## Flying With Mathematics!

### Kenneth BlackmanSanta Rosa District Schools

#### Description

Students fly miniature airplanes to discover characteristics related to velocity and average speed. After measuring the time and distance, the students calculate the speed and average velocity.

#### Objectives

The student applies formulas for finding rates, distance, time and angle measures.

The student solves single- and multi-step linear equations and inequalities that represent real-world situations.

#### Materials

- Wooden flying airplanes with rubber band propeller
- Tape Measures
- Stop Watches
- Data Chart (See Attached File.)
- Review Worksheet (See Attached File.)
- Group Evaluation Form (See Attached File.)

#### Preparations

1. Run Copies of review sheet for each student.
2. Run Copies of Data Sheet for each student.
3. Acquire 15 sets of airplanes.
4. Acquire 15 stop watches or watches.
5. Acquire 15 tape measures.
6. Copy Group Evaluation Forms (3 per group).

#### Procedures

Day One:

1. Discuss the speed of a SR71, (2100 miles per hour), and how long it would take to travel across the United States. Also discuss the history of aviation and the connection to mathematics.

2. Review the formulas related to distance, rate, and time. Work an example of each formula presented below.
Distance = Rate * Time
Time = Distance / Rate
Rate = Distance / Time

3. Model to the students sample problems of each type of formula. For example, “If the rate of 55 miles per hour and the time of 6 hours is given, what is the distance traveled?”

4. Have students work through the review worksheet, “Solving Rate Problems.” Instruct students to work in groups of two. Each student will be held accountable for the review sheet. Circulate around the room and use questioning techniques to check for understanding.

5. Review with the students concepts learned throughout the class period. Instruct selected students to come to the board and explain to the class how the problems are calculated.

Day Two:

1. Review with the students formulas covered from the day before. Allow students to work examples and explain their answers.

2. Group all students in to groups of two. Allow students to select a partner or the teacher can assign partners.

3. Take students outside to fly airplanes. Give the students the procedures for the activity before they begin flying the planes.

4. Have one group member measure the time the plane remains in the air, while the other member launches the plane. Then, have the students measure the distance the plane traveled using the measuring tape.

5. Instruct the students to measure the time and distance traveled four times and record the information on the data chart. Circulate around the flying area to insure the data is recorded in the correct place on the data sheet.

Day 3:

1. Review formulas related to rate, time, and distance. Instruct selected students to come to the board to work example problems. Allow them to explain their answers to the class.

2. Instruct the students to calculate the velocity from the data chart. Circulate around the room to check for understanding.

3. Discuss the concept of average speed as related to central tendency measures. Demonstrate to the students that the average speed is the mean of the velocities collected. Give several examples of how to take a set of numbers and find the mean.
Mean = The sum of the numbers in the set / The number in the set

4. Instruct students to calculate the average velocity from data collected on the data chart. Circulate around the room to insure the student's understand of the concepts. Use questioning techniques with each group to check for understanding.
-How is the word -mean- related to the average speed?-
-How do you find the average for the list of numbers?-
-Explain to me the formula for finding the average for a set of numbers?-

5. Select one member from each group to share the average velocity they calculated.

6. Discuss variables that would cause a difference in average velocity (wind speed, direction, friction, etc.).

7. Instruct students to evaluate other members of their group using the evaluation form. The teacher will also fill out an evaluation form on each student and the scores will be combined.

#### Assessments

Evaluate data sheets for completeness and understanding.
Evaluate review sheets for correctness. 70% of the students will make 80 or higher on the review sheet as documentation of student understanding.
Calculate the average velocity and question students to determine level of comprehension.
Record scores from group evaluation forms.

#### Extensions

This lesson contains science standards related to Physics concepts and could be used as an interdisciplinary unit between the math and science department. This lesson also contains social studies concepts related to the history of flight. The information collected in the data chart could be graphed using a broken line or bar graph.