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# 15. The Protractor Project

Students will design and print a customized protractor that is mathematically accurate.

Standards
CCSS.MATH.CONTENT.4.G.A.3 (Symmetry)
CCSS.MATH.CONTENT.8.G.A.4 (Geometry)
CCSS.MATH.CONTENT.8.G.A.3 (Geometry)
CCSS.MATH.CONTENT.HSG.SRT.A.2 (Geometry)

Standards for Mathematical Practice
CCSS.MATH.PRACTICE.MP1: Make sense of problems and persevere in solving them.
CCSS.MATH.PRACTICE.MP2: Reason abstractly and quantitatively.
CCSS.MATH.PRACTICE.MP3: Construct viable arguments and critique the reasoning of others.
CCSS.MATH.PRACTICE.MP4: Model with mathematics.
CCSS.MATH.PRACTICE.MP5: Use appropriate tools strategically.
CCSS.MATH.PRACTICE.MP6: Attend to precision.
CCSS.MATH.PRACTICE.MP7: Look for and make use of structure.
CCSS.MATH.PRACTICE.MP8: Look for and express regularity in repeated reasoning.

Learning Objectives

• Students will design and print a customized protractor that is mathematically accurate.
• Students will identify degrees in increments of a minimum of 15 on the protractor.

Recommendations
Group Size: 2 to 3 students, depending on how many protractors you would like to have created and how much time is available.

Class Size: up to 40 students

Materials Required

Introduction

• Students have a good understanding of 3D modeling. Prior to incorporating this lesson into a unit, it is recommended that students have had training on Google SketchUp.
• Students have a good understanding of SAE (Imperial) and/or Metric units.
• Students have a good understanding of using a ruler.
• Students have a basic understanding of fractions and the ability to count.

To begin the lesson, ask students to identify the angle of a variety of objects on a sheet of paper. Doing so may involve some help; if necessary, show students that a paper folded can demonstrate angles of 90, 45, and 22.5 degrees fairly easily. However, it is not the best way to measure the angles of an object. At some point, students should come to the conclusion that they should just use a protractor (or, if they don’t throw out the word protractor, they may declare that there must be an easier way to do this). While we don’t condone an extensive history of a protractor, giving student a background of how they were developed would be helpful.

Seeing what’s on Thingiverse would be a good way to show that there isn’t really a GREAT protractor available.

Next, present students with their challenge:

Design a protractor that is easy to use and mathematically accurate.

Using only paper, pencil, a straight edge, and a lot of imagination, have students design the 2-dimensional version of their protractor. The difficult piece of this will be to sketch out the curved aspect, but it shouldn’t take much time. To make this more useful for the students, have them create a protractor that is an improvement over one that we already use.

The Meat
Within a 3D modeling program, groups will need to design their layouts for the protractor. The maximum height of extrusion allowed should be set by the instructor to limit the filament being used, but 50 mm is a good place to begin. The height of the protractors should not exceed 3 mm to limit printing time and material use.

When printing, it is advisable to print at least 2 perimeter layers thick, so take this into consideration during the design. Each perimeter layer is 0.3 mm thick.

To ensure that everything measures out accurately, groups will check their classmates’ designs prior to showing the instructor. The instructor will need to confirm the students’ designs as best as possible before sending it to print.

Once the design has been printed, students will clean it up and verify all measurements for accuracy with a ruler and a protractor. The real test will be to see how accurate the angle measures are.

Discussion

• How did you come up with your design?
• What would you differently after seeing everyone else’s product?
• How could you get more precise with the measures on the protractor?

Each one of these questions can provoke thoughtful responses that are rich in mathematical reasoning.

Just like in a Research and Design lab for major companies, the feedback and reflection on these projects will be the best part. Give students an opportunity to talk within their group and among their classmates to seek advice on improvements. After completing their print, groups will then proceed to:

• Reflect on what went well and what they would improve on if they had a chance to print again.
• Create a marketing plan to sell your product to a specific group of people or industry.
• Set a desired cost for the protractor, including shipping, based on cost to create the product and cost of shipping.
• This might be a good fundraiser at the school and can even be printed in school colors!

For the advertisement, students have the option of their medium. Whether it is creating a website, video commercial, radio commercial, magazine ad, billboard, or many others, the key is to be creative in the area that the students are comfortable. During this portion of the project, students will need to work efficiently within a deadline provided by the instructor.

Following the creation, students will showcase their advertisement with the class. Students can vote on which one is the best to use as the model for the school.

Desired Outcomes
A desired outcome is a protractor that is mathematically accurate down to angles in 15 degree increments. An added bonus is the ease of use (a space to rest a pencil or pen as angles are being drawn and/or measured, for example).

Once You’re Finished
Everyone loves a practical fundraiser! These could easily sell for a dollar or two and customized with the school colors, initials, or small personal messages. Get creative with it and the possibilities are nearly endless.

Content & Instruction Developed by:
John Stevens – Airwolf 3D STEM Consultant
Instructional Coach – Technology
Chaffey Joint Union High School District
CUE Rockstar Faculty & Organizer

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