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Forums Grades Pre
K-2 Grades 3-5
Grades 6-8
Grades 9-12
Mathematics Governor’s Institute 2004
(Download as
Microsoft word document: Tennis Ball Lab.doc)
Names of group
members:
Danielle Retallack, Barb Lilley, Ray Brettle, Lawrence Lee
Topic/Theme: Data
Measurement and Statistics
Level: Pre-Algebra
Time
Element: 90 to 120 minutes
NCTM
Standards Addressed:
Measurement
Understand measurable attributes
of objects and the units, systems, and
processes
of measurement.
Apply appropriate
techniques, tools, and formulas to determine measurement
Data
Analysis and Probability
Analyze change in various
contexts analyze the nature of changes in
quantities
in linear relationships.
Formulate questions that can
be addressed with data and collect, organize,
and
display relevant data to answer them.
Select and use appropriate
statistical methods to analyze data
Algebra
Understand patterns,
relations, and functions
Use mathematical models to
represent and understand quantitative
relationships
Analyze change in various
contexts
PA Math
Standards Addressed:
2.1.8.D, 2.3.8.D,
2.6.8.F
Math
Assessment Anchors Addressed:
M 8.D.1.1, M 8.D.2.2, M
8.D.4.1, M 8.E.1.1, M 8.D.4.1
Reading
Assessment Anchors Addressed:
A 2.1, A 2.3, A 2.4, A 2.5
Objectives: To collect and display data in a
table and graph
To
analyze data and make predictions
To
enter data into the graphing calculator and display graphs
Instructional
Strategies and Plan (include strategies used to help different types of
learners, i.e. auditory, visual, etc):
Part One
Students will be broken up into random groups
of four.
The “waist height” – distance from each
child’s waist to the ground – will be measured in inches.
Hand out instruction sheet, and briefly
discuss directions.
Model activity.
Hand out tools. Students will perform
activity.
Procedures:
-Roles are assigned:
time keeper, counter, recorder, person bouncing ball.
-One
student begins bouncing a ball from waist
height while the timer
keeps time.
-The counter counts
as the ball is being bounced.
-At each ten-second interval,
the timer will call “time” and the counter will
call out the number of bounces.
-The recorder will
write this number down.
-For each ten-second
interval, the counter will start over.
-Continue bouncing
the ball for two minutes.
- When the two
minutes are up, the recorder will have to calculate the
cumulative number of bounces for each
interval.
-Roles will rotate to
each child.
-Once data has been
collected, students will graph the cumulative number
of bounces for each interval on centimeter
graph paper.
-Discuss results in
groups using the questions sheet.
Class will come together for discussion
What variables did you see in this activity?
What variables would affect the number of
bounces?
What do you predict would happen if you
bounce for 3 minutes, and why?
What if you bounced from shoulder height?
Does the initial position of the ball affect
the number of bounces?
Part Two
Pose question: Is there a
relationship between the “waist height” and number of bounces?
Hand out graphing calculators. Show students how to edit lists.
Survey each student for “waist height” and
cumulative bounces. The “waist height” (distance from each child’s waist to the
ground), will be measured in inches.
Enter data into lists.
Show students how to create scatter plot and
discuss any relationships.
Analyze class data using a different measure of central tendencies.
What is the range of total bounces?
What is the mean of total bounces?
Create box and whiskers plot of total bounces.
Materials/Resources:
Tennis ball, stop watch, graph paper, ruler,
graphing calculator, and TI-Presenter.
Interdisciplinary
Connections:
·
Reading
Reading directions
Vocabulary
Summarizing
Inferences and drawing conclusions
·
Technology
Graphing calculators
·
Other
Assessment
Strategies:
·
Formative
Evaluation (checking student understanding during the lesson):
Discuss questions after Part One.
Use participation strategy of pulling names out
of a hat to involve all
students in answering questions, or contributing to discussion.
·
Summative
Evaluation (How will it be determined that the objectives were achieved?):
Students will write a summary of the activity and discuss their findings as a closing activity. They will include their graphs and tables.
Correctives/Remediation:
Provide coordinate grid with axes labeled.
Work in groups when graphing.
Extensions/Enrichment:
Accelerated or gifted students will create a
formula that predicts the number of
bounces as a function of time, and a formula that predicts the number of
bounces as a function of height.
Discuss other activities that would result in
a linear function.
Create a histogram of class data.
Special
Accommodations (special needs students)
·
Description
of the Special Needs student selected:
Severe hearing loss
Language
comprehension and expressive skills – 4 years below grade level
Reading skills – 4
years below grade level
Above grade level in basic
math computation
Difficulty with work
problems and abstract concepts
Assistive listening
device
Difficulty with
lengthy verbal explanations
Needs visual
representation of information or process
No sign language
·
Accommodations
to use with this student:
-Have student’s group
work away from the rest of class, e.g., in hallway.
-Model the activity.
-Have student sit
near the front of the classroom during discussion.
-Include a peer in
the group capable of assisting this student.
-Use diagram of
graphing calculator and overhead calculator.
Closure
-Use summation
-Create a journal
entry
-Create their own
activity
BOUNCING
TENNIS BALLS
INSTRUCTION SHEET
1. Assign roles for timekeeper,
counter, recorder, person bouncing the ball.
2. Begin bouncing the ball when
the timer says, “go”.
3. The counter starts counting
when the timer says, “go”.
4. Every ten seconds the timer
says “time” and the counter will call out the number of bounces.
5. The recorder writes down the
number called by the counter on the data table.
6. After the timer calls “time”
the counter starts counting from one again.
7. After 2 minutes the timer
says, “stop”
8. The recorder then calculates
the cumulative number of bounces.
9. Rotate roles and repeat
steps 1-8.
Name____________________ Date_______________ Teacher_______________
Bouncing Tennis Balls
Time Number
of Bounces Cumulative Number
(seconds) during Interval of Bounces
0 __________ ___________
10 __________ ___________
20 __________ ___________
30 __________ ___________
40 __________ ___________
50 __________ ___________
60 __________ ___________
70 __________ ___________
80 __________ ___________
90 __________ ___________
100 __________ ___________
110 __________ ___________
120 __________ ___________
Name____________________ Date_______________ Teacher_______________
Bouncing Balls Worksheet
After completing the activity and recording your data on your graph, answer the following questions.
1.
What variables did you see in this activity?
2.
What variables would affect the number of bounces?
3.
What do you predict would happen if you bounce for 3
minutes and why?
4.
What if you bounced from shoulder height?
5.
Does the initial position of the ball affect the
number of bounces?
How To Create Enter Data into Lists on your Graphing Calculators
Turn your calculator ON. Press
STAT
You should get a menu with
the Edit option already selected.
Press the blue ENTER
key.
Make
sure your lists are cleared. To do this,
use the up arrow so that the list title is selected.
Then press CLEAR and
then ENTER.
Enter you data in each
column. If you have two lists of data,
use L1 and L2.
Now that you have your data
entered.
How To Create a Scatterplot on Your Graphing Calculator
Press 2nd and Y=
Then press ENTER.
Make sure you have the On
option selected.
Check to see if you have the
scatter plot option selected. It looks
like this
Make sure it says L1
for Xlist and L2 for Ylist.
If it doesn’t, put the
cursor at Xlist and press 2nd and 1.
Put the cursor at Ylist and press 2nd and 2.
Press the ZOOM button
and press 9.
To turn your calculator off
press 2nd and ON.
How To Create a Box and Whiskers Plot
Press 2nd and Y=
Then press ENTER.
Make sure you have the On
option selected.
Check
to see if you have the box and whiskers option selected. It looks like this 
Make sure it says L2
for Xlist.
If it doesn’t, put the
cursor at Xlist and press 2nd and 2.
Press the ZOOM button
and press 9.
To turn your calculator off
press 2nd and On.
Name____________________ Date_______________ Teacher_______________
Bouncing Tennis Balls
About Your Scatter Plot
Sketch your scatter plot in
the box below.
Label your axes in the
spaces provided. Don’t worry about the
numbers.
What can you say about
“waist height” and number of bounces.
Name____________________ Date_______________ Teacher_______________
Bouncing Tennis Balls
About Your Box and Whiskers
Plot
Sketch your box and whiskers
plot in the box below.
On your sketch label the:
minimum value ________
median ________
maximum value ________
What is the range of number
of bounces? ________
Calculate mean number of
bounces? ________
Are the mean and median the
same value? If not why?
Name____________________ Date_______________ Teacher_______________
Bouncing Tennis Balls
Enrichment and Extension
1. Write
a mathematical sentence that tells how you can figure out the number of bounces
based on the time that has gone by?
Example: You multiply the number of tacos by $1.30 to
get the total price.
2. Write that mathematical sentence as a formula?
No
words, use mathematical symbols.
3. Write a formula that tells how you can figure out the number
of
bounces
based on height.
4. List other activities that result in a linear pattern.
5. Use the
table below to make a histogram on your graphing calculator that shows the
frequency of bounces.
Class
Data
|
Range |
Frequency |
|
Below 100 |
|
|
101-125 |
|
|
126-150 |
|
|
151-175 |
|
|
176-200 |
|
|
Above 200 |
|
|
|
|
Name____________________ Date_______________ Teacher_______________
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