## Geometry in Nature

### Kenneth BlackmanSanta Rosa District Schools

#### Description

The students will explore how the circumference, diameter, and the relationship of Pi of a circle are related. The students will also determine the age of a tree by counting the summer growth rings.

#### Objectives

The student knows the appropriate operation to solve real-world problems involving fractions, decimals, and integers.

The student solves and explains problems involving perimeter, area, and circumference.

The student measures length, weight or mass, and capacity or volume using customary or metric units.

The student selects appropriate units of measurement in a real-world context.

The student knows that measurements are always approximate and that the degree of accuracy of a measurement depends upon the precision of the instrument.

#### Materials

- String--1 foot per student
- Cut sections of tree limbs---2 to 6 inches in diameter and about 1/2 inch thick
- Rulers- 1 per student
- Paper
- Pencils

#### Preparations

1. Obtain sections of cut tree limbs.
2. Have needed material available for students.
3. Put the needed formulas on the board.( C= Pi * Diameter)

#### Procedures

1. Discuss with the students the different parts that make up a tree trunk and the seasonal growth patterns.
2.Hand out the cut tree limbs to the students.
3. Have the students determine the age of their trees by counting the summer growth rings.
4. Discuss the concept of circumference and how it is related to a circle.
5. Hand-out the string and the rulers to the students.
6. Have the students measure the circumference of their tree limbs using the string and the rulers. The students will wrap the string around the tree limb and use the ruler to measure the length of the string.
7. Have the students measure the diameter of the tree limbs using their ruler.
8. Discuss the concept of pi and how it is calculated. (Circumference/Diameter).
9. Have the students calculate pi using their measurements from the tree limbs.
10. Compare their calculated number for pi to 3.14.
11. Review the formula , C= pi * Diameter, and why it is not always practical to use string to measure the circumference of a circle.
12. Have the students calculate the diameter when only the circumference is known.
13.Discuss with the students why this is important when forestors measure live trees.
14. Have the students review this concept by working practice circumference problems on the board.

#### Assessments

The students will be assessed by teacher observation and class participation. The students will also be evaluated on the review board problems given at the end of the period.
An additional assessment: Students exchange their tree limb pieces with a partner and remeasure using the string and then the ruler. Each student calculates the diameter with the string measurement and then the formula measurement. Partners compare answers. Differences in measurement calculations should be discussed. Groups should be able to point out why the two partners have different measurements. (because of the measurement instrument used)

#### Extensions

This lesson could also be used to teach finding the area of a circle.