Lesson Plan # 19 - The Circle

  1. (5 min) Mental Math
    1. Start with 23, double it, then subtract 7 [39]
    2. If x equals 8, what is 4x + 6? [38]
    3. What is 40% of 60? [24]
    4. Multiply 20 by 80 [1600]
    5. Multiply 20 by 800 [16000]

  2. (5 min) Review of homework #18 (<= 3 problems)

    Recommended materials for this lesson:
    1. A coffee can, felt tipped marker and masking tape
    2. As many calculators as you can obtain, to compute circle measurements that are decimals. One calculator for every 2 students is sufficient.
  3. (10 min) Introduce the circle:

    1. Draw a circle on the board and explain radius, diameter and circumference. Identify them with the letters "R","D" and "C". Show that the diameter is twice the radius. Use the equation
      D = 2R
      .
    2. Estimate using a coffee can and masking tape:
      1. Using scissors, cut a length of masking tape equal to the diameter. You may want to practice this beforehand to get this accurate.
      2. Remove the tape from the top of the can and place it around the can. Explain that the number of times the diameter goes around is the ratio C/D. Mark it's start and end points with a felt tipped pen. Move the tape around the can, marking it's end each time with the pen. Have the students count the number of times you do this.
      3. You should end up with 3 diameters plus a little bit left over.
        • Explain that this is the famous number , (pronounced "pie").
        • Write it's value down to 6 digits: 3.14159...
        • Explain that the digits go on forever and do not repeat.
        • Explain that we will use the approximate value 3.14 for our calculations.
      4. Write this equation on the board and explain it:
        C = D
      5. Pass out the circle notes at this point and briefly go over it. This is a repeat of the information you have already covered, except for the area of a circle. Give students the formula for the area of a circle:
        A = RR or ...
        You may use
        A = R2
        if students are familiar with squares.
      6. Work the examples at the bottom of the circle notes. If time permits, have students work additional examples with the following parameters:
        • Radius = 3 feet
        • Radius = 5.5 cm
        • Diameter = 8 in


  4. (Remainder of class) In-class Exercise.

  5. Hand out homework as students successfully complete the in-class exercise.
Note:
The explanation of the area of a circle on the back of the circle handout is for information purposes only. Do not present it to the whole class. It's purpose is to answer the question of an inquisitive student:
"Why is the area of a circle R2?"