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Susan Koppenol Lesson Title: Hotwheel Races Grade Level: Algebra I or 8th Grade Length: Two Class Sessions Topics Covered: Data Collection, Linear Equations, Measurement, Predicting from Graphs

OVERVIEW:

In this lab students will conduct an experiment involving acceleration and distance travelled to collect data and produce a line of best fit. From the line of best fit, the student will derive the equation of the line and use the equation to make predictions.

EXPECTED OUTCOMES:

student will accurately gather and record needed data
graph the data collected to produce a line of best fit
find the equation of the line of best fit
use the equation of the line to answer questions and make predictions

BACKGROUND INFORMATION:

the concept of acceleration and the factors that affect distance travelled
use of the measurement device, whether in inches or centimeters
independent and dependent variables
graphing points in the x,y coordinate plane
finding the equation of a line given a point and a y intercept

MATERIALS:

one matchbox car per group of two students
6 books per group (to raise the height of the ramp)
one ramp per group (made of heavy cardboard, at least 8 inches wide and 15 to 22 inches in length)
one sheet of graph paper per student
one measuring device per group
activity sheets - one set per student

OBJECTIVES:

Producing a line graph from a given set of data (D.1)
Finding a line of best fit
Finding the slope and y-intercept of a linear equation
Finding the linear equation in standard form and slope intercept form
Using a measuring device (in standard or metric forms) (M.3)
Using a graph or function to make predictions (A.5)
Graphing points in the x,y coordinate plane (A.3)

LESSON ACTIVITIES:

Teacher starts lesson with a demonstration of an object rollling down a hill, varying the height of the hill, then discussing as a class what affects the distance the object will travel.

Students should then copy and complete prelab questions individually and then discuss as a whole group. Make sure the concept of independent and dependent variables is clear.

Hand out all activity sheets and graph paper to all students, discuss the instructions for the lab, and that all experiments should be completed by the end of the class period. The next class period will be devoted to graphing the data and answering post lab questions.

Assign students to groups of two. Each group should collect one measuring device, one matchbox car, and one ramp. Each group should bring with them at least six textbooks to be used during the experiment. Try to space the groups apart as much as possible.

Teacher circulates among the groups to assure they are engaged and answer questions if needed.

The next class period should be devoted to each group working together to graph the data collected, producing a line of best fit, and finding the equation of the line. Although, students are working as a group, each student should have a completed lab packet to turn in.

At the end of the second day, discuss as a whole group the results of the experiment. Discuss the slope and y intercept of the line and what each represented in terms of the experiment. Was the line of best fit a good predictor for further results, or was there a point that it could not be used with respect to the length of their ramps.

As a conclusion, have the class list all the concepts covered both in science and math. Construct a concept map linking the two disciplines together.

Evalution of the activity can include: the cooperative groups and the lab packet and graphs.

EXTENTIONS:

Use of the graphing calculator
Predicting trends from other graphs
Non-linear equations
Using functions to make predictions

REFERENCES:
Algebra I Experiments Book by Addison-Wesley

PRELAB QUESTIONS:
1.    What is acceleration?
2.    How can the steepness of a hill affect the distance that an object will travel?
3.    What does independent and dependent mean?

ACTIVITY SHEETS: LAB- HOTWHEEL RACES

Group Members:

Date: Hour:

1. Objectives: Data Collection, Measurement, Problem Solving, Linear Equations,
Graphing, Cooperative Learning.

2.     Instructions:
         a. Gather materials needed.
         b. Start with one book, set the ramp so that one end is on the edge of the book
            and the other is on the floor. Place the car at the top of the ramp and allow the
            car to roll by itself down the ramp and onto the floor.
         c. Measure the height of the book and the distance the car rolled from the end of
            the ramp. Measure in a straight line and measure to the back of the car.
            (Measure to the nearest 1/2" or 1/2 cm.) Record the data.
         d. Repeat the experiment. Record the data.
         e. Repeat the experiment for 2, 3, 4, 5, and 6 books. Perform each experiment
            twice.

3. What materials did you use:

4. The independent variable is: , measured in: .

5. The dependent variable is: , measured in: .

Height of Book(s) Distance Travelled -
Trial 1 Distance Travelled- Trial 2 Ordered Pairs to be Graphed

1.

2.

3.

4.

5.

6.

6.   Instructions:
     a. Once you have gathered all the data, determine the points to be graphed.
           Use the longest distance in each trial for the dependent value.
     b. On the graph paper, make a rectangular coordinate system and graph
          the points. Be sure to label the axes with an appropriate scale and label
          the graph.
     c. Using at least two of the points draw the line of best fit. It should be a
          straight line.
     d. Answer the following lab questions.

POST LAB QUESTIONS:

1. Identify two points on the line of best fit ( , ) and ( , )

2. Using these points find the slope (m) of the line.

3. Identify the y-intercept (b) of the line.

4. Using the slope and the y-intercept, write the equation of the line in

a. slope-intercept form:

b. standard form:

5. What does the y intercept mean in terms of the experiment? Is it an accurate
value for the experiment?

6. What does your slope value mean in terms of the experiment?

7. How far would the car travel for a ramp height of 5 1/2"?

8. How high does the ramp need to be for the car to travel exactly 30"?

9. How high does the ramp need to be for the car to travel exactly 200"?

Height of Book(s)	Distance Travelled - Trial 1	Distance Travelled- Trial 2	Ordered Pairs to be Graphed
1.
2.
3.
4.
5.
6.