Area, Perimeter, and Circumference

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Objective

SWBAT: • Find the area and perimeter of irregular shapes by decomposing them into squares, rectangles, and circles.

Big Idea

Which option makes more pizza? Students apply their knowledge of perimeter, area, and circumference to calculate the perimeter and area of irregular shapes.

Do Now

8 minutes

Note:

  • Common Core has students work on circles during 7th grade.  I teach in Massachusetts where 6th grade students are expected to identify parts of a circle as well as calculate circumference and area.

See my Do Now in my Strategy folder that explains my beginning of class routines.

Often, I create do nows that have problems that connect to the task that students will be working on that day.  Today I want students to start thinking about how to find and compare the area of circles that are embedded in other shapes.  Some students may initially complain that they don’t know how to figure this out.  I encourage them to think about what the problem is asking and what they know.  I also encourage students to take a guess based on the pictures.

Some students may start to calculate the area of the pizza in each option.  They probably will not have time to complete their calculations.  We will return to this question during the closure.  Other students may look at the pictures and think that Option B will make more pizza because they think there is less empty space on the cookie sheet.  Some students may think that Option A will make more pizza because there are more pizzas.

I call on students to share what they think and why.  I want to know whether students are thinking about area or circumference in order to answer the question.  I encourage students to comment on the ideas of their classmates and explain their thinking.  Students are engaging in MP3: Construct viable arguments and critique the reasoning of others.

Group Work

27 minutes

Notes:

  • Before this lesson, I use students’ ticket to gos from the previous lessons to Create Homogeneous Groups.  Students work in groups of 3-4.
  • Some groups may complete fewer tasks than others, and this is okay.  I care more about the quality of the students’ work than the quantity of the work they complete.
  • It may save time to fill out the group to do lists before class.
  • I Post a Key for each task.

I tell students their groups and their assignments.  I have students move to their groups and I have a volunteer pass out materials and a Group Work Rubric for each groupStudents are engaging in MP1: Make sense of problems and persevere in solving them, MP2: Reason abstractly and quantitatively, MP4: Model with mathematics, and MP6:  Attend to precision.

As students work I walk around to monitor student progress and behavior.  If students are struggling, I may ask them one or more of the following questions:

  • What is going on in the problem?
  • What do you know? What are you trying to figure out?
  • Are you finding area or perimeter/circumference?  How do you know?
  • How do you calculate the circumference/perimeter/area?

When students complete their work, they raise their hands.  I quickly scan their work.  If they are on track, I send them to check with the key.  If there are problems, I tell students what they need to revise.  If students successfully complete the chart they can move on to the next task. 

Closure and Ticket to Go

15 minutes

For the Closure, I have students return to the do now question.  I give students time to work on it.  Students participate in a Think Pair Share.  I call on students to share their answer and explain their thinking.  The amount of square inches of pizza is actually the same for each option.  The area of one of the pizzas in option A is 16 times pi, and since there are four pizzas the total area is 64 times pi.  The area of the pizza in option B is 64 times pi.  Students are engaging in MP1: Make sense of problems and persevere in solving them and MP3: Construct viable arguments and critique the reasoning of others.

If I have time, I ask students to find the amount space on the cookie sheet that is empty. 

Instead of giving a ticket to go, I collect student work so I can analyze it.  I pass out the Homework.