1. Lesson Title: Geometry for Breakfast
2. Date of Implementation: 5/14/07
3. Lesson Author(s): Celia Lilly
4. Subject Area(s): Math
5. Grade Level: 7
6. Approximate Time Needed: 2-3 weeks
7. PA Content Standard(s): 2.9 Geometry
8. Objectives/Lesson Outcomes: Students will investigate cereal boxes and create a new cereal box design that will contain the same amount of cereal (or more) as the given existing box. The box needs to be cost effective so it may NOT contain any additional cardboard that the existing box. HINT: Surface must be reduced but volume must be same or reduced while using the same amount of cardboard.
9. Materials and Resources Required:
A. Technology (include location and equipment): http://jcrystal.com
http://illuminations.nctm.org
http://solidworks.com
B. Printed Materials:
Prepared worksheets on similarity, scale drawings, surface drawing, matching surface areas, shape recognition, area of regular polygons, surface area of cylinders, volume of your box, volume of prisms, solids worksheet.

C. Other Supplies: Existing, empty cardboard cereal box, rulers, scissors, scotch tape.
10. Lesson Procedures: ( Parts 1-8 involve your original cereal box. Part 9 is your new design.)
1. Determine whether any of the rectangles on your original cereal box are similar by measuring the edges of each rectangle to the nearest tenth of a centimeter. Then sketch each face of your box and record the measurements. Label the faces as bottom, top, sides, front and back. Prove, using what we have studied about similarity, whether or not any of the faces on your box are similar.
2. Make a scale drawing of your original cereal box by using similarity. Do this by using the measurements of your cereal box, decide on a scale that will allow you to draw your cereal box on a standard piece of paper. Use your knowledge of similarity and proportions to find the scale measurements of your box. Draw your box on the paper. Use a ruler. In the lower corner, include a key that tells your scale. List the original and scale measurements for the length, width and height of your box.
3. Find the surface area of your original cereal box. First, draw, using a ruler, the net of your cereal box. Label the dimensions along the edges. Calculate the surface area. Do your work neatly, explain and appropriately label.
4. Find three different geometric solids that have the same surface area as your
original cereal box. You may use the above mentioned websites to explore different 3D shapes.
Sketch the three geometric shapes you chose and label the dimensions. Calculate the surface area of each. Show all your work and label correctly. Make sure you include the surface area of your original box at the top of the page.
5. Some of you may be thinking of creating a new cereal box design with a base of a pentagon, hexagon, octagon, etc. Complete the regular polygon worksheet that deals with number of sides, triangles and angle measurements as well as the worksheet on calculating the area and surface area of regular polygons.
6. Find one cylinder that has the same surface area as your original cereal box. You may use the above mentioned websites to help you. Sketch the cylinder measurements. Show the calculations of the surface area. Write the surface area of your original box on the top of the page.
7. Find the volume of your original cereal box. Use the actual dimensions to calculate the volume. Show the formula you used and your calculations. Label the volume with the appropriate measurements.
8. Find one prism (other than a rectangular prism) and one cylinder that have the same volume as your original cereal box. You may use the above mentioned websites to help you. Sketch the prism and the cylinder with measurements labeled.
Calculate the volume of each, showing your work neatly. Clearly write the volume of your box on the top of the page.
9. Finally, using the web sites listed and the knowledge learned from the above calculations to create a new cereal box design. Remember, you need to draw a 3D sketch of your new design with dimensions labeled, draw a net of your new design

with dimensions labeled, calculate surface area of your new design accurately, calculate volume of your new design accurately, and use the cardboard from your original cereal box to create a new 3D cereal box with accurate dimensions and construction. Remember: The surface must be reduced but the volume must be the same or reduced while using the same amount of cardboard. Finally, write a paragraph indicating why your new design is a good one.
11. Modifications for Differentiated Instruction:
A. Remediation: Create models of 3D shapes using provided nets or straws and marshmallows prior to the actual construction of a new cereal box.
B. Enrichment: Promote the new cereal box design to the manufacturer by designing a poster, oral presentation, jingle, commercial, etc.
12. Student Assessment:
Student worksheets on original box will be graded to include:
___/2 make 3D sketch with dimensions labeled
___/2 make a net with dimensions labeled
___/2 calculate surface area and show work neatly
___/2 calculate volume and show work neatly
___/2 additional worksheet calculations (regular polygons)
Your new cereal box will be graded to include:
___/10 draw a 3D sketch with dimensions labeled
___/10 draw a net with dimensions labeled
___/15 calculate surface area accurately and show work neatly
___/15 calculate volume accurately and show work neatly
___/10 write a paragraph giving reasons why this is a good design
___/30 accurate dimensions and construction of new design