mathematics senior level capstone course unit...
TRANSCRIPT
UVA-SCPS Office of Mathematics Outreach with support from VADOE Mathematics and Science Partnership Grant Program NCLB Title II Part B
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Mathematics Senior Level Capstone Course
Unit Overview
Title of Unit:
PEEPS! Unit Designers:
(Name and School Division)
Mikhail Balachov (Arlington)
Su Chuang (Loudoun)
Mirela Geagla (Arlington)
Hunter Hagerty (Loudoun)
Kiera Poplawski (Loudoun)
Debora Strickler (Loudoun)
Edited by Diane Leighty, UVA-SCPS Office of Mathematics Outreach
Context:
Summary of the
issue, challenge,
investigation, or
problem.
Design one level of the video game, Angry Birds, and create mathematical
models to simulate the most effective and efficient method of completing this
level of the video game and hitting all your targets.
Number of Class
Hours:
Estimated 10 hours Unit Design:
___Task Based
_X_Project Based
Other Subject
Areas/Disciplines
Addressed:
Physics, Career and Technical Education, Writing
Driving Question:
How can you design a mathematical model to maximize the chances of hitting a target?
Mathematics
Content Addressed:
Quadratic Functions, Distance Formula, Projectile Motion, Pythagorean
Theorem, Right Triangle Trigonometry MPE
Addressed:
Problem Solving,
Decision Making,
and Integration;
Understanding and
Applying Functions
Assumption of Prior
Knowledge:
Understanding Quadratic Functions, basic right triangle trigonometry,
College and Career
Readiness/21st
Collaboration E Research
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Century Skills to be
taught (T) during
this unit or
expectation (E) for
student use during
this unit and
assessed (A):
BIE Page 35-37
Communication (Oral and/or Written): E, A Technology: Students will use Texas
Instruments’ CBR: Calculator Based
Rangers to model quadratics.
T
Critical Thinking/Decision Making E, A Other: (Describe)
Major Products
and/or
Performances:
Group – Design of a level in Angry Birds, Efficient Mathematical
Model simulating the completion of one level of Angry Birds,
Presentation of a real world application of quadratics.
Presentation Audience:
X Class
School
Individual – Mathematician’s Journals – prompts about
quadratics, applications, misconceptions of parabolas representing
path of objects.
Expert
Community
Other:
Launch: Event or
experience used to
engage the students
interest and inquiry:
Students will play several levels of the Angry Birds game (if available) or a free version of a similar game, Angry
Animals. http://hoodamath.com/games/angryanimals.php
The objective of the game is to hit various “targets” using a slingshot and an animal as a projectile. Students can identify
the “targets” on each level before releasing the projectiles in order to complete each level.
Evaluation: Formative Assessments
(During the Unit)
Interview X Practice Presentations
Mathematicians Journal X Notes
Preliminary
Plans/Outlines/Prototypes
Checklists
Rough Drafts X Concept maps
Field Tests X Other:
Summative Assessment
(End of Project)
Written Products, with a rubric X Peer Evaluation, with a
rubric
X
Oral Presentation with a rubric X Self Evaluation, with a
rubric
X
Other Product(s) or Performance(s),
with a rubric
X Other:
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Resources Needed: On-site people, facilities:
Facilitator/Teacher
Equipment/Technology:
Computers with Internet Access, Calculator Based Rangers (CBRs), graphing calculators,
Logger pro, which may be software available through the science department.
If CBRs are not available, a loaner set can be requested for free from Texas Instruments if
requested one month ahead of time. For more information, visit the following website:
http://education.ti.com/educationportal/sites/US/nonProductSingle/global_forms_loan.html
Logger pro is a data collection and analysis software. For this unit, Logger Pro will be used
to capture video of a projectile in motion and the data collected for analysis. If the software
is not available, a free 30-day trial is available for download at:
http://www.vernier.com/products/software/lp/
Materials:
Grid Chart Paper, graph paper, Ball (for CBR Activity)
Community Resources:
None
Reflection Methods: Individual, Group,
and/or Whole Class
Mathematicians Journal X Small/Focus Groups
Whole Class Discussions X Fishbowl Discussions
Survey Other:
Material Adapted From: NASA: http://search.nasa.gov/search/edFilterSearch.jsp?empty=true
Texas Instruments: http://education.ti.com/calculators/downloads/US/Activities/
Hooda Math: http://hoodamath.com/games/angryanimals.php
Template adapted from Buck Institute for Education: Project Based Learning for the 21st Century
UVA-SCPS Office of Mathematics Outreach with support from VADOE Mathematics and Science
Partnership Grant Program NCLB Title II Part B
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Virginia’s Senior Level Capstone Course
Instructional Plan
Unit Title: PEEPS!
Driving Question: How can you design a mathematical model to maximize the chances of hitting
a target?
Project: Design one level of the video game, Angry Birds, and create mathematical models to simulate
the most effective and efficient method of completing this level of the video game and hitting all of the
targets.
ENGAGE
How will
student’s
interested be
peaked so they
want to engage
in the inquiry
in this unit?
Number of
hours _1___
Begin this project by familiarizing students with the Angry Birds
game. This game can be downloaded onto iPods or iPad devices.
If students do not have access to these devices, a free version of a
similar game, Angry Animals, can be played online at
HoodaMath.
http://hoodamath.com/games/angryanimals.php
Have students play several levels of the Angry Birds game or the
Angry Animals game.
Teacher Note: Teachers who are not familiar with the Angry
Birds or Angry Animals games may want to play the games to
prepare for this unit.
If game play is not available, students can watch a video of Real
World Angry Birds -
http://www.youtube.com/watch?v=s9TxM3Jpo8o This video clip is of a real life simulation of the Angry Birds
game. The player uses a red ball to simulate the bird/animal as
the projectile and builds his own “targets”.
Discussion Points:
What kind of function does the path of the projectile follow?
Predict the path of the projectile given a starting point and the
location of the target.
Teacher Note: At this point, all classroom discussions about
parabolas can be general, without getting into the quadratic
equations or transformational graphing of quadratics.
Mathematician
Journal
Prompts
EXPLORE
Teacher
provides
guidance for
Title: Rolling the Ball Activity – (Introduction to the CBR)
Goal of the activity:
The Rolling the Ball Activity is an optional activity introducing
the use of the Calculator Based Ranger (CBR) technology and
Mathematician
Journal
Prompts
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the
explorations to
prepare
students with
the knowledge
and skills to
engage in the
task.
Students will
self-assess on
the prior
knowledge and
skills assumed
for the unit
Number of
hours: 3 - 4
reviewing quadratics.
Description of the Activity:
HO #1: Rolling the Ball Activity
In this activity, students create a ramp at different angles and roll
a ball down the ramp. The CBR device collects data on the
distance of the ball to the CBR over time.
Materials Needed:
Plank of wood to serve as a ramp
Large ball (basketball or dodge ball)
Calculator Based Ranger (CBR)
TI-83/84 graphing calculator
Directions for Instructors:
If CBR devices or TI graphing calculators are not available,
Texas Instruments has a product loaner program. The devices
can be requested for free on loan if requested one month
ahead of time. For more information, visit the following
website:
http://education.ti.com/educationportal/sites/US/nonProductSingle
/global_forms_loan.html
HO #1a: Rolling the Ball: Teacher Notes offers step by step
directions to set up the CBR activity. Screen shots of the TI
graphing calculator screen are available to guide this activity.
HO#1b: Rolling the Ball: Student Notes is the student
recording sheet for the activity. Teachers may want to prompt
students to justify their responses and predictions in their
mathematician’s journals.
Anticipated Reactions:
Depending on the results collected during the activity, the
data may appear to be linear. Teachers may want to use a
longer ramp to collect additional data and discuss why the
previous trials resulted in graphs that appeared to be linear.
Title: Bouncing Ball Activity
Goal of the Activity:
It is a common misconception that parabolic graphs always
represent the path of a trajectory. This CBR (Calculator Based
Ranger) activity can be used to address this common
misconception. In this activity, students are examining the graph
of the distance of a bouncing ball from the CBR over time.
Description of the Activity:
What are your
predictions if
the incline of
the ramp is
increased?
What would
your graph
look like and
why?
What are your
predictions if
the CBR
device is
placed at the
bottom of the
ramp? What
would your
graph look
like and why?
Before
conducting the
Ball Bounce
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HO #2: Bouncing Balls Activity
Students explore the rate of change at various points on the graph
and describe these points in the context of the bouncing ball.
Students also find the curve of best fit for their data.
Materials:
Large ball (basketball or dodge ball)
Calculator Based Ranger (CBR)
TI-83/84 graphing calculator
Directions for Instructors:
HO #2a: Bouncing Balls Instructions provides step by step
instructions for setting up this activity.
HO#2b: Bouncing Balls Data Collection is the student
recording sheet for the activity. Teachers may want to prompt
students to justify their responses and predictions in their
mathematician’s journals.
Mathematicians Journal Prompt: Teachers may want to offer
students a different type of ball and have them predict what
the graph might look like. Have students bounce two types of
balls and visually observe the height and frequency of
bounces. From those observations, have students predict and
justify their graph and the curve of best fit.
Anticipated Reactions:
Students may need to conduct this experiment several times to
obtain the best data. Teachers may want to conduct a whole
class demonstration of the bouncing ball activity prior to
student groups conducting the activity.
Exploring Transformational Graphing
The goal of this activity is to explore quadratic equations for
various “Angry Animals/Birds” from the Angry Birds/Angry
Animals games. Using transformation graphing, students explore
how variations to the path of trajectory may affect the quadratic
equation. (See attached HO #3, Angry Animals Worksheet)
What is the equation of a parabola that models the path of the
projectile? How accurate is your equation to the actual path of
the projectile needed to hit the target? (This may be done on a
white board, drawing the predicted path on the white board
and projecting the Angry Birds game over the predicted path.)
Teachers may choose to “zoom out” so that the entire Angry
Birds level is viewable without scrolling left and right. This
best allows for students to see the entire path of the projectile
and match that to their predicted path.
Activity,
predict what
your graph
would look
like (height vs.
time). Explain
what is
happening in
the ball
bounce to
yield your
predicted
graph.
Bounce your
original ball
and compare
that to the
bounce of a
different type
of ball.
Predict the
graph of the
different ball.
What do you
think the curve
of best fit
would be for
the different
ball? Justify
your response.
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Teacher Notes:
Potential Issue: Website may run slow, which could be an issue
with having a whole class of students on it at one time. Also, on
Level 4, it’s hard to see the change that’s happen at first. Let the
students replay the level a few times in order to figure it out.
Optional additional preliminary task: Refer to HO #4
It is suggested that you and your students play the game “Angry
Birds” before attempting the main project in order to understand
how it works. Or, teachers may implement some other real world
activities involving quadratics in various ways. These are some
ideas:
Activity involving shooting a basketball or paper into trash can
and using technology to help write equations of trajectory
Activity involving shuttle launch. (Check the NASA site).
EXPLAIN
Teacher
introduces the
main task of
the unit and
prepares
students to in
small group
independent
work...
Number of
Hours: 1
Introduce the project: Create your own level of angry birds using
three birds to potentially “destroy” the pigs.
Description of final product and/or presentation: Final product is
a blueprint of the level of play, one blueprint just of the level, and
a second blueprint that includes the quadratic equations that
model successfully “destroying” the pigs.
Prepare students for working independently in their groups.
Describe the expectations for how students will work in their
group, including a discussion of the peer/self-evaluation form, HO
#8.
Project: Student HO #5
Skills or knowledge needed: Ability to determine “best fit” for
data; how to create a blueprint
Materials/Equipment/Resources Needed:
Computers, smartphones or iPhone
Directions for Instructor:
For struggling students, you may want to provide them with the
three heights they are to use for the target pigs for their “level”.
Allow students to research the requirements for a blueprint prior
to creating one of their own.
Mathematician
Journal
Prompts
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ELABORATE
The student
groups are
working
independently
with teacher
consultations.
Number of
Hours: 2 - 3
Design and construct the Angry Birds level.
The teacher interviews students to make sure they understand the
task and are on the right path toward completing the project.
Students are to write a paper explaining their process in creating
their blueprint, including any problems they had along the way.
They should discuss what worked, what didn’t work, and any
improvements they are able to make to complete the project.
Mathematician
Journal
Prompts
EVALUATE
Working
groups submit
products or
make
presentations
Number of
Hours: 1
Students will submit their blueprints along with their paper
describing the process they went through to find the correct
equations. Rubric attaches as HO #6
Students will “solve” the level created by another group to the
best of their ability. Rubric attached as HO #7
Peer/Self-Evaluation Form – HO #8
Mathematician
Journal
Prompts
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Map the Unit
What do students need to know and be able to do to complete the task/project/problem
successfully? How and when will they assess their own necessary knowledge and skills? How
will they remediate their own gaps or weaknesses in knowledge and skills? Look at each major
task for the unit and analyze the tasks necessary to produce a high-quality product.
Task: Design one level of the video game, Angry Birds, and create mathematical models to
simulate the most effective and efficient method of completing this level of the video game and
hitting all your targets
KNOWLEDGE AND SKILLS NEEDED Assumed
already
learned
Students will
self-assess
Will be
taught
during the
unit
1. Quadratic Functions
X X
2. Distance Formula
X X
3. Projectile Motion
X X
4. Pythagorean Theorem
X X
5. Right Triangle Trigonometry
X X
6. Create a Blueprint
X
7. Using a CBR properly
X
8.
9.
10.
11.
What project tools will student’s use?
Know/need to know lists
Daily goal sheet
X Mathematician’s Journals
Briefs/Memos
Task lists
Planning Calendar
□ ________________________________
□ ________________________________
□ ________________________________
□ ________________________________
□ ________________________________
□ ________________________________
Attachments: Handouts With Title and Numbered Sequentially as H0#____
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HO #1a
Rolling the Ball: Teacher Notes
I. Data Collection
1. Answer question 1 on the Activity sheet. Use the protractor to set the ramp at a 15° incline. Lay the
CBR2 motion detector on the ramp and flip the sensor head so it is perpendicular to the ramp.
Mark a spot on the ramp 15 cm from the CBR2 motion detector. Hold the ball at this mark, while your
partner holds calculator and CBR2 motion detector.
HINT: Aim the sensor directly at the ball and make sure that there is nothing in its path.
2. Run the EasyData App.
3. To set up the calculator for data collection:
a. Select Setup (press WINDOW) to open Setup menu.
b. Press 2 to select 2: Time Graph to open
the Time Graph Settings screen.
c. Select Edit (press ZOOM) to advance to the number
of samples dialog.
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d. Enter 0.1 to set the time between samples in seconds.
e. Select NEXT (press ZOOM) to advance to the Number of Samples dialog window.
f. Enter 30 to set the number of samples. Data collection will last for 3 seconds.
g. Select Next (press ZOOM) to display a summary of the new settings.
h. Select OK (press GRAPH) to return to the main screen.
4. When the settings are correct, choose Start (press ZOOM) to begin sampling.
5. When the clicking begin, release the ball (don’t push) and step back.
6. When the clicking stops, the collected data is transferred to the calculator and a plot of distance vs.
Time is displayed.
Answer questions 2, 3, 4, and 5.
II. Explorations
1. Predict what will happen if the incline increases. Answer question 6.
2. Adjust the incline to 30°. Repeat steps 2 through 6. Add this plot to the drawing in question 6, labeled
30°.
3. Repeat steps 2 through 6 for inclines of 45° and 60° and add to the drawing.
4. Answer question 7.
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HO: #1b
Rolling The Ball: Student Handout
Data collection
1. Which of these plots do you think best matches the Distance-Time plot of a ball rolling down a ramp?
2. What physical property is represented along the x-axis? ___________________
What are the units? ________________________________________________
What physical property is represented along the y-axis? ___________________
What are the units? ________________________________________________
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3. Sketch what the plot really looks like. Label the axis. Label the plot at the points when the ball was
released and when it reached the end of the ramp.
4. What type of function does this plot, between the two points you identified, represent?
________________________________________________________________________
5. Discuss your change in understanding between the graph you chose in question 1 and the curve you
sketched in question 3.
_____________________________________________________________________________________
___________________________________________________________
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Explorations
6. Sketch what you think the plot will look like with a greater incline. (Label it prediction)
7. Sketch and label the plots for 0° and 90°.
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HO #2a
Name __________________________
Bouncing Balls Instructions
1. Run the RANGER program on your calculator. It can be accessed using the APPS menu, and
selecting CBL/CBR.
2. From the MAIN MENU of the RANGER program, select 3:APPLICATIONS.
3. Select 1:METERS, then select 3:BALL BOUNCE.
4. Follow the directions on the screen of your calculator. Release the ball. Press the TRIGGER
key on the CBR as the ball strikes the ground.
5. Your graph should have at least two bounces. If you are not satisfied with the results of your
experiment, press ENTER, select 5:REPEAT SAMPLE, and try again.
6. When you are satisfied with your data, sketch a Distance-Time plot. On the grid below. Label the
axes.
Note: The CBR is measuring the distance from the ball to the ground.
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HO #2b
Name __________________________
Bouncing Ball Data Collection
1. The goal here is to “capture” one complete curve. Choose the best curve that your bouncing ball
created. Press ENTER and go to 4: PLOT TOOLS. Choose 1: SELECT DOMAIN. Use the
right arrow to trace to a point near the lower left side of the parabola that you chose and press
ENTER. Continue tracing until you reach a point near the lower right side of this parabola and
press ENTER.
2. Now you are going to clean-up and perfect your graph. Trace on the graph to find the maximum
and use it and a few other points that you get from tracing to draw an accurate graph below.
3. In what interval(s) is the ball traveling the fastest? Explain.
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4. In what interval(s) is the ball traveling the slowest? Explain.
5. Why is the graph curved? What is the ball doing that makes the graph curve?
6. Write a paragraph describing what the graph tells us about the motion of the ball. Be sure to
interpret all the important features of this type of graph.
7. Using mathematical language, describe the type of graph and function that seems to fit this
motion.
Function type: _____________________Graph type: _________________________
8. Based on your knowledge of transformations, estimate an equation of the curve. Write
the equation here:
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9. Graph your equation along with the data from the ball drop. How well do they match?
10. You can use your calculator to find an equation of the parabola. This is called a quadratic
regression. Go to STAT, select CALC, then QuadReg and press enter. Write the quadratic
regression equation from your calculator. Use your finest algebra to compare the two
equations algebraically. Show your work here:
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HO #3
Angry Animals (adapted from Hooda Math)
Level 1:
Using the base of the slingshot as the origin, think about the Cartesian coordinate system. In
which quadrant, are you pulling the sheep back? In which quadrant, does the sheep fly out of the
sling shot?
Level 2:
Launch the first pig and click in mid-air to divide it into three pigs. Use the arrows
at the bottom of the game to scroll back to where the green pig magically turns into
three pigs. Assuming the parabolic formula for the original pig is y = -0.1x2 + x + 2, and
the parabolic formula for the highest pig is y = -0.1x2 + x + 3. What is the parabolic
formula for the lowest pig?
Level 3:
Launch a bull and click in mid-air to drop a milk bottle. Using the base of the slingshot as the
origin, estimate the equation for the line created by the dropping bottle to destroy the first alien
and the second alien assuming that each small bull shown in the large bulls’ path is one unit?
Level 4:
After you launch the chicken it follows along a parabola, but when you click in
mid-air the path of the chicken changes into a different parabola. Looking at the
parabolic formula2y ax b c . After the mid-air click, which number changes a, b,
or c? Does the number get smaller or larger? Explain.
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HO #4
Writing Quadratic Equations From Angry Birds
Possible Tasks:
Students can use smartphones to take a screen shot of a particular Angry Bird level. They will want to
launch a bird and take a screen shot of the path the bird made. Save this image as a JPEG. They can then
import the image into a Smartboard screen or project the image with a LCD projector. If they are using
the Smartboard, they can place a grid over the picture which will allow them to plot actual points that they
can use to write the equation of the path. If they are projecting the image using a LCD projector, they can
project onto a graph and again plot points. This could be done as a whole group or in smaller groups
depending on size of class.
I. Students are to plot at least 3 different paths and write the corresponding quadratic for each. They
will need to draw a simulation of the graph and list the points they are using for the quadratic.
II. Students will design a level of Angry Birds on paper and show the optimum point of impact for
the most damage. They will write the equation of the quadratic necessary to hit this point
using an appropriate scale.
III. Extension after this lesson: Students will research possible real-world applications for quadratic
equations. Projectile motion is used in many sports for success, hunting has a form of
projectile motion that incorporates parts of quadratic understanding-there are scopes and
range finders that calculate this information now for hunters and golfers. How are they
designed? What things are needed for them to work?
http://www.real-world-physics-problems.com/physics-of-sports.html
There are also projectile motion simulators where students can explore quadratics. They allow
students to take out the physics part and have only gravity as a force affecting the projectile. They
allow students to change angle and velocity to show how they affect the projectile. They can get
points by tracking time and height as they shot the simulator. Some possible simulators:
http://www.squadron13.com/games/projectile/projectile.htm
http://jersey.uoregon.edu/vlab/Cannon/
http://www.livephysics.com/simulations/mechanics/projectile-motion.html
I. Students will draw a simulation of what their projectile did-listing angle and velocity with
included points for use in regression models. They will need to do several of these
simulations to get a complete idea of what is going on with the quadratics.
II. Students will use a new projectile and predict what quadratic they will need to hit a specific target
in simulator. They need to describe angle and velocity and why they chose those values. They
will then run the simulator and describe what they find. Did they hit the target? If not, what
do they need to change to hit it?
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Real world simulation: If your school has a pitching machine, you can control velocity and angle so
students can see how these affect the projectile. The shots can be recorded and then used in programs
such as Logger Pro (http://www.vernier.com/products/software/lp/) or Tracker Video Analysis
(http://www.cabrillo.edu/~dbrown/tracker/) so that students can then write the equations for the
quadratics. One feature of using the pitching machine is that you can drop 4 or 5 balls in at the same
time and they will fly together so students can see the path better.
I. Students can place targets at specified distances and calculate the needed angle and velocity to hit
the target. Then run the launch and write about what happened and what they need to change
to hit target.
II. Students can import videos into one of the programs and look at the paths and data they will
collect and write about what they saw and make predictions for other simulations.
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HO #5
“Angry Birds” Project Directions
Your task is to create your own level of angry birds. You will have three pigs to “destroy” that
must be at three different heights. You will be given three red birds to “destroy” the pigs. For
the purposes of this activity, you must hit the pigs with a bird to “destroy” it.
Part 1: The Blueprint
Create a blueprint of your level. Then create a second blueprint which includes the trajectories
of the birds and the quadratic equations that go with them. Your blueprint without the
trajectories and equations will later be given to another group to “complete.”
Part 2: The Paper
Write a paper explaining how you chose your trajectories. Use the available technology
(graphing software) to simulate your proposed trajectories to “complete” the level of Angry
Birds. Did your proposed equations “destroy” each target? How would you change your
trajectories to hit all three targets? What are your new quadratic equations?
Part 3: Completing Another Level of Angry Birds
Switch blueprints with another group and complete that level of the Angry Birds game. Identify
the three “targets” and propose the quadratic equations that will “destroy” all three targets.
Using the available technology, run the simulation and determine whether or not the three targets
were “destroyed”. Evaluate your proposed trajectories and adjust your trajectories to complete
this level of Angry Birds. What are your new quadratic equations?
UVA-SCPS Office of Mathematics Outreach with support from VADOE Mathematics and Science
Partnership Grant Program NCLB Title II Part B
23
HO #6
Rubric for Blueprint and Paper
CATEGORY 4 3 2 1
Mathematical
Concepts
Explanation shows
complete
understanding of
the mathematical
concepts used to
determine most
economical use of
solar energy.
Explanation shows
substantial
understanding of
the mathematical
concepts used to
determine most
economical use of
solar energy
Explanation shows
some
understanding of
the mathematical
concepts used to
determine most
economical use of
solar energy
Explanation shows
very limited
understanding of
the mathematical
concepts used to
determine most
economical use of
solar energy
Mathematical
Reasoning
Uses complex and
refined
mathematical
reasoning to choose
the best energy
source.
Uses effective
mathematical
reasoning to choose
the best energy
source.
Some evidence of
mathematical
reasoning to choose
the best energy
source.
Little evidence of
mathematical
reasoning to choose
the best energy
source.
Explanation Explanation is
detailed and clear
to justify their
conclusion
mathematically.
Explanation is clear
to justify their
conclusion
mathematically.
Explanation is a
little difficult to
understand, but
includes critical
components to
justify conclusion.
Explanation is
difficult to
understand and is
missing several
components OR
was not included.
Strategy/Procedures Uses an efficient
and effective
strategy to solve
the problem(s).
Typically, uses an
effective strategy to
solve the
problem(s).
Sometimes uses an
effective strategy to
solve problems, but
does not do it
consistently.
Rarely uses an
effective strategy to
solve problems.
Neatness and
Organization
The work is
presented in a neat,
clear, organized
fashion that is easy
to read.
The work is
presented in a neat
and organized
fashion that is
usually easy to
read.
The work is
presented in an
organized fashion
but may be hard to
read at times.
The work appears
sloppy and
unorganized. It is
hard to know what
information goes
together.
Diagrams and
Sketches
Blueprints are clear
and greatly add to
the reader's
understanding of
the procedure(s).
Blueprints are clear
and easy to
understand.
Blueprints are
somewhat difficult
to understand.
Blueprints are
difficult to
understand or are
not used.
UVA-SCPS Office of Mathematics Outreach with support from VADOE Mathematics and Science
Partnership Grant Program NCLB Title II Part B
24
HO #7
Rubric for Solving Other Created Level
1-Insufficient
Understanding
2-Fair 3-Good
4-Excellent
Understanding of
Concept
(Writing and
Solving Quadratic
Equations)
Demonstrates no
understanding of
the main concept.
Demonstrates little
understanding of
the main concept.
Demonstrates partial
understanding of the
main concept.
Demonstrates
mastery
knowledge of
the main
concept.
Accuracy
Quadratic Models
Equations do not
represent
successful “hits”.
Most equations do
not represent
successful hits.
One equation does
not represent a
successful hit, while
others are accurate.
All equations
represent
successful
hits.
Summary No organization of
work or support for
final solution.
Very weak
evidence of
organization or
support for final
solution.
Organization needs
to improve and some
support for final
solution.
Well
organized with
clear
understanding
and detailed
support of
final solution.
UVA-SCPS Office of Mathematics Outreach with support from VADOE Mathematics and Science
Partnership Grant Program NCLB Title II Part B
25
HO #8
Peer/Self-Evaluation form: Peeps
The following is a list of statements to be answered by you and about each of your group
members. Think carefully about assigning rating values for each of the statements.
1- Strongly Agree 2- Agree 3- Neutral 4- Disagree 5- Strongly Disagree
Self: Teammate: Teammate: Teammate:
Was dependable
in attending class
Willing to accept
assigned tasks
Contributed
positively to
group discussion
Completed work
on time or made
alternative
arrangements
Helped others
with their work
when needed
Did work
accurately and
completely
Worked well with
other group
members
Overall was a
valuable member
of the team