• Lesson
6-8
2

In this lesson, students learn how to measure the area of the tire footprint on a car and to find air pressure using a tire gauge. Students then find the weight of the car using their fraction multiplication skills.

In preparation for this lesson, place a car in a safe location for the students to measure the tire footprints and pressure. In case of bad weather, find a covered location. Be sure to measure the tire footprint and the pressure (in PSI) of each tire ahead of time, so that you will be able check the accuracy of students' measurements. Also, check the accuracy of your calculation by comparing to it to the weight of the car listed on the sticker inside the driver's door or in the vehicle manual.

By the end of the day, data may change because air has leaked out of the tires while students were using the tire gauge. For safety, check the tires before driving home.

The table below represents sample data from a 2002 Toyota Camry.

 Length of TireFootprint (inches) Tire Width(inches) Area of Tire Footprint(square inches) Air Pressurein Each Tire (psi) Calculated Weight Tireis Supporting (lbs) Driver-Side Front Tire 5 3/4 6 1/2 37 3/8 33 1233 3/8 Driver-Side Rear Tire 5 1/8 6 1/4 32 1/32 32 1025 Passenger-Side Rear Tire 5 1/2 5 3/4 31 5/8 34 1075 1/4 Passenger-Side Front Tire 6 6 1/2 39 32 1248

To introduce the lesson, discuss weight and pressure with the class. Ask, "Would it hurt more if a cat or a cow stepped on your toe? How much weight would be on your toe?" Have students speculate on why the cow hurts more than the cat. Lead the students into a discussion about pounds per square inch and distribution of weight on each of the animal's four feet. Ask, "What else is measured in pounds per square inch (psi)?" [Tire pressure.] Also, ask questions that might remain unanswered until the lesson is complete:

• About how much air pressure is in a car tire?
• How do you measure it?
• Would knowing the pressure in a car tire tell us anything about the weight of the car?
• Why do large vehicles have larger or more tires?

These questions are meant to generate a discussion that will perk the interests of the students before doing the activity. They will discover answers as the lesson proceeds.

Students may have learned in science that Pressure = Force ÷ Area. This means that pressure is a measure of how the applied force is distributed over an area. In our case, the force is the earth's gravitational force on the car (i.e., the weight of the car.) This weight is distributed over the ground by the surface area of the tire touching the ground.

Arrange the groups of four students so that there are multiple levels of students in each group. Give each student in the group a job:

• Recorder: records all information on the Activity Sheet and makes sure that each student completes their own Activity Sheet. Recorder is a good job for someone who has low math skills.
• Area Measurer: measures the footprint of the tire and reports information to the recorder
• Pressure Measurer: uses a tire gauge to measure the air pressure in each tire and reports the information to the recorder
• Multiplier: does the multiplication in the chart without a calculator.

All students in the group should assist each other when needed and verify accurate results on all measurements and calculations.

Have students answer the Questions 1 and 2 on the How Much Does a Car Weigh? Activity Sheet.

Give students directions for how to find the data for the table in Question 3. Explain that they will use two pieces of poster board to find the length and width of the tire's footprint. They should slide one piece of poster board in front and one behind the tire, or one on either side, to see where the tire is touching the ground. They need to be sure that the poster board is straight at both ends. Students will use a ruler to measure the distance between the two pieces of poster board. (See photo below.) Because using a tire gauge can be challenging, they should have have a second group member check the pressure before recording it. For calculating the area, they can assume the footprint is a perfect rectangle, and to find the weight that the tire is supporting, they can multiply the area of the footprint by the air pressure.

When all the measurements and calculations are complete, have students complete Question 4. Then, discuss as a class the actual weight of the car before having students complete Question 5.

Prompt students to review what they have learned with a question they must answer on paper before they can leave the class. The following are possible questions that could be asked.

What have you learned today about:

• Weighing cars?
• PSI?
• Using a tire gauge?
• Tire footprints?
• Distribution of weight?
• Multiplying with fractions?
• Anything else?

Other questions might deal with how the students worked together in groups.

What have you learned today about:

• Working as a team?
• Being responsible for your job?
• Helping others?

### Reference

Every Student Counts Problem Based Instructional Task

Assessment Options

1. Compare each students results on their How Much Does a Car Weigh? Activity Sheet to the actual weight.
2. Have students write a journal entry to explain how 30 pounds per square inch of air in your tires can hold up a car that weighs two tons.

Extensions

1. Have students explain how they could use this method to estimate the weight of a load of corn in a wagon. They should identify what information they would need to know.
2. Have students use the weight of a car as identified by a manufacturer to predict how much weight each tire supports.
3. Ask, "Have you ever been to a State Fair? At the 2008 Iowa State Fair, Freight Train, a boar, set a record weighing 1,259 pounds. How much weight would each leg would? How would Freight Train's legs compare to those of a 600-pound boar?"
4. Give the students the weight that a tire is supporting and each tire's air pressure. Have students work the problem backwards to find the area of the tire footprint and a reasonable length of tire footprint and tire width.

Questions for Students

1. If the tire pressure is low does the tire cover more ground or less? What is the shape of the part of the tire touching the ground?
[The tire is flatter so the area should be larger and more rectangular in shape.]
2. When the tire pressure is high does the tire cover more or less ground?
[More air would raise the tire up higher so the area touching the ground would be smaller.]
3. What happens if we keep adding air to a tire? Will it raise the car up or lower it down?
[Raise the car up.]
4. Is there a relationship between pressure and area?
[The higher the pressure the smaller the area touching the ground; the lower the pressure the larger the area touching the ground.]
5. Do you think there are other factors that would impact this relationship?
[Students may discuss that the weight is not equally distributed over the footprint area and the sidewall of the tire may be thicker than the middle.]
6. Why do we need to collect data from all four tires?
[The weight of the car is distributed over the four tires. For various reasons, each tire may not be supporting the same amount of weight.
7. Are there ways that you could more accurately determine the weight of the car to see how close your estimate is to the actual weight?

[Use the scale at an elevator, state troopers have a device that you drive a tire on to weigh the vehicle, scale at a weigh station, manufacturer information.]

Teacher Reflection

• If you teach this lesson again, what would you do the same? What would you change?
• Are there additional ways you could assess student learning related to this lesson?
• Are there ways you could better support students who struggled with this lesson?
• How did your lesson address auditory, tactile and visual learning styles?
• Did you make sure that the students had the necessary skills of measurement and multiplication with decimals before starting the lesson?
• Did you set clear expectations so that students knew what was expected of them? If not, how can you make them clearer?

### Learning Objectives

Students will:

• Estimate weight of a large object.
• Use a ruler and a tire gauge to take measurements.
• Collect and record data.
• Review square units of measure.
• Calculate area by multiplying fractions.

### NCTM Standards and Expectations

• Develop and use strategies to estimate the results of whole-number computations and to judge the reasonableness of such results.
• Understand, select, and use units of appropriate size and type to measure angles, perimeter, area, surface area, and volume.
• Select and apply techniques and tools to accurately find length, area, volume, and angle measures to appropriate levels of precision.

### Common Core State Standards – Mathematics

• CCSS.Math.Content.6.G.A.1
Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.

• CCSS.Math.Content.8.SP.A.1
Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association.

### Common Core State Standards – Practice

• CCSS.Math.Practice.MP1
Make sense of problems and persevere in solving them.
• CCSS.Math.Practice.MP4
Model with mathematics.
• CCSS.Math.Practice.MP5
Use appropriate tools strategically.
• CCSS.Math.Practice.MP7
Look for and make use of structure.