Student Teaching Observation Lesson Plan 5: Area and Circumference of Circles

Transcription

1 Lauren Clarke April 23, 2013 Student Teaching Observation Lesson Plan 5: Area and Circumference of Circles Objectives: 1. Students will understand what area, circumference, diameter, radius, chord, and π are. 2. Students will measure the diameter and radius of several circles. 3. Students will know the formulas for the area and circumference of a circle and will know how to use the formulas. 4. Students will apply their knowledge to find the area and circumference of several circular objects using different methods. Learning Styles: Visual/Spatial o Students will create a visual diagram of area, circumference, diameter, and radius. Physical/Kinesthetic o Students will use their hands and sense of touch to find the area and circumference of various circular objects. Verbal/Linguistic o Students will engage in whole class discussions as well as with their small groups. Logical/Mathematical: o Students will reason different methods for finding the area and circumference of circles and how to find the diameter and radius when provided the area or circumference. Social/Interpersonal o Students will collaborate as they work in pairs during the hands-on activity. Solitary/Intrapersonal o Students will work independently on the independent worksheet that reinforces the skills learned throughout the lesson. Materials: Area and Circumference of Circles packets (25) Pieces of string (12) Rulers (12) Bags of unit cubes (12) Calculators (25) Bowls (12) Red Cups (12)

2 Dixie Cups (12) Plates (12) Multicultural Component: The teacher will discuss the history of pi which began with the Babylonians and Egyptians who had rough numerical approximations of the value of pi. The teacher will also discuss how later mathematicians in ancient Greece, especially Archimedes, then improved these approximations of pi. Motivation: Students are motivated to learn by the hands-on activity. Students are motivated to learn by working in pairs where they can collaborate with one another and share ideas. Procedure: Students will complete the following Do Now activity: o What are the area and perimeter of the following shape?(rectangle with a width of 6 feet and a length of 8 feet) The teacher will go over the Do Now with the class and ask the students how they found the area and perimeter (area= 48 ft² and perimeter = 28 feet). The teacher will discuss the definitions for area and circumference from the students packets. The teacher will ask the students, How do you think we can find the circumference of the base of this circle? while presenting students with a circular bowl (measuring with string and a ruler). In pairs, students will find the circumference of the base of the bowl (method 1) using string and a ruler. The teacher will present the formula for circumference and explain what diameter, radius, chord, and π are, referring to the definitions in the students packets. As a class, students will label area, circumference, diameter, radius, and chord on the blank circle diagram in their packets. Pairs will measure the diameter of the base of the bowl and find the circumference using the formula (method 2). As a class, the students will discuss how the circumference found with the string compares to the circumference found with the formula. The teacher will ask the students, How do you think we can find the area of the base of this circle? while presenting students with the same circular bowl (using unit cubes). In pairs, students will find the area of the base of the bowl using the unit cubes. The teacher will present and explain the formula for area.

3 Partners will measure the radius of the base of the bowl and find the area using the formula. As a class, the students will discuss how the area found with the unit cubes compares to the area found with the formula. In pairs, students will find the circumference and area of the base of a red cup, the base of a Dixie cup, and a plate. Students will work on an independent worksheet once they have completed the partner activity. Summary: When all pairs have finished the partner activity the teacher will go over the areas and circumferences students found. The teacher will discuss how using the formulas for area and circumference are more accurate than measuring with string or estimating with the unit cubes. As a class students will go through question 5 on the independent worksheet. Students will work on the independent worksheet time permitting. The independent worksheet will be finished for homework. Evaluation: The teacher will observe students understanding of circumference and area of circles during the discussion at the beginning of the class about the different methods and new vocabulary. The teacher will observe students understanding of circumference and area of circles as they work in pairs on the hands-on activity. The teacher will collect and read students packets to check for understanding during the partner activity and independent work as well as reflect on his or her teaching practices.

4 Name: Period: Date: Area and Circumference of Circles Area: The amount of space inside the boundary of a flat (2- dimensional) object. Circumference: The distance around the edge of a circle, like perimeter. Diameter: A straight line going through the center of a circle conneceng two points on the circumference. Radius: The distance from the center to the edge of a circle. The radius is half the diameter. Chord: A segment conneceng 2 points on a circle. π (pi): The raeo of the circumference of any circle to the diameter of that circle regardless of the circle s size. π =

5 Find the circumference of the base of the bowl in inches: Method 1: Circumference = C = π d or C = π 2r C = circumference d = diameter r = radius Method 2: Circumference =

6 Find the area of the base of the bowl in inches: Method 1: Area = A = π r² A = area r = radius Method 2: Area =

7 Direc:ons: Find the area and circumference of the following circular objects using the formulas. Use your calculator s value of pi and round your answer to the nearest tenth. Measure in cenemeters or inches based on the item. Area: Circumference: Base of the Red Cup Area: Circumference: Base of the Dixie Cup Area: Circumference: Bo[om of the Plate

8 Name: Period: Date: Area and Circumference of Circles Homework Direc:ons: Find the area of each circle. Use your calculator s version of pi. Round each answer to the nearest tenth. Remember : C = π d and A = π r² radius = 2.6 in Direc:ons: Find the circumference of each circle. Use your calculator s version of pi. Round each answer to the nearest tenth radius = 11.1 \

9 5. You have a cookie with a circumference of 33 cenemeters. a) How long is the diameter? b) How long is the radius? c) What is the area of the cookie? 6. You have a round table with an area of 4 feet. a) How long is the radius? b) How long is the diameter? c) What is the circumference?