Objective: Students will use a formula to find circumferences of circles and apply the formula to real-life situations.
CCSS.Math.Content.7.G.B.4: Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle
Materials: Paper, scissors, tape, pencils, rulers, crayons or colored pencils, shoe boxes, circular items to trace or compasses (optional)
Note: students should be familiar with the basic parts of a circle (radius and diameter) and should have some previous exposure to the concept of pi.
Step One: Introduction
Use either a real display or a picture of a dessert cart with circular objects such as pies, cakes, cookies, and cupcakes. Guide students in a discussion of the circular objects on the cart, pointing to the circumference of the various objects.
Explain to students that they will be creating their own dessert carts and finding the circumference of the items on their carts. Students can do this activity individually or with partners, depending on how they learn best.
Step Two: Simulation – Building and Filling the Dessert Carts
Give students time to fashion and decorate their dessert carts (using shoeboxes), and draw and cut out their circular items for the carts. If there is enough time, students may want to build a few 3D models of items such as cupcakes or layered cakes.
You may want to set a specific time to work (such as 20 or 30 minutes) so that students can get their items ready within a set time frame and maintain focus. Students should have the option of using objects to trace the circles or compass tools to draw accurate circles, so that they will have an easier time using rulers to take measurements of their objects later.
Step Three: Data Collection
Have your students use rulers to measure the diameter of each of the items on their dessert carts, noting the measurements in a chart like the one shown above.
Note: If students are working with flat paper objects and are having trouble finding diameter, students can fold the paper in half and use the crease as a guide for measuring diameter.
Special Needs Tip: You may want to provide pre-made dessert items with diameter lines drawn on them, so that students can focus on the skill of measuring the diameter with rulers.
Step Four: Application of Skill
Once students have measured the diameter of each of the objects on their dessert carts, display the formula for finding the circumference of a circle on the board:
2πr or πd (for this lesson, using πd will make the process more straightforward for students who have not previously used a formula to find circumference)
Demonstrate how students can use the formula, plugging in the numbers they are getting for the diameters of their dessert cart objects. Show students how to fill in the rest of their charts.
Students will then finish their charts, filling in the formula and the circumference for each circle. Circulate and check students’ understanding as they use the formula to find circumference.
Students who have finished their charts may decorate their dessert carts and the items on them.
Assessment: Collect the charts and check students’ computational skills to ensure that they were using the formula correctly. You may also want to end the lesson with a brief quiz, asking students to find circumference using formula when supplied with several randomly chosen diameter lengths.
Extension: Ask students to graph the diameter and circumference of each item, so they can see the relationship between increases in diameter and measurements of circumference. Advanced students might also be given the option of finding surface area or volume of any 3D models of dessert items they created for their carts.