Name: Date: Period:

8th

Grade Math Culminating Project Menu B

Part #1 – DUE: MONDAY, MAY 11TH

Part #2 – DUE: MONDAY, MAY 18TH

Part #3 – DUE: FRIDAY, JUNE 5TH

You have your choice of the projects listed below. You may choose any combination of projects for a total of up to

50 points for each part (i.e. – Part #1 is due on Monday, May 11th

. Select any combination of projects that total 50

points. Likewise, Part #2 is due on Monday, May 18th

. Select any combination of projects that total 50 points.) The

sum of the two parts will equal 100 points for the culminating project grade. (Part #1 and Part #2 will appear in the

grade book separately.) The projects completed in Part #1 cannot be duplicated for Part #2. Part 3 is a group

project of which you can select 1 project. Each project is worth 100 points.

All project choice descriptions and expectations are attached to this menu. If you have any questions, please ask.

Please refer to all resources (i.e., handouts, resource library, textbook, etc.) used during the school year to help with

concept ideas. YOU ARE CONTINUEALLY REMINDED ABOUT THE CONSEQUENCE TO

PLAGARISM THROUGHOUT EACH PROJECT CHOICE – YOU WILL RECEIVE A ZERO!

Projects will be worked on in class daily. Please come to class prepared everyday. None of the projects require

special supplies. The only requirements are those listed on the syllabus as school supplies you will use all year.

You need to bring your supplies daily.

LATE PROJECTS – Late projects will be accepted with a penalty of a 10 point deduction each day after the due

date. ALL PROJECTS ARE DUE AS YOUR TICKET-IN-THE-DOOR. IF YOU TURN IN A PROJECT

DURING THE CLASS PERIOD OR AT THE END OF THE CLASS PERIOD ON THE DUE DATE - THE

PROJECT IS LATE!

Put a check in the box for the projects you are choosing.

This sheet must be returned with your projects.

Worth up to 30 points each:

Famous Mathematician/Concept

Presentation

8th grade math Review Game

Worth up to 20 points each:

Raffalmania!

Reading in the Dark

Constructing the Irrational Number Line

Connection Arithmetic Sequences and

Linear Functions

The Many Faces of Relations

Window Pain

Group Project Choose 1 – Worth 100 pts

How Much Does it Really Cost?

Design a Shoe Line

Worth up to 15 points each:

8th grade math Illustration

Pythagoras Plus

Let’s Have Fun

Acting Out

Mineral Samples

Worth up to 10 points each (Can complete a

MAX of two (2) of these.)

Student Activity Sheets – must complete ALL

problems on the page or pages listed and If you do

not show your work you will not receive credit)

Pages 1 – 5

Pages 7 - 12

Pages 33 -35

Pages 37 -42

Pages 83 – 88

Pages 163 – 172

Pages 317 - 321

_______ TOTAL MENU SCORE

Name: Date: Period:

Famous Mathematician/Concept Presentation PowerPoint OR PodCast OR Script OR Prezi

Create a Power Point presentation or video skit or write a script or present the script for a TV

news reporter detailing the procedures, facts, over-arching process standards and how they are

used to inform and enrich the 8th

grade math content standards about a famous mathematician or

concept. You must include at least 5 facts about the person or concept, and the following

questions must be answered:

1) What is the background info on this person or concept?

2) What was going on in the world at this time?

3) Why is this person or concept important to the world of math?

Possible mathematicians/concepts (All others must be approved):

Pascal’s Triangle

Number Systems

History and Uses of the Pythagorean

Theorem

Golden Ratio

Fibonacci Sequence

Monies of the world and conversion

Four Color Problem

Magic Squares

Archimedes

Eratosthenes of Cyrene

Agnesi, Maria

DeMorgan, Augustus

Barrow, Isaac

Klein, Felix Christian

Clavius, Christopher

Halley, Edmond

Kepler, Johannes

Zeno of Elea

Sir Isaac Newton

Boyle, Robert

Galilei, Galileo

Russell, Bertrand

Einstein, Albert

Dodgeson, Charles Lutwidge

Euclid of Alexandria

Cartwright, Dame Mary Lucy

Hilbert, David

Plato

Pascal, Blaise

Aristotle

Copernicus, Nicolaus

Riemann, Georg

Fibonacci, Leonardo Pisano

Cantor, Georg Ferdinand

Hippocrates of Chios

Copying and pasting information from the Internet is plagiarizing. Plagiarized work will

receive a zero.

Review Game

Create a review game (like Jeopardy, Millionaire, etc…) that can be used to review one of the

following units: Unit 1, Unit 2, Unit 3, Unit 4, or Unit 5.

You must have at least 20 questions – in either multiple choice OR open response format.

The questions must be ORIGINAL – created by YOU, NOT COPIED. (That would be

plagiarism.)

Each element from each standard in the unit must be covered. (See

http://www.corestandards.org/Math/Content/8/introduction/ for a list of standards.)

Unit 1 – The number system Unit 2 – Expressions and equations

Unit 3 – Functions Unit 4 – Geometry

Unit 5 – Statistics and Probability

A ZERO WILL BE ASSIGNED FOR PLAGIARISM OR COPIED PROJECTS!!

Name: Date: Period:

8th

Grade Math Concepts Illustration

Draw an illustration (cartoon) that represents an 8

th grade math concept.

Use one (1) of the task projects attached to present the 8th grade concept (See tasks worth 20

points or 15 points).

The illustration or the characters in the illustration must accurately represent and/or explain the

8th grade math concept chosen.

Every question in the project must be answered in the illustration.

The illustration must be clear so that any reader can understand the concept.

Correct math language must used in the illustration.

A ZERO WILL BE ASSIGNED FOR PLAGIARISM OR COPIED PROJECTS!!

Raffalmania

The 8th

grade class of FAET has decided to hold a raffle to raise money to fund a trophy cabinet

as their legacy to the school. A local business leader with a condominium on St. Simon’s Island

has donated a week’s vacation at his condominium to the winner—a prize worth $1200. The

students plan to sell 2500 tickets for $1 each.

1) Suppose you buy 1 ticket. What is the probability that the ticket you buy is the winning

ticket? (Assume that all 2500 tickets are sold.)

2) After thinking about the prize, you decide the prize is worth a bigger investment. So you

buy 5 tickets. What is the probability that you have a winning ticket now?

3) Suppose 4 of your friends suggest that each of you buy 5 tickets, with the agreement that

if any of the 25 tickets is selected, you’ll share the prize. What is the probability of

having a winning ticket now?

4) At the last minute, another business leader offers 2 consolation prizes of a week-end at

Hard Labor Creek State Park, worth around $400 each. Have your chances of holding a

winning ticket changed? Explain your reasoning. Suppose that the same raffle is held

every year. What would your average net winnings be, assuming that you and your 4

friends buy 5 $1 tickets each year?

Reading in the Dark Task

In 1821, Frenchman Louis Braille developed a method that is used to help blind people read and

write. This system was based on a more complicated process of communication that was formed

by Charles Barbier due to an order from Napoleon who wanted soldiers to communicate in the

dark and without speaking. Braille met with Barbier and decided to simplify the code by using a

six-dot cell because the human finger needed to cover the entire symbol without moving so that

it could progress quickly from one symbol to the next.

Name: Date: Period:

Each Braille symbol is formed by raising different combinations of dots. Below is a sample of

the first three letters of the alphabet.

1) Using the six-dot Braille cell, how many different combinations are possible? Provide a

detailed explanation of how you know using complete sentences and correct math

language.

2) Do you think this is enough symbols for sight-impaired people to use? State why or why

not?

3) What are some reasons that some of the possible combinations might need to be discarded?

Use complete sentences.

4) An extension has been added to the Braille code that contains eight-dots with the two

additional ones added to the bottom. How does this change the number of possible

different combinations? Justify your answer by providing a detailed explanation of how

you know using complete sentences and correct math language.

Constructing the Irrational Number Line

In this task, you will construct a number line with several rational and irrational numbers

plotted and labeled. Start by constructing a right triangle with legs of one unit. Use the

Pythagorean Theorem to compute the length of the hypotenuse. Then copy the segment

forming the hypotenuse to a line and mark one left endpoint of the segment as 0 and the

other endpoint with the irrational number it represents.

Construct other right triangles with two sides (either the two legs or a leg and a hypotenuse) that

have lengths that are multiples of the unit you used in the first triangle. Then transfer the lengths

of each hypotenuse to a common number line, and label the point that it represents. After you

have constructed several irrational lengths, list the irrational numbers in order from smallest to

largest.

Name: Date: Period:

Connection Arithmetic Sequences and Linear Functions – Learning Task

YOU MUST USE GRAPH PAPER AND A RULER TO RECEIVE FULL CREDIT FOR

GRAPHS!!

For each of the sequences given in questions 1-5, determine

a) a recursive definition,

b) an explicit definition, and

c) a graph of at least the first six terms of the sequence.

1) 5, 9, 13, 17, 21, …

2) 21, 18, 15, 12, 9, …

3) 1, 4, 9, 16, 25, …

4) 38, 30.5, 23, 15.5, 8, …

5) -4, -1.3, 1.4, 4.1, 6.8, …

6) Only one of the sequences in questions 1-5 was not arithmetic. Which sequences in

questions 1-5 were arithmetic? For each sequence you identify, also state the common

difference.

7) Compare the recursive definitions of the arithmetic sequences in questions 1-5. How are

the recursive definitions of arithmetic sequences similar? How are the recursive

definitions of arithmetic sequences different from those of non-arithmetic sequences?

8) Compare the explicit definitions of the arithmetic sequences in questions 1-5. How are

the explicit definitions of arithmetic sequences similar? How are the explicit definitions

of arithmetic sequences different from those of non-arithmetic sequences?

9) Compare the graphs of the arithmetic sequences in questions 1-5. How are graphs of

arithmetic sequences similar? How are the graphs of arithmetic sequences different from

those of non-arithmetic sequences?

10) In question 6, you identified the common differences for the four arithmetic sequences.

How is the common difference for each arithmetic sequence represented in the recursive

definition for that sequence?

11) How is the common difference for each arithmetic sequence represented in the explicit

definition for that sequence?

12) In question 9, you should have identified the common characteristic of the graphs of

arithmetic sequences as being linear. On the graphs you drew for questions 1-5, draw the

extended lines through the scatterplots representing the sequences. Determine the slope

of each line you drew in question 12.

13) What are the common differences for each arithmetic sequence in questions 1-5? Explain

what this represents.

Name: Date: Period:

The Many Faces of Relations Task

1) Complete a survey of the students in your class. Expand the following table to include a row

for every student and gather the requested information from every classmate.

Class Survey

Student

Number First Name Last Name Height Number of Pets

#1

#2

#3

#4

2) How many different types of ordered pairs can be created from this survey data? You must

list all of the combinations of ordered pair to receive full credit. Use the complete list of

ordered pair to explain your answer. HINT: One type of ordered pair you could create from

the information you collected in your survey is (Student #, First Name).

3) If the first term of each ordered pair is the independent variable and the second is the

dependent, then which of the ordered pairs you identified in question 2 are relations? Which

are functions? Explain your answers using correct math language given the concept. HINT:

Use the relations and functions hand outs given in Unit 4. If you do not have them go to the

resource library or the homework handouts online.

Window Pain Task

Part 1:

Your best friend’s newest blog entry on MySpace reads:

“Last night was the worst night ever! I was playing ball in the street with my buds

when, yes, you guessed it, I broke my neighbor’s front window. Every piece of

glass in the window broke! Man, my Mom was soooooooooooo mad at me! My

neighbor was cool, but Mom is making me replace the window. Bummer!”

It is a Tudor-style house with windows that look like the picture below.

Name: Date: Period:

I called the Clearview Window Company to place an order. What was really weird was that the

only measurements that the guy wanted were BAD (60), BCE (60), and AG = 28 inches. I

told him it was a standard rectangular window and that I had measured everything, but he told

me not to worry because he could figure out the other measurements. It is going to cost me $20

per square foot, so I need to figure out how to make some money real quick.

How did the window guy know all of the other measurements and how much is this going to cost

me?

Because you are such a good best friend, you are going to reply to the blog by emailing the

answers to the questions on the blog along with detailed explanations about how to find every

angle measurement and the lengths of each edge of the glass pieces. You will also explain how to

figure out the amount of money he will need. (TO RECEIVE FULL CREDIT YOU MUST

SHOW YOUR WORK FOR EACH PIECE AND IDENTIFY EACH ANGLE

RELATIONSHIP USED TO FIND THE ANGLE MEASUREMENT!!)

Part 2:

(Two weeks later)

You just received a text message from your best friend and were told that the order of glass had

been delivered to the house by Package Express. Unfortunately, one of the pieces was broken

upon arrival and needed to be reordered by Clearview Window Company. Because you are very

curious, you think it would be a good idea to determine the probability of each piece of glass

being the one broken.

Write another email to your friend that explains the probabilities and how you determined them.

(YOU MUST ALSO SHOW YOUR WORK!!)

Pythagoras Plus

1) Find the exact area (in square units) of the figure below. Explain your method(s).

Name: Date: Period:

2) Find the areas of the squares on the sides of the triangle to the right. (Hint: How does the

large square below compare to the square in problem 1 above?)

a) How do the areas of the smaller squares compare to the area of the larger square?

b) If the lengths of the shorter sides of the triangle are a units and b units and the length

of the longest side is c units, write an algebraic equation that describes the

relationship of the areas of the squares.

c) This relationship is called the Pythagorean Theorem. Interpret this algebraic

statement in terms of the geometry involved.

3) Does the Pythagorean relationship work for other polygons constructed on the sides of right

triangles? Under what condition does this relationship hold?

4) Why do you think the Pythagorean Theorem uses squares instead of other similar figures to

express the relationship between the lengths of the sides in a right triangle?

Let’s Have Fun

Part 1

A survey was given to a group of eighth graders. They were each asked what their plans were for

the upcoming holidays. From the clues, determine how many eighth graders were surveyed.

Thirty-two students planned to visit relatives.

Twenty-three students planned to go shopping.

Thirty-one students planned to travel.

Twelve students planned to travel and visit relatives.

Eight students planned travel, visit relatives, and go shopping.

Seven students planned to travel but did not plan to visit relatives or go shopping.

Thirty students planned to do more than one of the three activities.

Eleven students did not plan to visit relatives, go shopping, or travel.

How many students were surveyed? Show how you know.

Name: Date: Period:

Part 2

Five of the students were talking about their travel plans. Their names were Albert, Donna, Fred,

Sam, and Victoria. They happened to noticed that each one was going to a different place and

were using a different type of transportation. The places that were to be visited were New York,

Miami, Anchorage, Boston, and San Diego.

The means of transportation were the family car, a recreational vehicle, a rented van, an

airplane, and a cruise ship. Where was each person going and how were they planning on

getting there?

The person that was going to New York in a rented van was best friends with Albert and

Victoria.

The person who was going to Anchorage was not in math class with the person that was

traveling by airplane, the person that was going to Miami, nor with Fred or Victoria.

The person planning to travel by airplane was not going to Boston; Sam was not going to

Boston either.

The person going to Miami was on the math team with Albert’s sister who tutored

Donna.

Donna and Victoria were not going to travel by land.

Albert and Fred noticed that their methods of transportation were both two words with

the same first letters.

Acting Out Task

Erik and Kim are actors at a theater. Erik lives 5 miles from the theater and Kim lives 3 miles

from the theater. Their boss, the director, wonders how far apart the actors live.

On grid paper, pick a point to represent the location of the theater. Illustrate all of the possible

places that Erik could live on the grid paper. Using a different color, illustrate all of the possible

places that Kim could live on the grid paper.

1) What is the smallest distance, d, that could separate their homes? How did you know?

2) What is the largest distance, d, that could separate their homes? How did you know?

3) Write and graph an inequality in terms of d to show their boss all of the possible

distances that could separate the homes of the two actors. REMEMBER TO USE

GRAPH PAPER.

Name: Date: Period:

Mineral Samples Task

Last summer Ian went to the mountains and panned for gold. While he didn’t find any gold, he

did find some pyrite (fool’s gold) and many other kinds of minerals. Ian’s friend, who happens to

be a geologist, took several of the samples and grouped them together. She told Ian that all of

those minerals were the same. Ian had a hard time believing her, because they are many different

colors. She suggested Ian analyze some data about the specimens. Ian carefully weighed each

specimen in grams (g) and found the volume of each specimen in milliliters (ml).

1) Can the data be represented as an equation or inequality? If so, write it.

2) Graph the data in the chart below.

3) Write your analysis of his data given below.

Specimen

Number

Mass or weight (g) Volume (ml)

1 17 7

2 10 4

3 13 5

4 16 6

5 7 3

6 24 10

7 5 2

Name: Date: Period:

Group Assignments

Maximum Number of members is 2

How Much Does it Really Cost?/Concept Presentation PowerPoint or Board or Prezi

Purpose: The purpose of this research is to familiarize students with cost of living, to

understand the value of money as well as the importance of saving while enhancing their

mathematical skills (by adding, subtracting, dividing , multiplying).

Overview: Students are given $800 to spend over a period of 4 weeks while documenting their

expenditures.

Goal: You must find out and research the total amount of money being spent in your household

weekly for a period of 4 weeks.

*Students will be utilizing the Scientific Method to conduct this project*

I. Question

A. How much money is spent in my household over a period of 4 weeks?

II. Research

B. You must calculate all expenditures in your household (if items do not apply,

please specify)

C. Items

Rent/Mortgage, water bill, electric bill (FPL), alarm (security), cable, phone

(house and/or cell), food, car payment, auto insurance, gas, groceries, clothes,

allowance, entertainment (i.e. movies, fair, etc), bus (week pass), lawn

maintenance, other businesses, school supplies, beauty salon/barbershop etc.

III. Hypothesis

D. How much money would you say your family/household spends weekly? Use this

figure to calculate the cost for 4 weeks.

IV. Research/Experiment

E. Each week you will be required to document the amount of money your

household spends in a spreadsheet (provided by Ms. Pryor/Mr. Harris - See

EXHIBIT A). In order to substantiate your research, you will need to provide all

receipts (with the exception of some items). ***Keep in mind you are given $800,

which means you must document your available balance after every week and/or

until you run out of money***.

V. Analyze Data/Bar Graph

F. After the 4 week experiment, students will analyze their findings in a 2 page

report. They will be required to demonstrate their data in a Bar graph (as a visual

Name: Date: Period:

aid). Students are expected to provide: 1) the reason they chose the figure in their

Hypothesis? 2) the difference between the original figure and their final figure?

3) during which period (week) we’re the expenditures the highest? and lowest?

and why?

G. Bar Graph

Your Bar graph must include the following: an original title, clearly labeled sub-

titles on the “x” and “y” axes, a bar for each individual week, clearly defined

increments and originality. Make sure you show/specify the week in which you

ran out of money ($800). You can choose to hand draw a graph or do it on the

computer.

VI. Communicate Results

H. To complete your Math project, you will communicate your results to your

classmates using PowerPoing, Prezi or on a display board.

I. Board/PowerPoint/Prezi

Your board must include the following: 1) Bar graph, 2) Hypothesis, 3)Receipts,

4)Graphics/Design, 5) Spreadsheets

VII. Presentation

Students will be given a presentation date weeks in advance. If you plan on being absent

the day of your presentation, you are required to re-schedule your date with Ms.

Pryor/Mr. Harris at least 1 week prior to your absence.

Presentation Dates

Monday, June 8, 2015

Tuesday, June 9, 2015

Wednesday, June 10, 2015

Name: Date: Period:

Exhibit A Name: ______________________________________

Period: ___________

Spreadsheet How Much Does it Really Cost?

Week 1 (cost)

Items Week 2 (cost)

Items Week 3 (cost)

Items

Ex: $124.18

Ex: Groceries

TOTAL

TOTAL

TOTAL

Name: ______________________________________ Period: ___________

Name: Date: Period:

Spreadsheet How Much Does it Really Cost?

Week 4 (cost)

Items Week 5 (cost)

Items Week 6 (cost)

Items

Ex: $124.18

Ex: Groceries

TOTAL

TOTAL

TOTAL

Name: Date: Period:

Group Assignments

Maximum number of members is 3

Creating a Shoe Line /Concept Presentation PowerPoint or Board or Prezi

Objective: Students are expected to work collaboratively while applying proper measurement

methods in order to design, construct, & present to their peers an archetype of their Shoe line.

Criteria:

A. Students may not use a pre-existing Brand (name, logo, concept etc.)

B. Students must submit 1 Proposal per group. 1) No more than 5 pages, 2) All 15 items (if

applicable) must be addressed in the Proposal, 3) Must have a Cover page, 4) Must have

Visual aids e.g. drawings &/or pictures.

C. Group must present their Shoe line to their peers (creative presentation). Dress

appropriately the day of your presentation.

D. Students must submit a prototype of Shoe design the day of the presentation

(construct/build with any material of choice, draw on paper or board, computer graphics).

Creating a Shoe Line

Students are required to submit a Proposal including the items listed below.

1. Type of Footwear: Shoes (heels, flats, men/women etc.), Sandals, Boots (hiking,

fishing, rain, astronaut, military, construction, cowboy, etc.), or Sneakers.

2. Name of Shoe line (be original). Provide 2 reasons for choosing the name.

3. Color(s) (be specific): e.g. sky blue, cherry red, etc

4. Shoe size (who are you marketing towards?)

5. Logo (must be original and nonexistent). Can be drawn or designed on the computer.

6. Age group targeted: A) infants, toddlers, pre-school = 1-5years old, B) School-age = 5-

12, C) Teens = 13-17, D) Adulthood 18+. You can choose more than one age-group.

List why you chose this age-group.

7. Material(s) used for Footwear (provide sample): e.g. leather, suede, etc.

8. Cost for material (Where can you find the material)?

9. Description of insole

10. Description of outsole

11. Description of heel (if applicable)

12. Description of laces (if applicable)

13. Price of Shoes (be reasonable)

14. Uniqueness of your Footwear (what makes your shoes distinctive, memorable &

unconventional)?

15. Marketing Strategy: Tell us why an individual would buy and/or wear your product.

Be specific & list 3 reasons.

Name: Date: Period:

Proposal Requirements

Label your pages with the Titles listed below & make sure to cover all applicable items. This

can be typed or handwritten in pencil only.

- Shoe Design Summary: Items #1-5 should be answered in the first 2 pages.

- Shoe Specs: Items #7-13 can be answered in 1-2 pages.

- Marketing: Items #6, 14-15 each item can be answered in one paragraph (3 paragraphs

total).

Cover Page Requirements

- Name of Students (all)

- Date of Presentation

- Name of Shoe Line

- Teacher’s Name

- Class/Period

- Drawings/pictures (Optional)

Note: All papers submitted must be stapled & must include a cover page. See EXHIBIT

B. Students will view and have access to a sample in class as well.

Presentation Requirements

- Group must have shoe Prototype in order to present their product.

- Each student in the group must have equal part in presenting the Shoe design.

- Presentation duration: No more than 5 mins

- Visual Aid (PowerPoint presentation, Display board or Prezi)

- Index cards (optional)

- Dress professionally (no jeans, slides, & t-shirts. Solid color sneakers allowed.

Name: Date: Period:

Names of Student #1:

Name of Student #2:

Name of Student #3:

Date of your presentation: Thursday, June 8th

, 2015

Mathematics Project

Exhibit B.

(Name of Shoe Line)

“Heels by Ms. J”

For: Teacher Name

Class/Period

Name: Date: Period:

Evaluation

1- You must submit Part I: Items #1-6 on Friday, May 8, 2015

2- You must submit Part II: Items #7-15 on Friday, May 22, 2015

3- Presentation & Prototype: June 2nd , June 3rd, June 4th

Students must notify teacher in advance if he/she will be absent the day of their

Presentation.

If group is not prepared to present on their assigned dates, a failing grade will

result for both students.

Presentation dates are subject to change. If students want to present sooner

than their actual date, they may elect to do so with Teacher approval.

Presentation Dates

Tuesday, June 2, 2015

Wednesday, June 3, 2015

Thursday, June 4, 2015

Students will be given the opportunity to select their presentation dates at random in class. In any

event both students (from the group) are absent, the teacher will select and assign the group’s

presentation date.