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

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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.

Launch

15 minutes

OpenerAs 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.

Explore

40 minutes

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!

 

Summarize

5 minutes

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.