# 5. Students Will Apply Their Knowledge of Volume Formulas to Design a Cup

## The Right Tool

Standards
A wide variety of Volume Standards are applicable, depending on the grade level and skill level of the students.

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.

Learning Objectives

• Students will design and produce a cup that holds 8 ounces of fluid.
• Students will apply their knowledge of volume formulas to design a cup.
• Students will test their product for reliability, applicability, and quality.
• Students will market their product to a specific audience using any form of advertisement.

Recommendations
Group Size: 3 to 4 students, depending on how many variations you would like students to compare within the class setting. For a smaller class, groups of 2 would be ideal.

Class Size: up to 36 students

Materials Required

• At least one computer per group, loaded with Google SketchUp
• Paper and pencil for drafting
• Airwolf 3D Printer
• Ruler to verify dimensions
• Samples of cups for students to get visuals to work with
• Measuring cups for verification purposes
• Download the free SKP (SketchUp) model here: Cup Design in SketchUp
• Download the free .STL model here: Cup Design .STL

Introduction
Assumptions being made:

• 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 Metric units.
• Students have a good understanding of formulas for volume.
• Depending on the level of the students and intricacy of cup, knowledge of Integration to find the area would be useful.

To begin the lesson, pose the students with the challenge of determining the volume of various cups that meet their current mathematics skill level. Using measuring cups and water, confirm the volume of any number of cups. This will give students an idea of volume and how it relates to the task that is coming their way.

Once students have had ample time (20-30 minutes) to determine existing volumes, use a google search to find unique cup designs present them with their challenge. Please note that there will be images of alcoholic beverages, so finding a few appropriate examples and having them ready when students walk in (please see images at the end of the lesson plan) would be advisable. Giving students a variety of visuals will help them break away from the standard cylinder or spherical designs that they are used to seeing. Next up is the challenge.

Challenge: Design a Unique Cup That Holds Exactly 8 Ounces of Fluid
Give students time to work in their small groups to design potential cups and a purpose for them. Why would somebody want to buy (or use) this cup? Is it simply unique and cool? Does it have a functional purpose behind the design?

After each group has come up with some brainstorm ideas, have them sketch their thoughts onto a piece of paper. Visualization of a unique product is a difficult chore, so this step is essential. Within a certain timeframe set by the instructor, students will need to commit to one specific design and work collectively to optimize its chances for success.

The Meat
On paper, students will work in groups to design a unique cup that they have described and sketched. All dimensions need to be included on the draft before showing the instructor. Furthermore, all portions of the cup need to be calculated to determine the interior volume.

For simple designs, using basic volume formulas will be sufficient. For more complex designs, starting in two dimensions to find the area, followed by the third dimension to complete the volume is recommended.

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. Following the check by the instructor, students will use a 3D modeling program, such as Google Sketchup, to design their product in 3D.

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’ drawings 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, pouring 8 ounces of water into the cup. Due to the variability in the project, it may be essential to note that we are looking for the group with the volume closest to 8 ounces. After marking down the actual volume for their cup, groups will then proceed to:

• Photograph their product for their advertisement (if it is a static ad)
• Test out their product to test for the purpose it is intended to serve
• 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 cup, including shipping, based on cost to create the product and cost of shipping (Look at sites like IKEA for reference)

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.

Discussion
What were some of the challenges in designing the cup? What did you learn during the project?

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 amongst their classmates to seek advice on improvements or modifications to obtain the ideal volume without compromising the uniqueness.

Desired Outcomes
A desired outcome is a cup that holds 8 ounces of fluid. The openness of the project limits the ability to predict an ideal product.

Some Possible Extensions/Modifications
To limit the amount of time spent printing, it would be possible to change the desired volume to 6 or 4 ounces (or a specific mL as well).

To bring this down a level, provide students with the task of recreating a cup that currently exists and testing it to verify that it is 8 ounces.

To step up a small amount, limit students to producing a cup that contains only cylinders and rectangular prisms. This will simplify the mathematics portion and improve the likelihood that their finished product is close to the desired 8 ounce outcome.

To bring this up a level, give the students a variety of obscure cups (Gatorade bottle, Blender bottle, etc.) and have them improve on a product like it. Whether it is a design that will fit the contour of their own hand a little bit better, become more efficient for a toddler, or any other number of specific challenges, this could really take off in a whole different direction.

Even more involved would be designing a cup that has a certain flow rate (straw hole, suction, etc.), but this would need to be for a high level group of students.

Once You’re Finished
Once finished with the project, have students give their product to someone who will use it on campus. They could decorate the cup with artwork and hand it off to office personnel, their favorite teacher, possibly even the custodian. If their cup has been designed for a toddler or young child, help students find teachers on campus with children/grandchildren that will benefit from a brand new and unique cup!

Content & Instruction Developed by:
John Stevens – Airwolf 3D STEM Consultant
Instructional Coach – Technology
Chaffey Joint Union High School District
CUE Rockstar Faculty & Organizer
Google Certified Teacher
TwitterBlogResourcesAuthor (Flipping 2.0)