Students find the volume and surface area of a rectangular box (e.g., a cereal box), and then figure out how to convert that box into a new, cubical box having the same volume as the original. As they construct the new, cube-shaped box from the original box material, students discover that the cubical box has less surface area than the original, and thus, a cube is a more efficient way to package things. Students then consider why consumer goods generally aren't packaged in cube-shaped boxes, even though they would require less material to produce and ultimately, less waste to discard. To display their findings, each student designs and constructs a mobile that contains a duplicate of his or her original box, the new cube-shaped box of the same volume, the scraps that are left over from the original box, and pertinent calculations of the volumes and surface areas involved. The activities involved provide valuable experience in problem solving with spatial-visual relationships.

To display the results from the previous activity, each student designs and constructs a mobile that contains a duplicate of his or her original box, the new cube-shaped box of the same volume, the scraps that are left over from the original box, and pertinent calculations of the volumes and surface areas involved. They problem solve and apply their understanding of see-saws and lever systems to create balanced mobiles.

Student pairs are given 10 minutes to create the biggest box possible using one piece of construction paper. Teams use only scissors and tape to each construct a box and determine how much puffed rice it can hold. Then, to meet the challenge, they improve their designs to create bigger boxes. They plot the class data, comparing measured to calculated volumes for each box, seeing the mathematical relationship. They discuss how the concepts of volume and design iteration are important for engineers. Making 3-D shapes also supports the development of spatial visualization skills. This activity and its associated lesson and activity all employ volume and geometry to cultivate seeing patterns and understanding scale models, practices used in engineering design to analyze the effectiveness of proposed design solutions.

The purpose of this lesson is to identify and describe prisms and pyramids (3-D shapes).

Included is a YouTube video to support Grade 3 Blended Learning Math - Unit 6.3: Geometry - Describing Prisms and Pyramids.

The purpose of this lesson is to activate prior knowledge about shapes and objects.

Included is a YouTube video to support Grade 4 Blended Learning Math - Unit 6.0: Geometry - Introduction.

The purpose of this lesson is to recognize and sort objects.

Included is a YouTube video to support Grade 4 Blended Learning Math - Unit 6.1: Geometry - Objects in Our World.

The purpose of this lesson is to construct prisms from nets.

Included is a YouTube video to support Grade 4 Blended Learning Math - Unit 6.3: Geometry - Exploring Nets.

The purpose of this lesson is to explore drawing objects.

Included is a YouTube video to support Grade 5 Blended Learning Math - Unit 6.7: Geometry - Drawing Objects.

The purpose of this lesson is to explore finding the volume of a rectangular prism.

Included is a YouTube video to support Grade 6 Blended Learning Math - Unit 6.9: Geometry - Volume of a Rectangular Prism.

The purpose of this lesson is to learn how to find the surface area of rectangular prisms.

Included is a YouTube video to support Grade 8 Blended Learning Math - Unit 4.3: Measuring Prisms and Cylinders - Surface Area of a Right Rectangular Prism.

Students find the volume and surface area of a rectangular box (e.g., a cereal box), and then figure out how to convert that box into a new, cubical box having the same volume as the original. As they construct the new, cube-shaped box from the original box material, students discover that the cubical box has less surface area than the original, and thus, a cube is a more efficient way to package things.