Fairview/Kansas City Middle School of the Arts – Kansas City Missouri School District
Group Members: Shari Gamache, Sharon Hayes, Natalie Lewis, Chris McTighe
Major concept:
Understanding patterns, relationships, and function
Grade Level: 7th
Missouri Standards:
Grade 7: GLE Algebraic Relationships – A1B7
Grade 7: GLE Algebraic Relationships – A3A7
Grade 7: GLE Algebraic Relationships – A4A7
KCMSD Curriculum Objectives:
Grade 7: Objective: Analyze patterns represented graphically or numerically using words or
symbolic rules
Grade 7: Objective: Model and solve problems using graphs and tables
Grade 7: Objective: Compare situations with constant or varying rates of change
Overview:
In this lesson, students will create and analyze graphs. Students will be able to compare and
decipher constant and varying rates of change represented in the graph. Students will be able to
apply knowledge to real-life examples.
Background:
 Basic graphing skills – creation and analysis
 Speed and time
 Increasing versus decreasing rate of change
 Understand and following directions
 Working in groups
 Understand the difference between constant and varying rates of change
 Basic graphing vocabulary: plot, TAILS, constant, varying, rates of change
Common student misconceptions:
 That the intervals for the x and y-axis are always the same
 That on a speed vs time graph, all flat lines mean no movement
 That you can read a graph from either left to right or right to left
 That faster speed is better than constant even if inconsistent
 That intervals don’t have to be evenly spaced.
 That the scale has to go up in increments of one.
 That all graphs start at zero.
Student Objectives:
1. The student will be able to analyze patterns represented graphically or numerically using
words or symbolic rules.
2. The student will be able to model and solve problems using graphs and tables.
3. The student will be able to compare situations with constant or varying rates of change.
Module Activities:
Activity 1 - Pre-test Assessment
Activity 2 - Elicitation - Read Aloud and Discussion – Tortoise and The Hare
Activity 3 - Development - Geometric Shapes/Perimeter Activity
Activity 4 - Assessment: Journal Summary Activities 2 & 3
Activity 5 - Development - PET Cycle 1 – Activity 4 Simulator
Activity 6 - Development – Volume/Height Activity
Activity 7 - Development – Savings Problem
Activity 8 - Assessment: Activities 5 & 6
Activity 9 - Consensus (Review Assessments given in Activities 4 & 8)
Activity 10 - Post-test Assessment
Materials:
 Chart paper
 Markers
 Color pencils
 One computer or Smart Board
 Rice
 Tablespoons
 Computers with Internet Access






Pet Simulator
Pattern Blocks
Graph Paper
Graduated cylinders (5)
Wide beakers (5)
Centimeter Rulers
Time Required:
7 – 45 minutes class periods
Assessment Tools:
Journal Entries
Group Presentations
Performance based
Cite References:
Pet Simulator Website - http://cpucips.sdsu.edu/petsims/
http://dese.mo.gov/divimprove/curriculum/mathexamples/algebra7index.html
Glencoe Mathematics Series
Activity 2
Tortoise and Hare (Elicitation Activity)
Alternate Activity – PET Cycle 1 (page 1-2)
Materials:
Chart paper
Markers
Book
Read story aloud or ask kids to recap story.
On your own, try to think of two different ways to visually represent the speed of the tortoise
and two different ways for the hare. You can use pictures, symbols, charts, diagrams or graphs.
Place students into groups of 3-4.
With your group, share your ideas. Listen to your group members’ ideas and try to agree on
one representation that best shows (displays) what happen to the speed of the tortoise and that of
the hare. (You should have a visual for each, one for the hare and one for the tortoise. Illustrate
these representations on chart paper. Each group will present their representations.
With the whole, discuss the various ideas shared. Analyze patterns represented graphically or
numerically using words or symbolic rules
Activity 3
Development - Geometric Shapes/Perimeter Activity
Materials:
Pattern blocks
Graph paper
Color pencils
Use 4 different pattern blocks. Start with 1 shape and then add 1 block at a time, making a row
with the shapes in a straight line. Identify perimeter of the new figure. Gather data, then plot
findings on graph paper. When finished do you see a pattern? If so explain.
Square
# of Squares
Perimeter (inches)
Triangle
# of Triangles
Perimeter (inches)
Trapezoid
# of Trapezoids
Perimeter (inches)
Hexagon
# of Hexagons
Perimeter (inches)
Activity 4
Assessment: Journal Summary Activity 2&3
Look at your graphs for Activity 3. Predict what the graph would look like for an 8-sided
polygon. Describe where this graph would fall relative to the others. Is there a shape that when
plotted, would give you a horizontal or vertical line? Explain your answer.
Compare your graphs from Activity 3 with the visual representation from Activity 2. What were
the differences and similarities between the two? Explain in details.
Activity 5
Development - PET Cycle 1 – Activity 4 Simulator
Materials:
 Computer monitor
 Pet Simulator Website - http://cpucips.sdsu.edu/petsims/
You are no doubt familiar with the idea of friction and its effects in slowing down and stopping
moving objects. Will it be easier to ride a skateboard on a wood floor, grass or pebbles? Predict
below how each surface will impact your speed.
What will your speed be like on the wood floor (no friction)? ____________________________
______________________________________________________________________________
______________________________________________________________________________
What will your speed be like on the grass (rough)? ____________________________
______________________________________________________________________________
______________________________________________________________________________
What will your speed be like on the pebbles (very rough)? ____________________________
______________________________________________________________________________
______________________________________________________________________________
Now, let’s use the simulator to see if your predictions are correct.
Let’s see what impact different road surfaces will have on speed versus time graphs. How will
the rates of change be impacted?
Step 1: Go to http://cpucips.sdsu.edu/petsims/. Double click on Cycle 1 – Activity 4 Setup
Step 2: To change the surface, first click on the rewind key, and then click on the selection tool
(arrow). Next double click on the picture of the cart, to change the surface. Select the
first surface type (no friction, rough or very rough).
Step 3: Press play to start the simulation. Sketch and label the speed time graph below.
Step 4: Repeat step 2 and 3 for the other surface types.
Speed of Skateboard vs Time
Discuss what the speed versus time graph would look like for a very, very rough surface. Sketch
and label this graph on the graph above.______________________________________________
______________________________________________________________________________
______________________________________________________________________________
For which surface was there no change in speed?_______________
How did this graph look in comparison to the others (steeper, vertical or horizontal)?__________
______________________________________________________________________________
______________________________________________________________________________
Which surface has the fastest rate of change? ______________
How did this graph look in comparison to the others (steeper, vertical or horizontal)?__________
______________________________________________________________________________
______________________________________________________________________________
Activity 5 Assessment - Rubric
Completeness
Accuracy
Evidence
3
Explanation
provided for all
three questions.
Answer is written
clearly and shows
logical reasoning.
Correctly identify
all three graphs
represented
All parts of
answer are
supported by
stating
information from
the graph.
2
Explanation
provided for two
questions. Answer
is somewhat clear.
1
Explanation provided
for one question.
Answer is unclear and
difficult to understand.
Correctly identify
two graphs
represented.
Part of the answer is
supported by
information from
the graph.
Correctly identify one
graph
represented
Answer is not
supported by
information from the
graph.
Activity 6
CPU Graphing Activity A1: Representing Volume vs Height
Materials:
Wide cylinder
Slim cylinder
Flask
Chart for data
Rice
Graph paper
Tablespoons
With your group: For each container shown below, add one tablespoon of rice and record
height. Repeat four times, recording height after each tablespoon. Then create a graph that will
best represent the volume versus height of rice. Discuss how you develop each graph and
especially how the graphs compare. In what ways are some similar and in what ways are they
different? How are the characteristics alike and different?
Slim Cylinder
Wide Cylinder
Volume(V) of
rice in container
(# of TBS)
Height(H) of
rice in the
cylinder
(cm)
Height to
Volume ratio
(H,V)
Flask
Volume(V) of
rice in container
(# of TBS)
Height(H) of
rice in the flask
(cm)
Height to Volume
ratio
(H,V)
Volume(V) of
rice in
container
(# of TBS)
Height(H) of
rice in the
cylinder
(cm)
Height to
Volume ratio
(H,V)
Activity 7
Development – Savings Problem: Constant versus Varying Rates of Change
Materials:
Chart paper
Markers
Problem:
Randy puts $5 per week in a savings account and continues to do this every week.
Susan puts $1 in a savings account the first week and then saves twice the amount saved the
previous week.
1. Complete the tables for the total amount saved by Randy and Susan at the end of each
week.
RANDY
Week
1
2
3
4
Total Saved ($)
5
10
15
20
Week
1
2
3
4
Total Saved ($)
1
3
7
15
5
6
7
8
5
6
7
8
SUSAN
2. Will Randy always have more in savings than Susan? Are both Randy and Susan saving
at a constant rate? Justify both your answers using graphs.
Activity 8 Assessment
1. We have three students riding a motorized scooter, all of equal build and model. Each rider
will be on a different type of surface. John will be on a wood floor (no friction), Mary on
grass (rough), and Kate on small pebbles (very rough). Below are three speed-time graphs,
identify which graph best represents each student. Explain your selection.
Graph A best represents __________________Explanation: _____________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
Graph B best represents __________________Explanation: _____________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
Graph C best represents __________________Explanation: _____________________________
1. ___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
_________
Activity 8 Assessment - continued
2. Tyrone started a savings account with $2. In week two, Tyrone put $5 in his savings
account, week three $11, week four $23. If the pattern continues each week, which graph
below best represents the relationship between the number of weeks saved and the total
amount saved?
Amount in Savings
B.
Amount in Savings
A.
Number of Weeks
Amount in Savings
D.
Amount in Savings
C.
Number of Weeks
Number of Weeks
Number of Weeks
Describe what is happening in the graph you selected.
__________________________________________________________________
__________________________________________________________________
__________________________________________________________________
__________________________________________________________________
__________________________________________________________________
Activity 9
Consensus (Review Assessments given in Activities 4 & 8)