Relationship Between Circumference and Diameter - What is pi?

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Objective

Students will understand the relationship between circumference and diameter.

Big Idea

Did you say pie? or pi? Bring in a circular item for class, and it if happens to be food - AWESOME!

Launch

10 minutes

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 work should individually, and then as table groups to discuss the methods for solving the questions, this allows time to critique one another's reasoning, MP 3. During this time I will assist those students who were absent the previous day, and any other students needing help. 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 targets are, “I can identify the constant ratio between the circumference of a circle and its diameter."

Explore

40 minutes

Pi Lab:  As an introduction to the unit, students will work with their table groups to explore the ratio between circumference of a circle and its diameter.  I ask students in advance to bring in one circular item, and if it is a consumable item I ask that they bring enough for their table.  I have a basket with four additional circular items on the tables just in case students forget. While the students are completing the discovery activity, I will monitor progress by walking around the room and providing assistance when necessary.  It is important that this be a student discovery, MP 1, however, so my help will be limited to procedures of wrapping string around item and finding the diameter - attention to precision MP 6 will be important as this will help with developing the formula later on.  As groups begin to finish the activity, we will come back together as a class and discuss their findings.  Hopefully a group will correctly identify the formula, and pi. Analyzing their findings and looking developing formulas brings in mathematical practices 7 and 8 - looking for repeated reasoning.  This lesson will not work for all students, so I have included some Scaffolding Ideas

 

Summarize

10 minutes

Exit Ticket: After all class work problems have been worked out on the board, I will wrap up the lesson by asking two questions: “How is the circumference of a circle related to its diameter?” and “How do we calculate the circumference of a circle given the diameter or the radius?”  I will have students write their answers on the back of their opener and turn in as an exit ticket.