using grid paper and markers.


15 minutes

I will ask the students how we measure area.  I may relate it to the lesson from 2 days before where floor tiles were used to model area.  I’ll ask how do we find the area of a rectangle/a triangle/and a trapezoid.  This will be review.  Students may refer to a reference sheet.  Then I will show an irregular shape and ask the essential question: How can you determine the area of a composite shape?  I will show some of the shapes in the lesson while students ponder this question.  If they are stuck, I will ask the students to identify what basic shapes could be put together to make the composite shape.  Again here is a brief opportunity to look for precision in language (MP6).  For example, if a student says they see a rectangle and a triangle, I may ask what type of triangle/rectangle?


Next I will explain to students how to transfer drawings to a graph paper.  They should treat all measurements as unit even though some are labeled feet, inches, cm, etc.   Students will then work with partners to solve GP1-GP4.  I may pass out markers for so that students can color in each basic shape of the composite shape.  Students show should how they found the area of each individual shape (most likely using a formula). We will then review answers.  I will focus on GP3 & GP4.  Why do we get the same area, even though we used different basic shapes?  We will then discuss briefly.  The point is to get students to see that no matter how the shape is subdivided its area will still be made up by the same amount of square units.  Before students begin the independent problem solving we will look to summarize how to find the area of a composite shape.  Answers should include something about finding the sum of the areas of the basic shapes. 

Problem Solving

20 minutes

Students begin independent work on the next 5 shapes.  I anticipate that some students will have trouble transferring problems 2 & 4 to a grid so I will be walking around to make sure that students are accurately drawing the shapes on grid paper.  I will suggest that they first draw all the known lengths.  Students may color the basic shapes in different colors.  Also, problem number 2 can be subdivided at least 3 different ways.  As we review solutions, I will make sure to show student work for different methods. 

Summary + Exit Ticket + Homework

15 minutes

We will again summarize our approach to finding area.  I will do this by asking the essential question and allowing for a brief THINK-PAIR-SHARE.  Students will then take the exit ticket.