Gadget: Math Description

Hot Wheels: Linear Equations Pre-lab

The pre-lab is a review of y=mx+b, its properties, and what a linear graph looks like. The pre-lab has two parts: a demonstration and a discussion. In the demonstration, you will show how to use the Hot Wheels launcher to gather time and distance data. Time and distance data will be used to calculate average speed. Average speed will then be graphed. In the discussion, you will make sure students know how to calculate slope and transform the data gathered in standard equation form: y=mx+b.

Preparation:  The launcher that comes with the track kit requires little assembly. Just loop a rubber band around the pull-back mechanism and pop the bottom panel on.  The launcher is fairly self explanatory. There are four settings (one click is the slowest setting, four clicks is the fastest setting). Pull the launcher back any number of clicks, place a car in the chute, and push the launch button.  The track kits come with extra parts that will not be used. You simply need a straight section of track attached to the launcher.  You will need to set up the track in a hallway or clear desks out of the way in the classroom so students can see the track.  Use enough sections to create a track at least 15 feet long. Mark the finish line at 15 feet.  You may want to put an empty data table (as on the student handout) on the board in advance.

Demonstration:  Tell students that this is how they will be collecting data in the lab.  Get a couple volunteers to help with the demonstration (a launcher and a timer).  One student stands at the starting line with launcher, one student at the finish line with a stopwatch.  Do four runs, one for each setting of the launcher.  Use the same car for each run.  Tell the launcher to give a signal so the timer can start the stopwatch when the car is launched. For example, “Three, two, one, GO!”  Tell the timer to stop the stopwatch when the car reaches the finish line (15 feet).  Enter data into a table on the board as students copy the data onto their worksheets.

Hot Wheels: Pre-lab Teacher Notes Page 1 of 5

© 2004 The University of Texas at Austin and the GE Foundation The car will be launched four times. Record Time and Distance for each run. Then calculate Average Speed with this formula: Speed = Distance/Time.

Launcher Distance Time Average Setting (feet) (seconds) Speed (feet/second) 1 click 15 ft (given) 2.16 6.94 2 clicks 15 ft (given) 1.94 7.73 3 clicks 15 ft (given) 1.60 9.38 4 clicks 15 ft (given) 1.50 10

Sample data – your results may vary.

After filling in the data, move to the graph.  Ask student volunteers to graph at least two of the four speeds on the board or large grid paper while other students create the graphs on their worksheets.  Discuss correct scales and how to figure out what the best scale to use is. o Students sometimes have a lot of trouble setting up the graph to most effectively see the data. . Have students give some ideas about what the scale should be and try some out. . Instead of using just one piece of graph paper, have more than one up so after trying different scales, students can see what effects the different scales have on the look of the graph. o This is also a good time to begin discussing slope. . Point out that when the scale is different, the slope is the same, if you calculate is correctly. . Students sometimes forget to calculate slope using the correct intervals because they count each line on the graph grid as 1.  The graphs should be on the same coordinate axis.  We recommend graphing the data for settings 1 and 4 so there is greater difference between the slopes.

Time vs. Distance Graph ) t e e f (

e c n a t s i D

Time (seconds)

Sample graphs for settings 1 and 4.

Discussion:

Use the following questions to lead a discussion on the parts of a linear equation.

This is the standard form for a linear equation. y = mx + b

1. What does “b” tell you about the line?

The constant “b” is the y-intercept. It tells you where the line crosses the y- axis (vertical axis).

The constant “m” is the slope (or steepness) of the line.

3. If b = 0, what does the equation look like?

If b = 0, y = mx+b becomes y = mx

4. If you know the slope (m) and one point on the graph, how can you determine b?

Example: Given a point (2,8) and a slope of 3, b=2. y = mx+b 8=3*2+b 8=6+b 2=b

Add this line to the graph to show the y intercept.

5. Given two points on the graph, how can you find m?

Discuss the equation used to mathematically determine m from two known points: rise y  y m   2 1 run x2  x1

Pick two points and demonstrate calculating m.

Point 1 = (2, 3) Point 2 = (4, 9)

y  y 9  3 6 2 1   x2  x1 4  2 2 m  3

__1__ Click(s) __4__ Click(s)

Point 1 (0,0) Point 1 (0,0) Point 2  (2.16, 15) Point 2  (1.50, 15)

y  y 15  0 15 y  y 15  0 15 m  2 1   m  2 1   x2  x1 2.16  0 2.16 x2  x1 1.50  0 1.50 m  6.94 m 10

equation: equation: y = 6.94x + 0 y= 10x + 0

7. Compare the slopes (m) to the average speeds in your data table. Are they the same? Why?

Yes, because the slope of the line represents the speed of the car.