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# Area of Irregular Figures - How do you break up a figure?

Lesson 3 of 18

## Objective: Students will be able to find the areas of irregular figures by decomposing the figures into shapes with known area formulas.

## Big Idea: Expert students will lead the lesson as students apply prior knowledge of area to composite figures.

*60 minutes*

#### Launch

*15 min*

**Opener: **As students enter the room, they will immediately begin working on the opener. The opener is a mixture of previously learned questions, and students should work individually, and then as table groups to discuss the methods for solving the questions, which incorporates **MP3**, critiquing the reasoning of others. After approximately 5 minutes, I will call on students to go to the board and solve the opener questions. Instructional Strategy - Process for openers

**Learning Target: **After completion of the opener, I will address the day’s learning targets to the students. In today’s lesson, the intended target is, “I can find the area of an irregular figure by decomposing it into shapes with areas that I know.” At this time, I will pass out the notes sheet, and ask students to omplete the formula brain dump at the top of the page.

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#### Explore

*40 min*

**Composite Figures Notes**: I will start the lesson with a short brain dump on the formulas for triangles, rectangles, and circles. After about a minute or so, I will take student volunteers to share the formulas with the class. From there, we will go into some practice problems - focusing on the two types of composite figures - those "stuck" together, and those inside one another thus creating a "shaded region." I will ask students guiding questions such as, “if we place a triangle on top of a rectangle, how would we find the total area?” and “if we cut a square out of the center of our paper, how do we find the area of what is left?” Using student responses, we will fill in the blanks on the notes sheet, and work one or two examples together. Then, students will work in their table groups to complete the remaining examples, and I will call on volunteers to come to the board. While students are working in table groups I will walk around the room and assist as needed. In an effort to support student talk and reasoning, I will not immediately provide assistance to any groups or individuals, until it is clear that they have had a discussion as a small group about how to do the work and all parties involved need assistance. Assistance will be provided as needed through guided questioning. The concept of irregular figures I find to be extremely challenging for students, therefore it is very important that they have the opportunity to grapple with the mathematics, **MP**** 1**.

Class Assignment: After the notes, I will have students work with their table groups to complete 8 problems. My goal is to pull cards associated with table numbers and have groups go to the board to present their solutions. If time runs short, or students struggle more than anticipated, the sheet may carry over to homework - not sure yet!

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#### Summarize

*5 min*

Instructional Strategy - Table Discussion**: **After all class work problems have been worked out on the board, I will wrap up the lesson by asking two questions: “how do we find the area of an irregular figure?” and “how do we find the area of a shaded region?” Students will jot down their answers on the white board at their table, and hold up responses to each question, so that I can gauge understanding of the learning target.

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- UNIT 1: Introduction to Mathematical Practices
- UNIT 2: Proportional Reasoning
- UNIT 3: Percents
- UNIT 4: Operations with Rational Numbers
- UNIT 5: Expressions
- UNIT 6: Equations
- UNIT 7: Geometric Figures
- UNIT 8: Geometric Measurement
- UNIT 9: Probability
- UNIT 10: Statistics
- UNIT 11: Culminating Unit: End of Grade Review

- LESSON 1: Relationship Between Circumference and Diameter - What is pi?
- LESSON 2: Circumference and Area of Circles
- LESSON 3: Area of Irregular Figures - How do you break up a figure?
- LESSON 4: Working Backwards with Formulas - How do I undo a formula?
- LESSON 5: 2D Figures - Review Time!
- LESSON 6: Composite Figures and Circles Test
- LESSON 7: Intro to 3D Figures and Cross-Sections - What shape do you see?
- LESSON 8: Volume of Prisms - How are base area and volume of a prism related?
- LESSON 9: Volume of Square Pyramids - What is the relationship between and prism and pyramid?
- LESSON 10: Volume of Prisms and Pyramids Fluency Practice
- LESSON 11: Surface Area of a Rectangular Prism - What shapes do you see?
- LESSON 12: Surface Area of a Triangular Prism - What shape is the base?
- LESSON 13: Surface Area of Triangular and Rectangular Prisms Fluency Practice
- LESSON 14: Surface Area of a Square Pyramid - What shapes are the faces?
- LESSON 15: Volume and Surface Area of Prisms and Pyramids Fluency Practice
- LESSON 16: Volume and Surface Area Review
- LESSON 17: 2D and 3D Volume and Area Test
- LESSON 18: Surface Area and Volume Centers -5 Days of Enrichment and/or Remediation