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# 7. Cookie Cutting and Fractions

Students will design a cookie cutter that cuts at least 6 cookies with equivalent dimensions.

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 a cookie cutter that cuts at least 6 cookies with equivalent dimensions.
• Students will design a cookie cutter with a frame that has the same thickness of material throughout its structure.
• Students will use their cookie cutter to represent various fraction addition and subtraction scenarios.
• Students will design an ornament using constructions and transformations prior to designing their 3D products.
• Students will create an advertisement to promote and market their ornament

Recommendations
Group Size: 3 to 4 students, depending on how many ornaments 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 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, give students an opportunity to discuss their favorite shape, or cutout, of a cookie. Is it a heart? A star? A square? Why? Getting some of these responses will validate what it is the kids are about to do. Once you have some responses and the discussion has started, show the class a variety of templates that could be used for creating crazy, cute, or delicious looking cookes. If it would help, have students bring in a sample cookie cutter from home (if mom and dad are OK with it, of course).

“At some point, though, cutting out cookies one at a time starts to get difficult. On top of that, most cookie cutters cut out HUGE cookies! Wouldn’t it be nice to cut out a lot of smaller cookies really fast that you could give out to your friends? Perfect.”

Next, present students with their challenge:

Create a cookie cutter that will cut out at least 8 cookies at a time with the same exact dimensions.

Using only paper, pencil, a straight edge, and a lot of imagination, have students design the 2-dimensional version of their cookie cutter. There will need to be a thickness to all edges, so a simple line will not do. For the most basic students have them create something that aligns with the look of an ice cube tray. For the most advanced students, have them do something more abstract or unique, just as long as they are consistent with their dimensions.

The Meat
Within a 3D modeling program, groups will need to design their layouts for the cookie cutter with a minimum width for each piece of 3 mm (just to make it easier to print). 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. Because there is likely going to be a lot of extrusion of surfaces within the modeling program, have students do a 360 degree inspection of their own design before sending to another group for review.

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. Also, since there will be instances during the print in which there is little (or no) support, reduce the speed of the print to allow for more time to cool.

To ensure that everything lines up 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.

Discussion

• How did you come up with your design?
• What would happen if you used a different shape?
• After seeing the other groups, what would you do differently?
• How are your products related to tessellations (if the difficulty necessitates this)?

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 cutter, including shipping, based on cost to create the product and cost of shipping.

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. If there are local business owners who can come in, this would also be a great addition. Contacting the local bakery or cupcake shop would be an outstanding outreach.

Desired Outcomes
A desired outcome is a cookie cutter that aligns with the appropriate objectives, whether the teacher chooses to maintain the ones suggested here or modifies them to meet the needs of the students in the class.

Some Possible Extensions/Modifications
To scale this down for students who need it, give them a template that has some of the basic dimensions and have them work with the model to create something unique from it.

The scale this project up for students who can take it on, require at least one irregular polygon. Maybe you’ll make it so that students need to have the same area, yet they can have different shapes.

The instructor may also choose to use a Geometry approach to address similarity, congruence, and tessellations.

The real benefit here is the introduction of fractions. Using the cookie cutters and Play-Doh or other materials, have students cut out pieces and use them to represent a whole. From there, have students take out 3 of the whole, half of the whole, 1 of the whole, and let them represent that using images and/or fraction notation.

If you want to continue the idea of creating their own product, have students make Oobleck from water and cornstarch (here is the instruction list… very simple). Oh what fun!

Once You’re Finished
Wrap them up and give them to the parents for the holidays (or just for fun!).

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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