# Srinivasa's Spheres

Exercises in working with circles and pi.

Adapted from an original project of Alisa Martines

#### by Miriam Garcia and Dana Tunison

CA Mathematics Standards Alignment
Algebra and Functions 3.1
Measurement and Geometry 1.1, 1.2
Mathematical Reasoning 1.0
Number Sense 1.2
Mathematical Reasoning 1.0
Algebra I 1.0, 4.0, 25.0

Students use real-world objects to understand the concept of a constant such as pi. Pi is used in conjunction with using the formulas for the circumference a circle. The students apply their knowledge of pi to a real-world application.

#### DUTIES:

2. The Scribe records all data on the data sheet.
3. The Listener measures all the items listed; asks the teacher questions from the group.
4. The Materials Manager uses the calculator to make necessary calculations.

#### MATERIALS:

1. 1 tape measure
2. 5 different objects to measure
3. 1 globe
4. 4 pencils
5. 1 calculators
6. Data Sheet

#### DIRECTIONS:

##### Part I
1. The listener picks first item to measure.
2. Measure around the edge of the item using the tape measure; use the centimeter side of the tape measure. This is the CIRCUMFERENCE of the circle.
3. Scribe records this measurement on the data sheet.
4. Look for the black dot on the bottom of the item. Measure across the item from one edge to the other passing through the black dot. This is the DIAMETER of the circle.
5. Scribe records this measurement on the data sheet.
6. Materials Manager uses the calculator to divide 1st measurement (CIRCUMFERENCE) by 2nd measurement (DIAMETER).
7. Scribe records this result.
8. Repeat steps 1 to 7 for the other four items.
9. As a group, answer the questions found below your chart in the data sheet.
10. Listener gets Part 2 sheet of paper; proceed with work.
##### Part II
Challenge Problem: Use the globe, tape measure, and apply what you learned from Part 1.
If a tunnel is dug directly from the North Pole to the South Pole, how long will this tunnel be? Express your answer in miles.

(Scale: 1 cm = 200 miles )

(Note: Algebra 1 & A students must come up with an equation.)

EXPLORE:

PLAN:

SOLVE:

EXAMINE:

#### PRODUCT:

1. Completed Data Sheet and Part 2 paper.
2. The Scribe checks off the station on the recording sheet.

#### CLEAN-UP:

1. Put the tape measure, the 5 objects, the pencils, the calculator back in the basket.
2. Place Data Sheet and Part 2 paper in the group folder.