## Building a Better Cereal Box

### Beginning at the End

The goal of this STEM PBL is for students to create a cereal box, in a shape other than a rectangular prism, using a 20-inch x 30-inch sheet of cardboard or poster board. The cereal box must be self sealing, openable, and reusable. Students will present their product, and all of their findings.

### What to Know BEFORE You Start

#### Background Information

• This STEM PBL is aimed at on-level high school students.
• For this STEM PBL to be successful, students must: know how to find the area of two-dimensional shapes, be familiar with developing and using formulas to find area and volume of shapes and solids, be familiar with multiple representations of shapes and solids.
• Students should be grouped so that each students talents complement the talents of the other members.

#### Content Objectives

Mathematics

• Calculate surface areas and volumes of prisms, pyramids, spheres, cones, cylinders, and composites of these figures in problem situations.
• Calculate areas of polygons, circles and composite figures.
• Use nets to represent and construct 3D figures.
• Analyze the relationships between 3D geometric figures and related 2D representations and use these representations to solve problems.

English

• Work productively with others.
• Participate in teams, building on ideas of others, contributing to relevant information, developing a plan for consensus-building, and setting ground rules for decision-making.
• Write expository and procedural or work-related texts to communicate ideas and information that include organized and accurately conveyed information.
• Write persuasive texts to influence the attitudes or actions of a specific audience on specific issues.
• Write an argumentative essay to the appropriate audience that includes an analysis of the relative value of specific data, facts, and ideas.

Visual Media Analysis and Production

• Produce visual representations that communicate with others.
• Use a range of techniques to create a media text and reflect critically on the work produced.

Physics

• Use a systematic approach to answer specific laboratory and field investigative questions.
• Communicate valid conclusions supported by the data through various methods such as lab reports, labeled drawings, graphic organizers, journals, summaries, oral reports, and technology.

Art

• Communicate ideas through artwork using a variety of media with appropriate skills
• Express thoughts and ideas creatively while challenging the imagination, fostering reflective thinking, and developing disciplined effort and progressive problem-solving skills.
• Use visual solutions to create original artwork by problem solving through direct observation, original sources, experiences, narrations, and imagination.

#### STEM Connections

Technology

• Use a variety of technology tools to gather information.
• Use technology tools to present data and information.

Engineering

• Discuss the purpose of teams, discuss the functions of different roles within the teams, and actively participate within teams, and actively participate within one with a positive attitude.
• Use consistent units for all measurements and computations.
• Engage in design and prototype development.
• Complete work according to established criteria.
• Develop a plan for implementation of an individual product.

Mathematics

• Calculate surface area, volume, and perimeter of shapes and solids.
• Use precise measurements.
• Use and construct nets for 3D shapes.

### Now, here's the plan.

#### Materials Needed

20" x 30" sheets of thin cardboard (8 per group), scissors, glue, markers/colored pencils, computers, access to colored printers, grid paper, and rulers

### Now it's time to take the plan into action!

#### DAY 1 (50 MINUTES)

To engage the students, the following two videos will be presented to the class.

Next, the students will use a Venn Diagram to capture similarities and differences between old and new designs as a class.

Following this, students will be put into groups of 4 to 5 for a challenge activity. This challenge activity will have students find all of the possible nets for a cube while racing against a clock set at 10 minutes. Groups will share and discuss. If possible, extend this activity to drawing nets for square pyramids, triangular prism, cylinder, cone tetrahedron, octahedron and dodecahedron.

In the spirit of learning... it's your turn to make a net! We might not all be familiar with how to do this, so here is a video to show you how to make a not only draw a net of a rectangular prism, but also how to put it together!

#### Day 2 (50 minutes)

Students will work together in their groups from day 1 to determine formulas for finding the surface area and volume of a rectangular prism, square pyramid, triangular prism, cylinder, and cone.

Students will end this day by constructing their own formula chart to use throughout the remainder of the PBL.

#### Day 3 (50 minutes)

• Groups will discuss specific characteristics of a cereal box that are valued by the consumer.
• Interviews of teachers, students, administrators, etc. will begin outside of class to generate data to settle on a list of the most important characteristics of a cereal box.
Example of a cereal box currently on the market.

What parts of a cereal box do you value?

#### Day 4 (50 minutes)

Creation of 3-5 prototype boxes from a sample piece of cardboard using perviously designed nets. The goal is to choose the net that would allow for the greatest volume.

#### Day 5 (50 minutes)

Students design the artwork that they will put on their final cereal box. Artwork has to include required nutritional information as well as corporate logos. Students are encouraged to develop packaging that attracts the millennial age group.

An example of cereal box artwork creation using technology.

#### Day 6 (50 minutes)

Students survey their peers regarding box preference and other elements of the rubric. 100 millennials must be surveyed.

#### Day 7 (50 minutes)

Students make changes, if necessary, to their prototype based on feedback from the survey on day 6 about their prototype and the current cereal box design on the market.

#### Day 8 (50 minutes)

The creation of the presentation!

#### Day 9 (50 minutes)

Students present their projects to an expert panel.

### Can you add more to this PBL? Of course you can!

Platonic Solids Extension Activities

• Activity 1: Identify all 5 Platonic solids. Draw a net of each.
• Activity 2: Create a table cataloging the number of vertices, edges, and faces. Identify any patterns in a chart. Can you discover Euler's formula? What might "complementary solids" mean?
• Activity 3: Sketch (draw and/or narrate) a process by which you could find the surface area and volume of any Platonic solid.

### Why should you choose THIS project for your classroom?

This STEM PBL evokes creativity from students because not only do they have to redesign the shape of a common item, they also have to make the new cereal box appealing to the viewer, present their creation in a meaningful way.

This STEM PBL could also be applied to different grade levels. As it is currently written, it is aimed towards high school level students. However, it could easily be applied in an elementary classroom if the mathematics requirements were adjusted.

### How would you use this STEM PBL in your classroom? Would you have changed anything?

It's okay to say yes! Everyone's classroom is different, especially whenever it comes to ages! I teach fourth grade, so it would have to be adjusted content wise, for sure! Here are some things I would do differently to fit me and my students:

• Allow students to make a rectangular prism
• Have students create a new cereal and brand, and then sell their product
• Use smaller groups (2-3)
• Present their cereal boxes to other classes and/or other grade levels

### References

McKissiick, S. & Whitfield, J.G. (2016). In Capraro, M. M., Whitfied, J. G., Etchells, M. J., and Capraro, R. M. (Eds.), A companion to interdisciplinary STEM project-based learning, pp. 11-18. Rotterdam, The Netherlands: Sense Publishers.