v = d/Δt     Average Speed     Velocity     Distance      

1. The students will follow the procedures to conduct an experiment and record their data accordingly.
2. The students will apply their knowledge of average speed being the total distance traveled by an object divide by total time by using the speed equation to accurately calculate the average speed of their car.
3. The students will accurately graph their data using the distance and time interval data as well as include labels for each axis on the graph as well as title their graph.
4. Based on the experiment and their graphs, the students will accurately describe the relationship between the elevation of the ramp and the speed of the car.  (The slope of the line on a distance-versus-time graph varies as speed changes; steeper slopes represent faster speeds).
5. The students will complete word problems to apply their knowledge to real life situations.
6. The students will think about and discuss what happens to the speed when the distance or the time increases.

One 50 minute period

Each pair of students needs the following:

• 1 Ramp 4’ x 1’ (can be made of Plywood)
• 1 meter stick
• Masking Tape
• Coats, Rags or other items to act as a cushion for the bottom of the ramp
• 1 Car (a bigger car such as one used for Little People works best)
• Textbooks used to elevate the ramp
• A stopwatch
• Graph paper
• Lab Sheet (see below)
• Pencil
• Calculators
• Colored Pencils
• Enough Red and Green cups for one per partner group

Students will learn a variety of skills such as conceptual understanding of data collection, graphing, and how to interpret data as well as procedural knowledge of how to organize and graph the data as well as make predictions.  In addition to the core standards, this lesson includes problem solving, reasoning and making connections.  The lesson can be adapted and enhance to meet the needs of all learners.  All instructional adaptations are marked with a yellow highlighter for below level learners and green highlighter for advanced level learners/enhancements.

** Before beginning the activity, use the pre-assessment below to establish which type of learner each student is.  In order to give the teacher ample time to assess learning, this pre-assessment should be administered the day before the lesson begins.

Advanced level learners will be able to complete all tasks accurately graphing and answering all questions in full, complete sentences with 90% accuracy.  Mark these papers with a triangle.

On level learners will be able to complete the questions and accurately graph the information but may not be able to find the slope of the line (75% accuracy). Mark these papers with a Circle.

Below level learners may need help graphing and answering questions.  They may be able to find the line of best fit, but not always.  Finding the slope of the line will need to be explicitly taught, and is not a skill yet acquired. Mark these papers with a star.

1.  Think-Pair-Share Quick Review:  Have students answer the following questions, then go over as a class.  (This will be prior knowledge that needs to be taught prior to this lesson.  It is included in a handout below).

1. What two pieces of information do you need to know about an object in motion in order to determine the speed?  Distance traveled and time in motion
2. What is the definition of speed?  The distance traveled in a unit of time
3. What is the symbol for speed?  v
4. What units are used to describe speed?  Give an example. 

Distance/unit of time such as miles per hour

1. What is the equation for calculating speed?  v = d/Δt
2. If you know an object is traveling at 45 kilometers per hour, how can you determine how far it will go in ten hours?

                                         d = v X Δt = 45 x 10 = 450 kilometers

2.  Turn and Talk:  Suppose you wanted to figure out how fast a bicycle was going.  How would you go about it?  Come up with a specific problem solving procedure and make sure you include all of the steps.  Have groups share their procedures and determine which one is the best.  It should be:

• Establish a starting position, x_i
• Establish an ending position, x_f  (This establishes distance)
• Time how long it takes for the bike to travel the distance from x_i to x_f
• Use the speed equation to calculate the average speed.  v = d/Δt     

3.   Tell the students, in order to determine an object’s speed, we need to measure the distance the object moved, and we need to measure how long it took to move that distance.  We know how to measure distance-we use a meter tape.  So how can we measure the time it takes for an object to move?  Have the students brainstorm things we can use to measure time.

4.  Go over how to read a stopwatch.  Hours, minutes, seconds and 100^th of a second.  Then have the students practice using the stopwatches. 

• Have them stop the stopwatch close to 1 second
• With their eyes closed, have them try to stop it at 5 seconds, etc  . .

5. Introduce the experiment.  Tell the students that they are working in groups to answer the following questions:

• How long does it take your car to travel 200 cm ramp?
• What is your car’s average speed as it travels 200 cm down your ramp?

For below level learners (stars) you can sit them all together, so if you need go over the lab procedures step by step and answer any questions  they will be sitting in proximity .

6.  Give the students the lab sheet. Have the students (triangle and circles) work in pairs to independently set up the experiment by reading the directions in their lab sheet.  Assist if necessary.   For below level learners, go over procedures for the experiment. Show the students the ramps and how to set it up. Also make sure the students are putting jackets at the end of the ramp in order to stop the car safely.  Also, hand out the lab rubric to remind the students how they will be graded while working in groups.  You may want to go over this specifically if you feel it necessary depending on your students.

7.  Divide your students into teams of four and assigned each group an elevation in multiples of 4 cm if you have eight groups, up to 32 cm.  If you have fewer teams you can use multiples of 5 cm. 

8.  After the students properly set up their ramps, have them time several runs with their car as it travels 200cm down the ramp and record it on their lab sheet.

As students are working, you can have green and red cups sitting on the desks.  If students are successfully working their way through the lab, they should have the green cup on top.  If they have a question or get stuck, instruct the to put the red cup on top and continue to try and figure out the problem, you will be around shortly. Since partner groups will be working at varying paces, there are natural stops in the lab.  When a partner group comes to that stop, they should also put the red cup on top so that I can formatively assess their accuracy up to that point in the lab.  Pairs can continue to analyze until teacher makes it around to every pair.

9.  When all groups are finished, gather the students and ask the following questions of the class:

• Did your car travel the same speed the whole run?
• How fast was it going in the beginning?  (0 cm/s)
• How fast was it going in the middle of the run?  At the end?  (Can’t tell)

10.  Tell the students that it’s difficult to know how fast an object is going at any specific time because speed changes all the time.  It is not constant.  To get around this problem, we can use the object’s average speed to determine how fast it was going.  If we know how far something went, and how long it took, we can calculate the object’s average speed.    Average speed is the total distance divided by the total time needed to travel the distance. 

11.  For example, if I recorded times for three runs down a 10 cm ramp of 2.52 s, 2.66 s and 2.62 s, I would add them up and divide by three to find the average speed.  So 2.52 + 2.66 + 2.62 = 7.80 s.  Then divide 7.80/3 (or the number of runs) which equals 2.60 s; that is our average speed.

12.  Back in their groups, have the students calculate the speed for each run, then calculate the average speed of their car.

13.  Once the average speed for each elevation is calculated, have one speaker from each group share the data with the other groups.  Each group needs to record the average speed for each elevation in their data table.

14.   Finally, have the students graph the results, labeling their graph. (Time on the x-axis, Distance on the y-axis). F

For below level learners give them graph paper already labeled and numbered for them.  Graph the data together as a class. 

15.  After graphing the students should answer the following questions, which car went the fastest?  Which car traveled the slowest?  How do you know?  What is the relationship between elevation and speed?  (The steeper the slope the faster it goes/greater the speed).  Go over these answers as a class and discuss.

For below level learners complete this as a class with guiding questions such as what does the graph look like? What can you tell from the line?

To enhance this lesson for advanced level learners let them analyze the data on their own or with their partners without any guiding questions.  Then have them write a paragraph in complete sentences to describe the results.

16.  Ticket Out the Door:  (See handouts below)

1. A biker rode up a 20 km hill in 2 hours and down the hill in .5 hour without stopping.  What was his average speed
   1. going up hill?  v = d/Δt = 20 km/2 h = 10 km/h
   2. going down hill? v = d/Δt = 20 km/0.5 h = 40 km/h
   3. for the whole trip?  v = d/Δt = 40 km/2.5 h = 16 km/h

       2.   When looking at a graph for speed, how can we tell who is going the fastest

                                The steeper the slope, the greater the speed

For below level learners help with the set up of this problem.  Give them the equation and help them fill it in if necessary.  Guide them through problem solving by identifying the known, unknown, set up the equation and then have them solve. This will help them when looking for speed or other unknown variables. 

                   Known:

                   Unknown:

                   Equation:

                  Solve/Work:

• Upon completion of this activity, below level learners will be able to calculate the average speed of their car, graph data and describe the relationship between elevation and speed.  Given a graph, they will also be able to pick out which car is going the slowest and which is going the fastest based on the slope of the line. 
• Regular education learners will be able to calculate the average speed of their car, graph data and describe the relationship between elevation and speed.  Given a graph, they will also be able to pick out which car is going the slowest and which is going the fastest based on the slope of the line.  They will also be able to complete word problems to apply their knowledge to real life situations.
• Enhanced or advanced level learners will also be able to calculate the average speed of their car, graph data and describe the relationship between elevation and speed.  Given a graph, they will also be able to pick out which car is going the slowest and which is going the fastest based on the slope of the line.  They will also be able to complete word problems to apply their knowledge to real life situations, as well as think about what happens to the speed when the distance or the time increases.

See below.  The first lab sheet is for below level learners (star), the middle for regular education students (circle) and the last is enhanced for advanced level (triangle) or gifted students.  The rubric below the lab sheet will be used to evaluate the lab and how well the students work together during the activity.

How Fast Did It Go Speed Pre-Assessment.docx
How Fast Did It Go Quick Review.docx
How Fast Did It Go Lab Sheet - Star (Below Level Learners).docx
How Fast Does It Go Lab Sheet - Circle (On Level Learners).docx
How Fast Did It Go Lab Sheet - Triangle (Above Level Learners).docx
How Fast Does It Go Lab Rubric.docx
How Fast Does It Go Ticket Out The Door.docx