# Changing the Shape of Breakfast

 Author: Gina Ogden Unit Title: Changing the Shape of Breakfast Grade Level: 7th/8th Subject Matter: Math Estimated Duration: 10 days – 100 minute class periods Background Knowledge: How to determine surface and volume of three dimensional shapes How to measure lengths accurately to the nearest millimeter Date: May 2013
##### The Big Idea

Students will explore volume and surface area of different 3-D shapes.  They investigate the volume and surface area of different brand name cereals.  Students will be given the challenge of redesigning the General Mills cereal, Cheerios, to create a more environmentally friendly box design while holding the same amount of cereal.

##### Essential Questions
1. What impact does the size of a cereal box have on the environment?
##### The Challenge

Students will take on the role of package designers for an advertising company. The advertising company has been hired by General Mills to change the box of their popular cereal, Cheerios. The box must use less cardboard while holding the same volume of cereal.

##### The Hook

Look at 15 examples of how cereal boxes have changed over time.  Discuss how and why the box designs have changed.  Talk about how the current cereal boxes might look in the future.

##### Guiding Questions
1. What has driven the change in cereal box designs?
2. What different sizes of cereal boxes can you buy in a store?
3. What did you notice about the packages and the products inside?
4. Would you consider these packages to be environmentally friendly?
5. How do cereal boxes compare in terms of surface area?
6. How does the volume of different cereals compare?
7. Why are some boxes of cereal smaller/larger than others?
8. What could you do to change the packages to reduce the excess packaging?
9. How does the box design affect the shelf storage and visual appeal?
10. What is the relationship between the surface area of a box and the volume of the cereal in it?
##### ACS (Real world applications; career connections; societal impact)

A – Students will understanding that consumers are a driving force behind the packaging of products.

C – Product design engineer creates the initial blueprints and schematics for various structures, systems, machines, or equipment involved in producing a product.  Industrial engineer determines the most effective ways to use machines, people, and energy to make products.  Environmental engineer to provide input on total environmental impact of producing the product.  Mechanical engineer is involved in managing the equipment that is used to produce the product.  Graphic designer  works with the clients to determine the budget, concept, graphics and layout for product illustrations.

S – Cereal is the most popular breakfast food.

##### Engineering Design

Students will be presented with a problem that will require the use of the engineering design process. They will explore the surface area and volume of various cereal boxes.  They will then be challenged to create a more environmentally friendly box design while holding the same amount of cereal.  Students will brainstorm possible solutions for the challenge, prototype a solution, test and evaluate the effectiveness of the prototype.  The evaluation will determine if the prototype needs to be modified and tested again.  Students will continue modifying their designs as needed until the best solution has been found for the problem.

• Solve problems involving proportional relationships and scale factors; e.g., scale models that require unit conversions within the same measurement system.

• Analyze problem situations involving measurement concepts, select appropriate strategies, and use an organized approach to solve narrative and increasingly complex problems.

• Understand the difference between surface area and volume and demonstrate that two objects may have the same surface area, but different volumes or may have the same volume, but different surface areas.

• Describe what happens to the surface area and volume of a three-dimensional object when the measurements of the object are changed; e.g., length of sides are doubled.

7.G.6 Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.

8.G.9 Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.

##### Assessments

Pre and Post Assessment (Net, Surface Area, and Volume)

Students will test the volume of their redesigned cereal box.

Post Test: Nets, Surface Area and Volume.

##### How to Make This a Hierarchical Unit

This is a Middle School Unit. This lesson could be modified for high school by expanding on the number of cereal boxes the students are required to redesign.  Students could also be challenged to make a box with the smallest surface area possible and still hold the same volume of cereal.