## Speeding by the Numbers

### Ryan StokesSanta Rosa District Schools

#### Description

Students determine speed (velocity) by running/walking a given distance and dividing the distance by the time it took them to do so. This lesson involves measurement and number sense, concepts and operations, and can be easily modified into a science lesson.

#### Objectives

Adds, subtracts, multiplies, and divides real numbers, including square roots and exponents using appropriate methods of computing (mental mathematics, paper-and-pencil, calculator).

Relates the concepts of measurement to similarity and proportionality in real-world situations.

#### Materials

-A measured distance on the school track or parking lot (50 yards=150 feet or 100 yards=300 feet)
-1 stopwatch (or a digital watch capable of stopwatch functions) per group
-Student copies of the Activity Flow Chart & Directions worksheet (See Associated File)
-Student copies of rubric (See Associated File)
-Simple 4-function calculators (at least 2 per group)

#### Preparations

1. Have the distance to be used already measured and marked off either at the school track or in a safe and secure area in the school parking lot.
2. Have enough stopwatches available to give at least one to each group.
3. Have worksheets and rubrics (See Associated File) duplicated and available to hand out with a few extras.
4. Have enough calculators available to give at least a couple to each group.
5. If the weather does not permit this experiment to go on outdoors, ask if the gymnasium can be used.
6. Know the speeds of other objects such as a car, bicycle, cheetah, etc. for students to compare their own average speeds to later.

#### Procedures

1. Ask who the fastest student is in the classroom and at what speed they can run.

2. Challenge the students that you are faster if you feel up to a challenge. (THIS IS OPTIONAL.)

3. Ask the students to divide themselves into small groups (3-4 students per group).

4. Tell the students they will be given a certain distance (50 yards=150 feet or 100 yards=300 feet) to travel by running or walking.

5. Make sure each group of students has a stopwatch or digital watch to measure time. If they do not, then supply them with one.

6. Tell the students that one student per group must travel the specific distance (either by running or walking) while another student in their group measures and logs the time it took them to travel that distance.

7. Repeat this procedure until every student has participated by running or walking.

8. Instruct each student to divide the distance they traveled by the time it took them to do so. This determines their average speed. Remember to tell them to keep up with the units they are measuring. If they are measuring distances in feet, then the answer should have feet in it, not yards or inches. Time should be measured in seconds so the final answer should have second in it.

9. Pass out worksheets and rubrics (See Associated File) that describe the step-by-step process of how to conduct the activity. Work an example problem on the board and give plenty of opportunities for students to ask questions if they do not understand.

10. Write your average speed in the final column. Determine the average speed of all group members.

11. Ask students to compare the average speed data that they found on themselves with speeds of other moving objects. (You will need to gather some data, or make it up, but it needs to be realistic. For example, average car speed=55 MPH, average bicycle speed=9 MPH.)

12. Tell students to compare/contrast their speeds to objects such as a car, bicycle, cheetah, etc. Help them convert their speed to miles per hour to see how they would match up to a car and the other objects given.

13. Show them how to create a ratio to see the proportionality of their average speed to the speed of the other objects. Allow time for students to do the calculations and have a quick discussion and demonstration of the ratios. Ask if there are any questions.

#### Assessments

Each student is given a worksheet, Activity Flow Chart & Directions, which describes step-by-step procedures to complete the task. (See Associated File) Flow charts assure students are following each step of the procedure in the correct sequence. Observe students' work to make sure worksheets are filled out properly.

Calculations are formatively assessed for accuracy. Calculations will vary from student to student. Average speed calculations will depend on how well the student measures time with a stopwatch.

A rubric pertaining to this lesson is included in the associated file along with the Activity Flow Chart & Directions worksheet.

Proportions are reviewed by the instructor to see if they are relatively accurate. The entire benchmark will not be assessed due to lack of addition, multiplication, square root and exponent procedures.

#### Extensions

1. This exercise can easily be adapted to a science or physics lesson. Ask students what they now know from the change in an initial velocity of standing still to an average velocity of what they calculated. How does this acceleration compare to that of the acceleration of gravity?

2. Modifications can be made to this lesson to include science topics such as acceleration, force, work and power. Some of these topics would require changes to be made to the worksheet found in the associated file. Information such as mass would need to be known and formulas for force, work and power would have to be discussed.

#### Attached Files

This file contains the Activity Flow Chart & Directions worksheet and the rubric.ĀĀĀĀĀFile Extension: pdf