"Just Flakes Cereal" needs your help! CCSS.Math.Content.7.G.B.6

Looking back through my files, I found a project-based learning task that I'd like to replicate and improve.  I used it last with a group of 8th graders but that was several years ago.  With the advent of the Common Core State Standards, this set of labs would fit better in grades 6 or 7.  The CCSS.Math.Content.7.G.B.6 says, 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.

The set of activities consists of two labs that lay the foundation for the project.  The topic is exploring volume and surface area of rectangular prisms.

I asked students to work in small groups (2 - 4 students) to complete the activities.  For the lab activities, students were expected to create lab reports.  Basic information for all lab reports include students' names, a title for each activity, hypotheses, labeled drawings, and math computation.

Lab Activity #1

How many different shapes of rectangular prisms can be formed with 36 cubes, each of which is one cubic inch?  Sketch your responses and label the dimensions.

(a) Of these, which has the greatest surface area?

(b) Given a specific volume, can you predict which shape will have the greatest surface area?  the least surface area?  Explain using complete sentences and correct mathematical terminology.

(c) Test your prediction using a different number of cubes, each of which is one cubic inch.  Again, sketch your responses.  Label the dimensions and the surface area of each.

Lab Activity #2

You will need 7 pieces of 9” x 12” construction paper.  Using one piece of paper, cut a 1” square from each corner, fold up the sides, and tape them.  This creates an open box.  Now, repeat this procedure, each time cutting a larger square (1.5”, 2”, 2.5”, 3”, 3.5”, and 4”) from each corner, creating a series of boxes. 

a)    Without measuring, put your set of boxes in order from the least volume to the greatest volume.  Sketch your response.

b)    Now measure each box, find the volume of each.  Were your choices in (a) correct?  Explain in complete sentences. 

c)    Assuming each box has a “lid”, find the surface area of each box.  A complete response will include a sketch of each box, with the dimensions.  Include the volume and surface area of each.

Project:  As food costs increase, many manufacturers are looking for ways to cut costs.  The Just Flakes Cereal Company is interested in packaging their cereal with less cardboard.  They have come to you for help.

Use a standard cereal box for this project.

a)    Measure the cereal box carefully.

b)    Draw a net of the box on graph paper.

c)    Find the volume and the surface area of the box.

d)    Create a box with approximately the same volume using less cardboard. 

e)  Create a presentation for the Just Flakes Cereal Company demonstrating how they could use less cardboard for their cereals.

f)  Your opinion please:  why do you think manufacturers of cereal use the size boxes that they do instead of ones that use less cardboard?

I like to use cereal boxes in math because of their easy availability.  If you Google cereal box math pages of ideas pop up!