**Rate the Racers**

Cindy Boyd Anthony Ice Phyllis Slayton Barb Steinbrunner

**Class: ** Algebra I

Time Required: 1-2 days

Materials: Per group: toy car (Match Box or Hot Wheels type), meter stick or tape measure, stopwatch, race track pieces are helpful to guide cars and build launch ramps

Goal: Students will form a better understanding of the equation distance=rate*time while experimenting, solving for different variables in the equation, and making predictions from data collected about a specific car.

Background: Students need to know and be able to apply the equation d=r*t, as well as to chart and interpret data.

Setting: Students are to pair off (or form groups of three or four) and choose a toy car to simulate the soap-box derby racing trials. Distances are to be measured off, and car travel times recorded. With this information, students will determine the average rate the car travels. Using this same rate (as best as possible), students are to predict how long it will take their car to travel a specific distance, which is the length of the race.

Problem: Get-Up-'N'-Go Inc. is preparing to enter a car in the annual soap-box derby. The Get-Up-'N'-Go race team continues to hear rumors of the speeds of their competitors and are beginning to worry. This team cannot afford any expensive equipment but wants to know how the speed of their car compares. Perform some test runs and help the Get-Up-'N'-Go team determine their average speed. Once their average speed is determined, use this to predict how long it will take the Get-Up-'N'-Go race team to complete the race.

**Teacher Notes**: Allow students to determine their own test distances on flat surfaces, as well as how the cars are to be put in motion. Students are striving to achieve a relatively constant, measurable speed, so the method of starting the cars should always remain the same. Some examples are: giving the car a beginning push with a finger, starting off on a decline or ramp preceding the flat distance measurement, or using a plunger or motorized device. Having students use toy race track pieces will help keep the cars going in a straight path, allowing for more accurate measurement. Also, race track ramps could be used to begin the car movement, rather than building ramps of books or other materials. When using ramps to initiate car movement, the possible distance to cover is limited, so a maximum distance of a yard or meter (depending on the measurement system being used) is recommended. It is beneficial to choose cars that roll well enough to cover longer distances. If desired, students could be allowed to use electric race cars on a track.

The length of the soap-box derby is determined by the teacher, should not exceed the meter or yard length (unless using motorized cars), and is announced briefly before the testing of the predictions. Students are to calculate and announce the prediction, then individually test their car. It may be beneficial to allow up to three tests at this distance. If predictions are not coinciding with the actual race times, have groups, or as a class, discuss what could be influencing the actual race times as compared to the predictions (such as friction slowing the cars on the longer distances or having less effect over the shorter distances).

**Extensions**: If students are using motorized cars, have the students predict the winner from the various groups and simulate the soap-box derby. Perhaps a prize could be given to the winner or the most accurately predicted race performance.

Other objects, such as tennis balls, could also be used as test items, rather than the toy cars.

Students could estimate the speeds of passing cars by marking off a given distance and timing the passing of the vehicles. Can they catch anyone speeding?

**Evaluation**: Items to consider in evaluation include:

Assumptions

Data collected

Method(s) used in calculating average speed

Average speed

Description of prediction method

Sources of error

**Rate the Racers**

Get-Up-'N'-Go Inc. is preparing to enter a car in the annual soap-box derby. The Get-Up-'N'-Go race team continues to hear rumors of the speeds of their competitors and is beginning to worry. This team cannot afford any expensive equipment but want to know how the speed of their car compares. Choose your car, name it, and perform some test runs to help the Get-Up-'N'-Go team determine their average speed. Once the average speed is determined, use this to predict how long it will take the Get-Up-'N'-Go race team to complete the race. (The distance and location of the race are secret and will be revealed only moments before the start of the race.)

Accuracy is of utmost importance, and Get-Up-'N'-Go Inc. wants written justification of your prediction of the travel time necessary for the car to finish the race. Submit a report carefully detailing any assumptions made, data collected, the method(s) used in calculating the average speed of the car, the average speed, and the method by which the race length prediction will be made once the distance is revealed. Also include possible sources of error for your prediction.

*Funded in part by the National Science Foundation and Indiana University 1995*