Speed/Graph Module
By
Sherry Rich
Jennifer Morgan
Niki Evert
Allen Staley
John Leimer
Ken Presley
Chris Buehre
Craig Ericks
Speed/Graphs Module
Major concepts covered
1.
2.
3.
4.
Measuring Speed
Time and Speed Graphs
Calculating Speed
Graphing
Grade Levels
7th and 8th
Missouri Standards
ST2/1/A/c,d
The motion of an object is described as a change in position, direction, and speed
relative to another object (frame of reference)
c. Given an object in motion, calculate its speed (distance/time)
d. Interpret a line graph representing an object’s motion in terms of distance over time (speed)
using metric units
Module Overview:
Students will have previously completed a unit in scientific method and metric
measurement. Leading them up to this module which starts with graphing a skill needed
to collect data during scientific investigations. Students will then investigate speed time
graphs when an object’s speed changes. Students will then participate in activities that
will help them understand the concept of distance and time and calculating the speed of
the object. After the module students in 7th grade will investigate Newton’s three laws of
motion. 8th grade students will use the graphing skills in a variety of scientific
investigations.
Student Objectives:
Create a line graph representing an objects motion.
Interpret a line graph representing an objects motion.
Background:
The more force that is added the faster the objects speed will change. The slope of
the line will be steeper if more force is added and the speed will change at a higher
rate.
When force is added to an object such as the cart the
object will speed up as long as the force is being
added.
When an objects rate of speed decreases the
line on the graph will go down
When traveling at a constant speed the line on
the graph will be horizontal
This graph shows an objects
A speeding up
B going at a constant rate
C slowing down.
B
A
C
Websites:
http://library.thinkquest.org/C0110840/speed-time.htm
http://www.a-metrics.com/graphing.htm
http://unlhepcl.unl.edu/cl/141/lecture2/index.html
Sources:
PET Curriculum
Background information for constructing a graph:
Purpose – a graph shows relationships between two variables. With this activity the
focus is on making a graph using the acronym TAILS. The acronym is intended to help
guide students in constructing graphs. T stands for title, A for axes, I for intervals, L for
labels, and S for spacing. The title needs to include the relationship between the two
variables (example: speed vs. time). For A, axes, ensure that two axes are present, one in
the positive x direction and one in the positive y direction. Normally the x-axis is known
as the independent variable and the y-axis contains the dependent variable. With
intervals, I, it is expected that students make increments of equal length. Here also we
look for the scale to easily include the minimum and maximum value on both axes. L for
labels – both axes need to be labeled with the variable itself and the units used to measure
them.
Finally, S, spacing, it is expected that students use their entire space given so the graph is
easily read.
Common problems with graphing: Students entering middle school can usually construct
a bar graph, but not a line graph. Students do not always realize they are supposed to see
a relationship between two variables. Also, students do not always pay attention to the
units of measure used on a graph.
Materials :
Changing speed graphs Activity
Cart
Track
Several Wood Blocks
Go Motion Sensor/Computer
Colored pencils
Lab Sheet
Graphing Activity
Quiet foam pattern blocks
Lab Sheet
Graph paper
Calculating Speed
Marbles
Ruler
Stopwatch
Markers
Masking tape
Lab sheet
Time Requirements:
All activities and Assessment will take about 6 class periods (45 mins x 6)
Pre/Post Assessment 45min (1 class period
Changing Speeds Graph Activity 4-5 45min class periods
Graphing Perimeter Activity 45 mins (1 class period)
Assessment Tools:
Pre/Post Inventory-see attached
SPEED / GRAPHING ACTIVITY
Elicitation:
How could you represent motion involving speeding up, slowing down, and constant
speed?
Initial Ideas:
Imagine you were riding your bike to school. You push off to start moving and then
pedal to get up to a reasonable speed. You begin to coast at a constant speed. As you
enter the school parking lot, you apply the brakes and come to a stop. How could you
represent the motion of your bike throughout your trip to school?
On your own, think of 2 different ways to represent each part of your journey (speeding
up, cruising at a constant speed, and slowing down). Be creative! You may use pictures,
arrows, diagrams, graphs, symbols, etc.
In groups of 3-4 students, discuss your ideas. Choose the best two ideas to put on the
white board. You will be describing your ideas to the class.
Discuss as a class.
Activity #1: How does a speed-time graph represent speeding-up and slowingdown?
Background Information:
A line that slopes up to the right indicates speeding up, while a line sloping down to the
right indicates slowing down. The steeper the line of the graph, the faster the rate of
change. Knowledge of how to use the Go Motion Sensor. You also need access to
Logger Pro 3.4.5. These lessons and activities should take 4 to 5 45 minute class periods.
Curricular Link: Interpret a line graph representing an objects motion.
Missouri Standard 2/ 1/A/ a,b,c,d
Misconceptions:
Some students will have trouble generating a straight, horizontal line for constant speed
due to misconceptions about friction.
Name
Hour__________
Activity: Perimeter Graphing
Purpose:
In this activity, students will form relationships between different geometric
shapes and perimeter size. Students will then complete data tables and graph their
information.
Materials:
Quiet pattern blocks with all 1 inch sides:
6 triangle shapes
6 square shapes
6 trapezoid shapes
6 hexagon shapes
Step 1:
Lay out one triangle block. Count the number of sides which is a measure of the
perimeter. Record in data table.
Step 2.
Add one triangle block next to the first block. Count the number of exposed sides and
record in data.
Step 3.
Continue to add triangles one at a time in a straight line counting the number of exposed
sides and record.
Step 4.
Repeat above procedure using the square and record.
Step 5.
Repeat using the trapezoid and then hexagon.
Data Tables:
Triangle
# of
triangles
1
2
3
4
5
6
# of
exposed
sides
Square
# of
squares
# of
exposed
sides
1
2
3
4
5
6
Trapezoid
# of
# of
trapezoids exposed
sides
1
2
3
4
5
6
Hexagon
# of
hexagons
# of
exposed
sides
1
2
3
4
5
6
Graphing:
On graph paper, construct a line graph for each table using a different color. Be sure to
include a key.
Remember to include all parts of TAILS to double check that your graph is complete.
Name: ________________________________________
Hour: _________
Purpose: To interpret a graph when an object is speeding up, slowing down, or
remaining at a constant speed.
Materials:
Cart
Track
Several Wood Blocks
Go Motion Sensor
Colored pencils
Procedure for Experiment #1:
1. Open Cycle 1, Activity 1 in the Motion Sensor files on your computer. This will
open to a blank speed-time graph.
2. Place the motion sensor on the track.
3. Place one wood block under the track at the sensor end to raise the track.
4. Place the cart about 20-30 cm in front of the sensor and release it. DO NOT
PUSH IT!
5. After practicing this 5 times, record the speed-time data with the Motion Sensor.
6. Sketch the graph below.
? Explain how the graph showed your cart was increasing in speed.
?
Predict how your cart would behave if you added a second block of wood on top of
the first. Do you think your cart would speed up in exactly the same way, or would it
behave differently? If you think it will behave differently, how would this show on the
graph? Explain your reasoning.
7. Draw your prediction in the graph below.
8. Run the cart with the second block of wood under the sensor end. Collect the
data. Using a different colored pencil sketch the line on the graph above. Label
each of the lines.
?
How did adding the second block of wood change your speed-time graph? Show
evidence to support your answer.
9. Remove the two blocks of wood from under the track. Place one of the blocks
under the opposite end of the track, making it tilt in the opposite direction.
10. Place the cart 20-30 cm in front of the motion sensor. Practice giving the cart a
quick push away from the sensor (your cart will be moving uphill).
?
Predict how you think the speed will change as it moves along the track, AFTER the
initial push. Explain why you think the graph will look this way.
? Now sketch your idea, including the initial push, on the graph below.
11. Imagine now that you have added the second block under the first block of wood,
under the track. Predict what you think will happen to the speed of the cart on the
graph above. Mark each line, one block and two blocks.
12. Now run the motion sensor for one block, then run it for two blocks. Be sure to
sketch each line on the graph below. Mark each line, one block and two blocks.
?
Do your predictions match the actual data? Give evidence to support your answer.
Procedure for Experiment #2:
Predict what the graph would look like if the cart were traveling at a constant speed for a
period of time. Sketch your idea on the graph below. Give evidence to support your
answer.
1. Your task is to try and make the cart move at a constant speed. You are allowed
to use the wood blocks and/or a manual push to make this happen. The cart needs
to be moving at a reasonably constant speed for a short period of time.
2. Use the motion sensor to record your data. Sketch the line on the graph above
using a different color pencil. Label each line as prediction and actual.
3. Place a circle on the actual line where the speed of the cart is constant.
4. What strategy worked best for your group to achieve constant speed of the cart?
Name: _________________________________
Hour: _________
MOTION ACTIVITY – MOTION CHALLENGES
Materials:
Motion Sensor
Meter stick
Activity: This is an activity where you will be the object that moves away
from the motion detector. You will be “challenged” to match your
movement to that which is drawn on the each of the three challenge
graphs. In each of the three challenges, it is very important that you work
with your group to PREDICT your movements before you actually try it.
1. Open the file that says “Motion Challenges.” Then open the first activity
labeled “Logger Pro_ Act I-A1_MLB.2.” Look at the graph, notice the
axes, and predict your movement. Write down on the graph below what
you will do to match this graph (i.e. move at constant speed, rest, etc)
2. Now test your predictions. Try to match the graph as carefully as
possible. Keep trying until you get it as close as possible. Please print
out your results. Compare your walk to the challenge line and write down
any places where you deviated and WHY. Discuss results with your
group.
3. Repeat steps 1 with “Logger Pro_ Act I-A1_MLB.3.”
4. Compare your walk to the challenge line and write down any places where
you deviated and WHY. Discuss results with your group.
Racing Marbles
Name: ____________________________________
Hour: _________
Problem: What effect does the height of the track have on the speed of the marble?
Hypothesis: ____________________________________________________________
________________________________________________________________________
_______________________________________________________________________.
Experiment:
Materials:
book
ruler
marble
chalk
stopwatch
calculator
Independent Variable: _____________________________________________________
Dependent Variable: ______________________________________________________
3 Constant Variables: _____________________________________________________
Control Group: __________________________________________________________
Experimental Group: _____________________________________________________
Procedure:
1. Mark a starting point on the floor with the chalk. From the starting point measure a
distance of 100 cm. This will be the distance for all three trials.
2. Make an incline by placing one end of the ruler on the starting point and the other end
on a book. The incline will be directed toward the distance mark.
3. Place a marble at the top of the incline and let it accelerate down the ruler.
4. Begin timing the marble when it reaches the starting point.
5. Time how long it takes until the marble crosses the 100 cm mark.
6. Repeat 2 more times.
7. Find the average time and record in your data table.
8. Repeat steps 2 through 7 for two books and three books.
Trial 1
One book
Two books
Three books
Trial 2
Trial 3
Average Time
Calculate Speed
Using the average times for each distance, calculate the speed of the marble. Show all of
your work using the formula and correct units below.
Distance
Average Time
Speed
One Book
Two Books
Three Books
Explain the relationship between the height of the ramp and the speed of the marble?
Give evidence to support your answer.
Create a bar graph showing the relationship between the height of the track and speed.
Conclusion: My hypothesis was ___________________ because __________________
_______________________________________________________________________
_______________________________________________________________________.
Summary Questions: Comparing Changes in Speed
You have seen how speed – time graphs can be used to represent motion of an object. It
is also useful to be able to compare the motion of two objects.
Below is the graph of speed vs. time for two separate objects.
1. Compare the speed of the carts in the two runs on the graph above. Explain your
thinking.
2. John said the cart had a higher speed in Run 2 than in run 1. Do you agree or
disagree with his statement? Give evidence to support your answer.
3. Sally said the cart started out with a higher speed in run 1, but ended up with a
higher speed in run 2. Do you agree or disagree with her statement? Give
evidence to support your answer.
4. Joe said the cart sped up more quickly in run 2 than it did in run 1. Do you agree
or disagree with his statement? Give evidence to support your answer.
5. What is different about the way the two carts sped up at the beginning of the two
runs? What do you think caused this difference?
6. Using the graph above describe the behavior of the speed of the object represented. In
your explanation, describe how you came to this conclusion by looking at the graph.