Minimum Coverage

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Objective

SWBAT create dimensions that maximize volume and minimize surface area

Big Idea

How do you adjust for maximum inside and minimum outside?

Launch

5 minutes
  • POD

As students enter the room, they will have a seat, take out their Problem of the Day (POD) sheet and begin to work on the question on the SMARTboard. The POD allows students to use MP 3 continually based on the discussions we have about the problem each day.

The previous lesson introduced the application of surface area to students. The POD today will ask students to elaborate on their understanding of surface area and volume. I want to ensure that students recognize the difference between the two and can describe that difference.

Describe the difference between the surface area of a figure and the volume of a figure. Use an example if it strengthens your explanation.

Explore

30 minutes

Students will work in small groups today as we explore the idea of minimum surface area. Each group will get a copy of the “Minimum Coverage” record sheet and several sheets of centimeter grid paper. Using centimeter cubes, students will create different rectangular prisms and determine the surface area of each prism. I will tell them to make every possible prism they can using 12 cubes. Students will record the dimensions and the surface area of each of the prisms created. I want them to put a star next to the prism with the least surface area. I also want them to draw a net for each of the prisms on the grid paper. When all of the work is finished for the prisms made of 12 cubes, I want them to use 18 cubes and complete the same process.

Once the process is completed , I want groups to analyze their results. What dimensions have the least surface area? What dimensions have the most surface area? Is there any similarity between the prisms of 12 cubes and the prisms of 18 cubes with regard to the dimensions of the boxes with the least and the most surface area.

Once the discussion is finished, students will be tasked with designing the box with the greatest volume possible that has the surface area of 414 square centimeters (same area as the sheet of grid paper). They are to waste as little of the paper as possible so they need to think about what dimensions will result in the largest volume with the least surface area. They can cut the grip paper apart to reassemble it into a net if they want. Groups will share their boxes with the class and explain how they determined their dimensions when they finish.

Landing

5 minutes

The exit ticket today will ask students to create the largest volume using dimensions for a prism that has a surface area of 300 sq. centimeters. I want to see if students can generate the dimensions and volume on their own. Can they determine the length, width, and height without working in a group? Do they understand the concept of surface area well enough to manipulate the area of the faces of that figure to create greater volume? As a formative assessment, this exit ticket will help determine if we need to continue working to build understanding of the concept.