End of Year Projects

7/30/2019 End of Year Projects

1/12

End-of-Year Projects

Geometry

Below you will find 10 project options, each with a brief description. More complete

information, with the requirements for each project, can be found on the following pages. You

will choose three (3) of them to complete and submit by the last day of school. You will be ableto work on these projects in class as well as at home.

1. String Art ProjectYou will create a piece of art made up of curves using only straightlines.

2. 3D ConstructionsYou will construct various figures using paper folding.3. 2D ConstructionsYou will use a compass and straightedge to construct various figures.4. Properties of Real Numbers PosterYou will make a poster illustrating the properties of

real numbers.5. Formula PosterYou will create a poster of the formulas used throughout this course.6. End-of-Course AssessmentYou will complete the end-of-course assessment in your

textbook.7. The Three MathematiciansYou will write a paper about 3 mathematicians.8. Geometry Reference Book - You will create an illustrated reference book of theorems.9. Digital ScrapbookYou will create a scrapbook of examples of geometric figures in our

world.10.Geometry DictionaryYou will create an illustrated dictionary.


2/12

Project Option #1

String Art Project

Task: You will create a piece of art made up of curves using only straight lines.

Necessary Components:1. Create an original design on paper.a. You are to incorporate geometric concepts into your design and label them on the

plan you submit. Color-code the design with colored pencils and make two copies

(one to submit and one to help in nail/hole placement).2. Completed String Art design

a. The final project should be between 8 inches square and 14 inches square.Remember to put a hanger on the back of your project, along with your name,

date, and period.3. Write a reflection paper which is at least one page in length (typed or hand written),

addressing the following aspects:

a.

The title or name of your completed piece of geometric artb. The shapes that can be found in your original designc. The materials usedd. Where you got your designe. Any problems you may have had with decision as to what shape to use, getting

the materials, or construction of the string art.

f. How you addressed each of the problems you identified above.Grading:

Original Design 30 points

Completed String Art 45 points

Reflection Paper 30 points

Total: 105 points possible


3/12

Project Option #2

3D Constructions

Task: You will create a mobile of the five Platonic solids

Necessary Components:1. Create a net for each solid2. Construct each solid from net3. Display the solids using a mobile4. Answer the question: What makes a Platonic solid different from other three-dimensional

solids?

5. Create a table which includes the following information for each of the solids:a. Shape of each Faceb. Number of Facesc. Number of Verticesd.

Number of Edgese. Number of faces which meet at vertex

Grading:

Each of the five Platonic solids 10 points each (50 points)Create the mobile 20 points

Answer to the question 10 points

Table of information 1 point per cell (25 points)

Total 105 points possible


4/12

Project Option #3

2D Constructions

Task: You will use a compass and straightedge to construct various figures.

Necessary Components:1. Choose 15 of the 20 constructions provided below to complete.a. All given information should be in BLACK PEN. Everything added to the given

must be in a different color (blue, green, purple, orange, etc). Final step must be

in RED.b. You may use a ruler or protractor to create the GIVEN information if a specific

size is listed.

2. Explain what you did for each construction, using complete sentences.3. Label each construction with the appropriate number.4. Display the constructions in a manner which is neat and pleasing to the eye.

Grading:Each of the constructions correctly completed 3 points each (45 points)

Explanations of what you did 2 points each (30 points)

Label each construction 1 point each (15 points)

Display is neat and pleasing to the eye 15 points

Total 105 points possible

Construction #1

To construct congruent segments

Given: Segment AB = 3 inches

Construct: Segment XY such that XY

AB

Construction #2

To construct the midpoint of a segment


Construct: M, the midpoint ofSegment AB

Construction #3

To construct the bisector of a segment


Construct: Line XYAB

Construction #4

To construct congruent angles

Given: 45BAC

Construct: YXZBAC

Construction #5

To construct the angle bisector

Given: 70BAC

Construct: Ray AX so XACBAX

Construction #6

To construct a line to a point on a line

Given: Point P on line L

Construct: Line PZ Line L

Construction #7

To construct a line perpendicular to a point

not on the line

Given: Point P NOT on line L

Construct: Line PZ Line L

Construction #8

To construct the Centroid of a triangle

Given: Isosceles ABC with legs 3 inchesand base 4 inches

Construct: Centroid X of ABC


5/12

Construction #9

To construct the orthocenter of an isosceles

triangle

Given: Isosceles ABC with legs 3 inches

and base 4 inches

Construct: Orthocenter X of ABC

Construction #10

To construct the orthocenter of a scalenetriangle

Given: Scalene ABC with sides 7cm, 5cm,and 3 cm

Construct: Orthocenter X of ABC

Construction #11

To construct an equilateral triangle, and then

two congruent trianglesGiven: Segment AB = 6 cm

Construct: An equilateral ABC with sides

6 cm, then create two congruent triangles

Construction #12

To circumscribe a circle about a triangle

Given: Isosceles ABC with legs 2 in and

base 3 in

Construct: Circle with center X

circumscribed about ABC

Construction #13

To inscribe a circle in a triangle

Given: Right ABC with sides

3, 4 and 5 in

Construct: Circle with center X inscribed

in ABC

Construction #14

To construct parallel lines

Given: Line L with Point P not on LConstruct: Line K through point P and

parallel to line L

Construction #15

To divide a given segment into 3congruent

segments

Given: Segment AB

Construct: Points C and D such that AC

CD DB

Construction #16

To construct a 4th

segment in proportion

with three given segments

Given: Segment A = 2in,Segment B = 4in, and Segment C = 1in

Construct: Segment D such that

A:B = C:D

Construction #17

To construct the Geometric Mean betweentwo given segments

Given: Segment A = 4cm and

Segment B = 6cm

Construct: A segment of length C such that

A:C = C:D

Construction #18

To locate the center of a circle

Given: Circle with unknown center

Construct: location of center X

Construction #19

To construct a line tangent to a circle at a

point on the circle

Given: Circle O with radius 2in and Point P

on the circle

Construct: Line T tangent to Circle O at

Point P

Construction #20

To construct a line tangent to a circlethrough a point not on the circle

Given: Circle O with radius 2 in and Point

P Not on Circle O

Construct: Line PT tangent to Circle O


6/12

Project Option #4

Properties of Real Numbers Poster

Task: Design and create a poster to illustrate the properties of real numbers.

Necessary Components:1. Identify each of the properties of real numbers (Hint: Geometry look on page 841;Applied Geometry, look on page 879).

2. Provide at least 3 specific examples to illustrate each property.3. Choose 3 equations to solve, showing every step. Justify each step with the appropriate

property. Each must require at least 2 steps to solve; one must require distribution.

4. Choose 3 inequalities to solve, showing every step. Justify each step with the appropriateproperty. Each must require at least 2 steps to solve; one must require distribution.

Make sure that your final product is neat and all information is legible. It can be hand-written ortyped.

Requirement 4 3 2 1 0 Points

Properties ofNumbers

All properties areprovided, withcorrectdefinitions.

The propertiesare listed withincomplete oruncleardefinitions.

The propertiesare listed withat incorrectdefinitions.

The propertiesare listed, withno definitionsprovided.

No propertiesare provided.

____ * 7

Examples ofProperties ofNumbers

Each propertyhas 3 correctexamples.

Each propertyhas 3examples,with no morethan 4incorrect.

There arefewer than 3examples foreach propertyor more than 4incorrectexamples.

The examplesprovided areincorrect.

There are noexamplesprovided.

____ * 7

3 Equations with

Justifications

3 problems

chosen, correctlysolved and

justified.

3 problems

chosen,solved and

justified withno more than2 errors.

3 problems

chosen,solved and

justified withmore than 2errors.

3 problems

chosen andsolved, withno

justificationsprovided.

No equations

provided.

____ * 3

3 Inequalities withJustifications

3 problemschosen, correctlysolved and

justified.

3 problemschosen,solved and

justified withno more than2 errors.

3 problemschosen,solved and

justified withmore than 2errors.

3 problemschosen andsolved, withno

justificationsprovided.

Noinequalitiesprovided. ____ * 3

Neatness The poster isclean and neat,

with legible textand illustrations.

The poster isnot legible.

____ * 3

Creativity The poster iscreative andoriginal in itsdesign.

The poster isvery creative;only a fewdesignelements arecopied.

The posterhas manydesignelements, butthey are notoriginal.

The posterhas only a fewdesignelements.

The poster isjust a list oftherequirements.

____ * 3


7/12

Project Option #5

Formula Poster

Task: Design and create a poster to illustrate formulas.

Necessary Components:1. Identify each of the formulas used in Geometry (Hint: Geometry look on pages 838-839;Applied Geometry look on pages 876-877)

2. Provide an illustration of each formula.3. Choose 3 formulas; create and solve a problem which uses the formula.

Requirement 4 3 2 1 0 Points

Formulas All formulas areprovided andcorrect

The list offormulas isincomplete orcontainserrors (lessthan 2).

There arebetween 2 and5 missingformulas orerrors in theformulasprovided.

There aremore than 5errors in theformulasprovided.

No formulasare provided.

____ * 7

Illustration Each formula hasa correctillustration

Each formulahas anillustration,with no morethan 2incorrect.

Each formulahas anillustration,with more than4 incorrect.

Theillustrationsprovided areincorrect.

There are noillustrationsprovided.

____ * 7

3 Problems 3 problemsprovided andcorrectly solved.

3 problemschosen andsolved with nomore than 2errors.

3 problemschosen solvedwith more than2 errors.

Fewer than 3problemschosen andsolved

No problemssolved.

____ * 6

Neatness The poster is

clean and neat,with legible textand illustrations.

The poster is

not legible.____ * 3

Creativity The poster iscreative andoriginal in itsdesign.

The poster isvery creative;only a fewdesignelements arecopied.

The posterhas manydesignelements, butthey are notoriginal.

The posterhas only a fewdesignelements.

The poster isjust a list oftherequirements.

____ * 3


8/12

Project Option #6

End-of-Course Assessment

Task: Complete the end-of-course assessment.

Necessary Components:1. You will write each question, including illustrations.2. You will show all work.3. You will record the correct answer. For Multiple Choice, include the letter of the choice

and the answer. For Short Answer and Extended Response, your answer should be incomplete sentences.

Grading:

All problems written and solved: 64 points (1 point each)Correct answers for problems 1-61: 30.5 points ( point each)

Problems 62-64 will be graded as follows:

Problems 62 and 63 will each receive 2 points for a correct answer AND completeexplanation. They will receive 1 point for a correct answer with an incomplete OR

incorrect explanation.

Problem 64 will receive 4 points for a correct answer AND complete explanation. It will

receive 3 points for a correct method with one computational error. It will receive 2points for a correct answer and an incomplete explanation. There will be 1 point awarded

for a correct answer with no explanation given.

Total: (102.5 points possible)


9/12

Project Option #7

The Three Mathematicians

Task: You will write a research paper on three mathematicians

Necessary Components:1. Choose three of the following mathematiciansa. Euclidb. Rene Descartesc. Archimedesd. Leonhard Eulere. Blaise Pascalf. Pythagorasg. Brahmaguptah. Eratosthenesi. Carl Friedrich Gaussj.

Charles Dodgson2. Write a research paper of 6-9 pages (in your own words), with 2-3 pages on each

mathematician, which addresses at least the following information:

a. Information about life and educationb. Information about contributions to mathematics, with special focus paid to

geometry

3. Complete a title page and a works cited pageGrading:

Title page 5 points

2-3 pages on each of three mathematicians 30 points each (90 points total)

Works Cited page 10 points



10/12

Project Option #8

Geometry Reference Book

Task: Create an illustrated reference book of theorems, corollaries, and postulates.

Necessary Components:1. You will write each theorem, corollary and postulate, in order, from the textbook. Foreach one, you will type the theorem, corollary, or postulate and provide an illustration.

2. You will then choose 24 theorems and write a proof of the theorem. You can write theproofs as a two-column proof or a paragraph proof.

3. Your reference book will need a title page and a table of contents. The table of contentswill include the subdivisions by chapter and will include page numbers for the start of

each new chapter. The proofs will be in a separate section of the reference book.

Grading:

Write and illustrate the theorem, corollary, or postulate: 71 points ( point each)

Write a proof of the selected theorems: 24 points (1 point each)Create a Title Page and Table of Contents: 10 points (5 points each)



11/12

Project Option #9

Digital Scrapbook

Task: Create a digital scrapbook of geometric figures in our world.

Necessary Components:1. At least 20 digital illustrations.2. Label each illustration, identifying the type of geometric figure.3. Explain how you know the figure is what you say it is.

Grading:

20 illustrations provided 40 points (2 points each)

Each illustration labeled correctly 20 points (1 point each)Correct explanation of the figure 40 points (2 points each)


1 additional illustration can be provided for possible extra credit of 5 points


12/12

Project Option #10

Geometry Dictionary

Task: You will create an illustrated dictionary of all the geometry terms we have used this year.

Necessary Components:1. List all of the vocabulary terms from every chapter, alphabetically.2. Write definitions for each term.3. Create an illustration for each term.4. Create a table of contents with page numbers for each letter.

Grading:

Write each definition, listing the words alphabetically: 50 points

Create an illustration of each definition: 50 pointsCreate a Table of Contents: 5 points


End of Year Projects

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