     Home | Overview | Frameworks & Standards | Lesson Plans | Student Handouts | Student Work Samples | Resources & References | Comments Perimeter, Area, and Circumference
 Discovering Pi    Overview of Lesson: The students will be using Microsoft Excel to organize and analyze the data they collected in Lesson Five. On a spreadsheet, the students will organize their measurements of radius, diameter, and circumference they recorded in the previous lesson. After all of the data for the circles is listed, the students will use the formula function to calculate pi for each circle. When all of the pi values have been calculated, the students will average their pi values to see if they can come close to the actual value of pi. The average will also be calculated using the formula function in Microsoft Excel.

Standards:

Measurement:

(See Standards Link for Complete Standards)

Number Sense and Operations- 6.N.13

Patterns, Relations, and Algebra- 6.P.4

Measurement- 6.M.5

Data Analysis, Statistics, and Probability- 6.D.1

Technology:

(See Standards Link for Complete Standards)

Basic Operations and Concepts- 1.1, 1.3, 1.4

Social, Ethical, and Human Issues- 2.4, 2.5

Technology Productivity Tools- 3.2

Technology Productivity Tools- 4.1

Technology Problem-Solving and Decision Making Tools- 6.1

Student Outcomes: By the end of this lesson, the students will create a spreadsheet using their information from Lesson 5. The students will be able to find the value of pi, using the function tool, and dividing the circumference by the diameter. The students will also be able to take what they learned from their spreadsheet and calculate pi and area of their circles.

Lesson 6 of 9

Length of Lesson: 1 Hour

Instructional Mode: Independent Activity

Multiple Intelligences: Logical-Mathematical, Visual-Spatial, Intrapersonal

Essential Questions:

How does the diameter relate to circumference?

Does the circumference increase as the diameter increases?

What is pi? Where did pi originate?

How do we use pi to then calculate the circumference and area of a circle?

Materials/Resources Needed:

1. Computer Lab
2. Microsoft Excel (or equivalent spreadsheet program)
3. Worksheet from Lesson 5

Instructional Strategies/Procedure:

1. The students will open a new spreadsheet in Microsoft Excel.
2. In cell A1, type "Circle Number." Press Enter.
3. In cell B1, type "Diameter (in)." Press Enter.
4. In cell C1, type "Circumference (in)." Press Enter.
5. In cell D1, type "Pi." Press Enter.
6. Click on "3" on the left side of the page. The entire row should be highlighted. Set this row to size 12, bold, and centered.
7. Adjust the column width so that the titles fit in the column. To do this put the cursor between "A" and "B" at the top of the page until a double arrow appears. Click and drag the arrow to the right until all of the text is visible. Column A is now the appropriate size. Do the same for columns B, C, and D.
8. Type the numbers 1 through 8 in the appropriate cells under circle number. (Example - A2 should be 1, A3 should be 2, etc.)
9. Using their worksheets from the "Measuring Radius, Diameter, and Circumference" lesson, students will type the values corresponding with the circle number in the cells for diameter and circumference. Be sure to enter all the values for all of the circles.
10. Highlight all of the cells where you entered the data. Change the size to 12 and center the text.
11. Click the cursor inside cell D2. In the formulas bar at the top of the page, type "=C2/B2". Hit "Enter." This will take the Circumference for circle one and divide it by the diameter for circle one. The resulting number will be the value for pi. This value will appear in cell D2 if entered correctly.
12. Click the cursor inside cell D3. In the formulas bar at the top of the page, type "=C3/B3", hit "Enter." Continue using this formula modified slightly each time for the remaining circles.
13. In cell C12, type "Average Value of Pi." Press Enter.
14. Move the cursor to cell D12. Click on the formula tool in the toolbar (Fx). When a new window opens, double click on the Average function from the menu. Another window will come up. You must edit this formula so that it reads "=Average(D2:D9)", Press Enter.
15. The average value of pi received should be somewhere close to the actual value of pi (3.14).
16. Have the students type their names somewhere on the spreadsheet before printing.
17. Once all of the spreadsheets are printed, discuss what the students received for their average value of pi and discuss why it may or may not be exactly the value of pi.
18. Collect all of the spreadsheets for evaluation.

Example Spreadsheet:

 Circle Number Diameter (in) Circumference (in) Pi 1 8 25.25 3.16 2 27 84.75 3.138889 3 5 15.75 3.15 4 3.5 11 3.142857 5 12 37.5 3.125 6 8.75 27.5 3.142857 7 2.25 7 3.111111 8 6 19 3.166667 Average Value of Pi 3.14

Assessment: The spreadsheets can be collected and analyzed for assessing the students' knowledge with Microsoft Excel. The average value of pi that they received should also be analyzed. The discussion following the activity will lend itself as a good evaluation of the learning that occurred throughout the activity.

Evidence that Student Learning Occurred: The students' average value of pi should be relatively close to the actual value of pi if the activity was successfully completed and their measurements were accurate. The students should also be able to analyze their value of pi and be able to discuss the reasons why their value for pi may not be exact (human error).

Technology Skills Required or Developed: The students must have some prior experience with using Microsoft Excel or an equivalent spreadsheet program. The teacher must also know the program and be comfortable teaching other children how to use the basic functions of the program.    Student Work- Discovering Pi