##
* *Reflection: Problem-based Approaches
Area of Composite Shapes Using a Grid - Section 1: Opening

In the resource, I specified how I wanted students to solve problem GP3 and GP4. You will see that they are the exact same shape but that I have asked students to subdivide them into specific ways. Some students completely ignored or misunderstood what I wrote and came up with a third and equally valid subdivision. This one included a trapezoid and a triangle.

I think in the future, I may launch the lesson with this particular problem. I will remove any suggestions as to how to subdivide the shape. Then, I'll give students about 5 minutes to come up with their own solution before sharing with a partner or a group. Instead of receiving guidance from me, the various ways to solve the problem will be student generated.

*Variations on a Shape*

*Problem-based Approaches: Variations on a Shape*

# Area of Composite Shapes Using a Grid

Lesson 3 of 37

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

*50 minutes*

#### Opening

*15 min*

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.

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#### Problem Solving

*20 min*

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.

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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.

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- LESSON 1: Explore Perimeter and Area of Composite Shapes
- LESSON 2: Perimeter of Irregular Rectilinear Shapes
- LESSON 3: Area of Composite Shapes Using a Grid
- LESSON 4: Area of Composite Shapes
- LESSON 5: Area of Regions Formed by Inscribed Shapes
- LESSON 6: CORNERSTONE:Circle Ratios: Diameter to Radius; Circumference to Diameter
- LESSON 7: CORNERSTONE: Circumference Formula
- LESSON 8: Area of a Circle
- LESSON 9: Circumference & Area Fluency Practice
- LESSON 10: Finding the Radius From a Given Circumference or Area
- LESSON 11: Circumference from Area / Area from Circumference
- LESSON 12: Circle Designs: Finding the Area and Perimeter of Shapes Composed of Arcs and Line Segments
- LESSON 13: Assessment_Area and Perimeter (Circumference) of Composite Shapes and Circles
- LESSON 14: Drawing Prisms & Pyramids
- LESSON 15: Describe Prisms and Pyramids Using Algebra
- LESSON 16: Using Nets to Find the Surface Area of Prisms
- LESSON 17: Using a Formula to Find the Surface Area of Prisms
- LESSON 18: Finding the surface area of triangular prisms using a net
- LESSON 19: Finding the Surface Area of a Triangular Prism Using A Formula
- LESSON 20: Discovering the Formula for the Surface Area of A Cylinder
- LESSON 21: Finding the Surface Area of Cylinders Using a Formula
- LESSON 22: Practice Day: Surface Area of Prisms & Cylinders
- LESSON 23: Surface Area of Prisms and Cylinders Assessment
- LESSON 24: Finding the Surface Area of Pyramids Using Nets
- LESSON 25: Finding the Surface Area of Pyramids Using a Formula
- LESSON 26: Surface Area of Composite Shapes
- LESSON 27: Surface Area of Composite Shapes With Holes
- LESSON 28: Surface Area Assessment
- LESSON 29: 3-D Models from 2-D Views
- LESSON 30: Exploring Volume and Surface Area with Unifix Cubes
- LESSON 31: Explore Volume of Rectangular Prisms
- LESSON 32: Find the Volume of Prisms Using a Formula
- LESSON 33: Volume Of Cylinders Using a Formula
- LESSON 34: Volume of Composite Shapes
- LESSON 35: Volume and Surface Area - Accelerated Math Fluency Day
- LESSON 36: Volume of Pyramids
- LESSON 37: Surface Area and Volume Final Assessment