SUMMER MATHEMATICS PROJECTS - Piscataway …phs.piscatawayschools.org/UserFiles/Servers/Server_805570/File/Math... · SUMMER MATHEMATICS PROJECTS ... Piscataway High School Honors

SUMMER MATHEMATICS PROJECTS Dear Students Entering Honors Geometry: Congratulations on your recommendation into Honors Geometry. You are about to embark on a mathematical adventure. Geometry is a very exciting and important subject. To be successful in mathematics, you must be willing to devote time to practice. To prepare for the rigor of the course, the mathematics department is requiring that all students entering Honors Geometry complete the “Honors Geometry Summer Assignment”. DIRECTIONS: Complete parts 1 &2 of the summer assignment. Be prepared to spend a few hours completing all tasks. Your new mathematics teacher will collect the packet on Wednesday, September 6th. The grade on this assignment will be your first quiz grade in your new mathematics course. The project will be scored according to the enclosed rubric. Work on this packet throughout the summer. It will provide you with many of the skills that you are expected to have when entering Honors Geometry.

The project can be found by going to the district website at http://www.piscatawayschools.org.

Navigate to Piscataway High School Choose “Our School” and then “Mathematics Department” In the side menu, click on “Summer Assignments” Find your child’s summer assignment posted by the course they are entering for

the 2017-2018 academic school year.

Have fun on the packet. Enjoy the summer. If you have any questions about the project, please email me at [email protected] or call me at 732.572.2289 x2539 and leave me a message. I will check my messages periodically and return your inquiry when I have the chance.

Sincerely,

Daniel J. Ross, Esq. Supervisor of Mathematics 7-12

Piscataway High School Honors Geometry Summer Assignment 2017

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Piscataway HS Honors Geometry Summer Assignment

Name_______________________________________ Due Date: September 6, 2017

PART 1: Deltamath.com

Part 1 of the summer assignment will review prerequisite skills and will be completed online

using Delta Math (deltamath.com).

DIRECTIONS: If you don’t have an account from a former class, create one. Click on:

The next page shows the topics included in the summer project. Examples are given for each topic.

1. Create New Account

2. Specify the code 747048

Enter your information and

the proper class:

� Honors Geometry 2017-2018

If you have an account from a former class, click on Add Teachers.

Enter the code 747048

Enter the proper class:

� Honors Geometry 2017-2018


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If you need assistance, you may click on to see additional examples. Provide your work for each section on a separate paper (label each section). If you get a problem wrong, the work may be included.


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Part 2: Constructions For this assignment you will construct various figures to practice your skills with the basic tools of Geometry (compass, protractor, and straight edge/ruler). Make sure that you follow the rubric provided to ensure you complete the assignment fully and receive the maximum number of points per section. Procedure:

1. Use the Construction Reference with Web Video Resources to familiarize yourself with basic constructions.

2. Complete the Construction Practice using your compass and straight edge (ruler) leaving all marks and confirming with protractor as directed.

3. You will be assessed on these skill during the first marking period in Honors Geometry. 4. Review the grading rubric to ensure your assignment has all required components and is

complete.


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Constructions Reference

Construct the perpendicular bisector of a line segment. Or, construct the midpoint of a line segment.

1. Begin with line segment XY.

2. Place the compass at point X. Adjust the compass radius so that it is more than (½)XY. Draw two arcs as shown here.

3. Without changing the compass radius, place the compass on point Y. Draw two arcs intersecting the previously drawn arcs. Label the intersection points A and B.

4. Using the straightedge, draw line AB. Label the intersection point M. Point M is the midpoint of line segment XY, and line AB is perpendicular to line segment XY.

Web Resource: http://www.youtube.com/watch?v=5bvjnleMn5A

YX

YX

A

B

YX

X Y

A

B

M


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Given point P on line k, construct a line through P, perpendicular to k.

1. Begin with line k, containing point P.

2. Place the compass on point P. Using an arbitrary radius, draw arcs intersecting line k at two points. Label the intersection points X and Y.

3. Place the compass at point X. Adjust the compass radius so that it is more than (½)XY. Draw an arc as shown here.

4. Without changing the compass radius, place the compass on point Y. Draw an arc intersecting the previously drawn arc. Label the intersection point A.

5. Use the straightedge to draw line AP. Line AP is perpendicular to line k.

Web Resource: http://www.youtube.com/watch?v=1krqS8hSip0

k

P

k

P YX

k

P YX

k

A

P YX

k

A

X YP


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Given point R, not on line k, construct a line through R, perpendicular to k.

1. Begin with point line k and point R, not on the line.

2. Place the compass on point R. Using an arbitrary radius, draw arcs intersecting line k at two points. Label the intersection points X and Y.

3. Place the compass at point X. Adjust the compass radius so that it is more than (½)XY. Draw an arc as shown here.

4. Without changing the compass radius, place the compass on point Y. Draw an arc intersecting the previously drawn arc. Label the intersection point B.

5. Use the straightedge to draw line RB. Line RB is perpendicular to line k.

Web Resource: http://www.youtube.com/watch?v=35iBLh-1tG8

kR

kR

YX

k

YX

R

k

B

YX

R

k

B

YX

R


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Construct the bisector of an angle.

1. Let point P be the vertex of the angle. Place the compass on point P and draw an arc across both sides of the angle. Label the intersection points Q and R.

2. Place the compass on point Q and draw an arc across the interior of the angle.

3. Without changing the radius of the compass, place it on point R and draw an arc intersecting the one drawn in the previous step. Label the intersection point W.

4. Using the straightedge, draw ray PW. This is the bisector of QPR.

Web Resource: http://www.youtube.com/watch?v=lIwvSzfUkOY

Q

RP

Q

RP

P

Q

R

W

P

Q

R

W


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Construct an angle congruent to a given angle.

1. To draw an angle congruent to A, begin by drawing a ray with endpoint D.

2. Place the compass on point A and draw an arc across both sides of the angle. Without changing the compass radius, place the compass on point D and draw a long arc crossing the ray. Label the three intersection points as shown.

3. Set the compass so that its radius is BC. Place the compass on point E and draw an arc intersecting the one drawn in the previous step. Label the intersection point F.

4. Use the straightedge to draw ray DF.

EDF BAC

Web Resource: http://www.youtube.com/watch?v=AkvNo6PQsRs

D

A

E

B

C

D

A

F

ED

C

B

A

F

ED

C

B

A


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Given a line and a point, construct a line through the point, parallel to the given line.

1. Begin with point P and line k.

2. Draw an arbitrary line through point P, intersecting line k. Call the intersection point Q. Now the task is to construct an angle with vertex P, congruent to the angle of intersection.

3. Center the compass at point Q and draw an arc intersecting both lines. Without changing the radius of the compass, center it at point P and draw another arc.

4. Set the compass radius to the distance between the two intersection points of the first arc. Now center the compass at the point where the second arc intersects line PQ. Mark the arc intersection point R.

5. Line PR is parallel to line k.

Web Resource: http://www.youtube.com/watch?v=d5YxbX_9hto

k

P

kQ

P

kQ

P

k

R

Q

P

k

R

Q

P


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Given a line segment as one side, construct an equilateral triangle. This method may also be used to construct a 60 angle.

1. Begin with line segment TU.

2. Center the compass at point T, and set the compass radius to TU. Draw an arc as shown.

3. Keeping the same radius, center the compass at point U and draw another arc intersecting the first one. Let point V be the point of intersection.

4. Draw line segments TV and UV. Triangle TUV is an equilateral triangle, and each of its interior angles has a measure of 60.

Web Resource: http://www.youtube.com/watch?v=t-ZtoNhEYWQ

UT

UT

V

UT

V

UT


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Constructions Practice Complete each of the constructions using a pencil, compass, and straight edge. Leave all compass marks.

1. Construct a perpendicular bisector of XY , label the midpoint M and the perpendicular

bisector AB

. Confirm with a protractor that the lines are perpendicular.

2. Given point P on line k, construct a line m through P, perpendicular to line k. Confirm with a protractor that the lines are perpendicular.

X Y

k P


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3. Given point R, not on line k, construct a line j through R, perpendicular to line k. Confirm with a protractor that the lines are perpendicular.

4. Construct the bisector of ABC . Confirm with a protractor the measurements of these angles.

5. Construct an angle congruent to a given angle using the ray provided. Confirm with a protractor the measurements of these angles.

k

R

B C

A

B C

A


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6. Given line k and point A, construct a line n through the point A, parallel to line k.

7. Construct an equilateral triangle ABC given side AB .

k

A

A B


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Honors Geometry Summer Assignment Grading Rubric DUE DATE: SEPTEMBER 6, 2017

Score Criteria

PART 1‐ Deltamath.com Students will complete the online deltamath.com portion of the project. The score on this portion will be 50% of the summer project grade.

Score:

PART 2: Constructions Students should complete the constructions practice portion of the project. The score on this portion (see rubric below) will be 50% of the summer project grade.

5 (100%)

The constructions practice has a complete response to each question with a detailed explanation where necessary. The work has no math errors and shows complete understanding of the questions, mathematical ideas, and processes.

4 (90%)

The constructions practice has a good solid response to each question with a clear explanation where necessary. The work has no major math errors or serious flaws in reasoning and shows substantial understanding of the problem, ideas, and processes.

3 (80%)

The constructions practice has a response to each question with explanations where necessary. Work may contain some misunderstandings or the explanations may lack clarity, but overall shows a basic understanding of the problem, ideas, and processes.

2 (65%)

The constructions practice has incomplete or missing responses to some questions and given explanations are unclear. The work includes some serious math errors or flaws in reasoning and the responses show only some understanding of the problem.

1 (50%)

The constructions practice responses miss key points or several components of the project are not completed. The work includes major math errors or serious flaws in reasoning with responses showing a complete lack of understanding for the problem.

0 (0%)

Project is not handed in.

Final Score for Summer Project:

Late Projects

All late projects will be graded according to the above criteria. Once a grade has been determined, the

student will lose 5 points for each day the project is late.

Example

If the students receives a 3, which is 85%, and hands the project in 2 days late, their final grade will be

75%. They lost 5 points for each of the 2 days late for a total of 10 points deducted.

Documents

SUMMER MATHEMATICS PROJECTS - Piscataway …phs.piscatawayschools.org/UserFiles/Servers/Server_805570/File/Math... · SUMMER MATHEMATICS PROJECTS ... Piscataway High School Honors