mathematics senior level capstone course unit...

UVA-SCPS Office of Mathematics Outreach with support from VADOE Mathematics and Science Partnership Grant Program NCLB Title II Part B

1

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


2

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:

http://hoodamath.com/games/angryanimals.php


3

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

4

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.


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


http://www.youtube.com/watch?v=s9TxM3Jpo8o



5

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





6

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.



7

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



8

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



9

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#____



10

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.



12

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? ________________________________________________



13

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.

_____________________________________________________________________________________

___________________________________________________________



14

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°.



15

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.



16

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.



17

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:



18

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:



19

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.



20

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?

http://www.squadron13.com/games/projectile/projectile.htm

http://jersey.uoregon.edu/vlab/Cannon/

http://www.livephysics.com/simulations/mechanics/projectile-motion.html



21

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.


http://www.cabrillo.edu/~dbrown/tracker/



22

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?



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


solve problems, but

does not do it

consistently.

Rarely uses an


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.



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.



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

mathematics senior level capstone course unit...

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