Summary
This lesson has students explore how the properties of a circle, including area and circumference, relate to one another and to the world around them. The goal is for students to analyze the dimensions of a circle and correlate these to familiar, real-world situations.
Essential Question(s)
How can one part of a circle help determine the measure of another part?
Snapshot
Engage
Students engage in an Agreement Circles activity to make predictions related to ratios of a circle.
Explore
Students visit a series of stations to analyze the ratio between circles’ circumference and diameter.
Explain
Based on their findings, students determine which of two pizzas with different diameters is more cost-effective.
Extend
Students broaden their knowledge by solving a real-world problem involving ratio and area of a circle.
Evaluate
Students complete a Caption This activity to reflect on what they have learned.
Materials
Lesson Slides (attached)
Rulers and measuring tapes
A collection of round objects for students to measure
Circle Ratio Claim Evidence Reasoning handout (attached, one per pair of students)
Extend and Evaluate handout (attached, one per student)
Paper
Pencils
Speaker
Engage
Follow along with the lesson using the attached Lesson Slides. Display slide 3 as students are entering the classroom. Students will begin the lesson by engaging in an Agreement Circles activity based on the following statement:
No matter the size of a circle, the ratio of its measurements is the same.
Instruct students to move inside the circle if they agree with the statement or stay outside the circle if they do not agree. Have students find a partner who made the same choice and discuss why they decided to be on the inside or outside of the circle. Encourage them to use mathematical language in their discussion.
After students wrap up their discussions, display slide 4 to share the lesson’s Essential Question: How can one part of a circle help determine the measure of another part? Slide 5 identifies the lesson’s learning objectives. Review these to the extent you feel necessary.
Explore
Go to slide 6. Pass out a copy of the Circle Ratio Claim Evidence Reasoning handout to each pair of students. Using the CER: Claim, Evidence, and Reasoning strategy, pairs will first make a claim based on their agreement or disagreement with the statement. They should write this in the Claim section.
Next, pairs will go around the room to three different stations to measure different sized circles and record their findings in the Evidence section.
Explain
Go to slide 7. As a class, discuss the following question:
Going back to the statement, "No matter the size of a circle, the ratio of its measurements is the same," does your CER statement support this statement or not?
Ask students to present their findings and back up their CER statements through evidence-based reasoning from their measurements and calculations. Make sure students are aligned with the understanding that no matter the size of a circle, the ratio of its circumference to its diameter is always the same and equal to pi.
Go to slide 8. Have students look at the definitions while you draw a circle on the board. Have them talk about similarities and differences of the definitions and how they will apply to problems moving forward. While talking about the definitions, stress that not all problems will give them the radius or diameter of the circle, but they should have enough information to find those values on their own.
Go to slide 9. On their own piece of paper or however notes are taken in your classroom, have students work individually or with a partner to try to solve the problem. Before they begin, talk about which formula they should think about using and why. Once it is clear that the area formula is their better option, walk around the room while they are figuring out which pizza is more cost effective. If students are struggling, guide them by asking which numbers should be in the formula and why? Can you use any measurement? Once the students have solved the problem, have them help you walk through the problem. By understanding how to break down this particular scenario, it will help them as the next scenario increases in difficulty.
Extend
Go to slide 10. Pass out a copy of the Extend and Evaluate handout to each student.
Without much prompting, present students with the second pizza scenario:
Lucy and Harry ordered two different size pizzas. What fraction of Lucy’s 6-inch diameter pizza contains the same amount of pizza as one slice of Harry’s 12-inch diameter pizza of the same thickness cut into 12 equal slices?
Have students work through the problem, either with a partner or individually, using the space provided on their handout. Remind them that there are several components to this problem and it requires application of ratios as well as the area of a circle.
Evaluate
Go to slide 11. Bring the lesson to a close by having students complete a Caption This activity.
There are four photos on the slide. Ask students to select one photo and caption it using words and concepts that they have used in their learning.
Direct students to their Extend and Evaluate Handout to complete this activity. Students should enter the letter of the picture they chose in the box and write their caption in the remaining space.
This activity will wrap up the lesson and give you an idea of what students have learned, how they can apply the vocabulary regarding circles to another scenario, and what gaps you need to address moving forward.
Resources
K20 Center. (n.d.). Agreement circles. Strategies. https://learn.k20center.ou.edu/strategy/157
K20 Center. (n.d.). Caption this. Strategies. https://learn.k20center.ou.edu/strategy/82
K20 Center. (n.d.). Claim, evidence, reasoning (CER). Strategies. https://learn.k20center.ou.edu/strategy/156