Lesson plan - Study Island



|Math Lesson: Circles |Grade Level: 7 |

|Lesson Summary: Students calculate the circumference, diameter, and radius of a circle and derive the formula for the area of a circle. They consider a real-world |

|question related to the circumference of a basketball and basketball rim. Advanced students research how Eratosthenes determined the circumference of the Earth |

|2,000 years ago. Struggling students calculate the circumference and diameter of different sports balls and consider how size would affect play. |

|Lesson Objectives: |

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|The students will know… |

|formulas for the area and circumference of a circle. |

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|The students will be able to… |

|solve problems using the formulas for the area and circumference of a circle. |

|give an informal derivation of the relationships between the circumference and area of a circle. |

|Learning Styles Targeted: |

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|Visual |

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|Auditory |

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|Kinesthetic/Tactile |

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|Pre-Assessment: |

|Determine whether students can find the area of a rectangle. |

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|Draw a rectangle on the board. Label the length 12 units and the width 4 units. Ask students to find the area. |

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|Identify students who cannot calculate the area of a rectangle and reteach the concept. |

|Whole-Class Instruction |

|Materials Needed: Different-sized circular lids or other circular objects, string, rulers, calculators, and grid paper |

|Procedure: |

|Presentation |

|Review the procedure for calculating the area of a rectangle. Then draw a circle on the board. Ask students to identify the circumference, the diameter, and the |

|radius, and ask how they might use this information to find the area of a circle. Accept all answers. |

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|Divide the class into pairs, or small groups, and provide each pair with at least five lids or circles of different sizes, a length of string, and a ruler. |

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|Use the string and ruler to measure the diameter and circumference of each circle and record it in a seven column chart: Lid ID; Diameter (d); Circumference (c); |

|c÷d; Estimated Area; Radius (r); and Radius Squared (r2). |

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|Ask students how many times bigger the circumference is than the diameter of each circle. (about 3 times bigger). |

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|Have each pair confirm that the relationship between the circumference and the diameter of each of the circles is the same, no matter the size of the circle. This |

|is a constant. Explain that this constant ratio between the circumference and diameter of a circle is a number called pi. Pi equals about 3.14 or exactly 22/7. A |

|circle’s circumference divided by its diameter is about 3.14 or 22/7. |

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|Write pi and its symbol ∏ on the board. Have students use a calculator to divide the circumference of each circle they worked with by its diameter, round the |

|number to the nearest hundredth, and record it on the chart. Confirm that the numbers are about the same. |

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|Guided Practice |

|Distribute several copies of grid paper. Ask students to estimate the area of each circular lid or paper circle they have. Encourage students to trace the circles |

|on the grid paper and count the number of squares that are inside the circle. Record the estimate. |

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|Students measure the radius of each circle, square it, and record the measurements in the chart. |

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|Ask how the radius squared and pi are related to the estimate of the area of the circles. (the area divided by the radius squared is about the value of pi, 3.14). |

|Have students test this relationship to show that it is true for all the circles. |

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|Have students write area of a circle = pi ( r2 as you write it on the board. |

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|Independent Practice |

|Present this problem: The rim of an NCAA regulation basketball hoop has a diameter of 18 inches. A regulation NCAA basketball has a maximum of 30-inch |

|circumference. Have students figure out how much bigger the circumference and diameter of the hoop are than the basketball. (Ball circumference: 30 inches; Rim |

|circumference: 56.52; Ball diameter: 9.554; Rim diameter: 18). |

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|At a carnival, a basketball game has a basketball hoop that is 14 inches in diameter. Have students write an explanation as to how that would affect the ability to|

|get a basketball through the hoop. |

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|Closing Activity |

|Ask students how they can find the area of a circle, if they know the radius. (Multiply the radius by itself and then multiply by pi). |

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|Ask student explain how to find the area of a circle if they know the diameter? (Divide the diameter by 2 to get the radius and multiply this number by itself, and|

|then multiply the result by pi). |

|Advanced Learner |

|Materials Needed: Internet access |

|Procedure: |

|Students research how Egyptian Eratosthenes correctly deduced the circumference of the Earth over 2,000 years ago. Have them investigate the Noon Day Project, |

|which replicates this calculation. |

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|Students present their findings to the class. |

|Struggling Learner |

|Materials Needed: A variety of balls (ping pong, golf, baseball, soccer ball, and so on), string, ruler, and calculator |

|Procedure: |

|Work with students to measure the circumference of each ball and then find the diameter and radius. |

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|Discuss the different purpose of each size and how changing the circumference and diameter would affect play. |

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|Students describe their results and explain their reasoning. Review and discuss their answers, and then allow students to complete the independent practice |

|activity. |

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