Teach Surface Area and Volume in the Most Engaging Way!

Build a Zarcon-proof home as a math activity that will provide tremendous advantages for engagement, for differentiation, and for mastery of concepts.

By Barry Nitikman


Example of project

There is a world of creativity that can be employed with something as simple as a cube and a rectangular prism. Have your class work intimately with the concepts of surface area and volume as they create Zarcon-proof homes, which are protected from deadly rays by aluminum foil. To construct these homes, your pupils can do something as simple as take a rectangular prism, place a cube on top of it, and call it their “home.” Depending on ability level, you can also have them add on some cones, triangular pyramids, or any other shape. Then, they will measure the surface area, being careful to subtract any areas that are covered by another structure (such as where the cube is placed). They will use the surface area measurement to order (from the teacher) the correct amount of foil needed to protect the home. That in itself is a sufficiently complex problem to challenge a normal fifth grader, let alone a struggling one. 

You can conduct this as a solo project, a project for pairs of learners, or for small groups; it’s entirely your choice. I have provided a complete set of formulas for the various shapes as part of the handout at the end of this article. However, these worksheets are universally available on the Internet, and you can easily find a set of shapes that will work for your learners. This project can be adapted for grades higher than fifth grade by simply changing the shapes used.

Project Advantages

You will have the flexibility to provide for easy differentiation from your most challenged learner, to the most brilliant. The shapes can range from the simplest (cube or rectangular prism), to the much more involved (cones, cylinders, spheres, rectangular pyramids, icosahedrons, etc.). Allow your struggling kids to complete the project by using a single cube or rectangular prism. Your advanced learners can take it as far as they are able, which gives them the opportunity for a great deal of added complexity and challenge.  

This is intended to be about a weeklong project (three or four class sessions), and should culminate in students being assessed on the math concepts and demonstrating their mastery. The idea is that this will bring the math to life and force the kids to interact with surface area and volume, rather than just working on problems in a book. Many teachers augment their textbook work by having the kids work with manipulatives, which can be effective. However, I believe this project goes a step further in acquainting them with the concepts because the project itself is inherently high-engagement, and provides extensive practice in using surface area and volume.


  • Boxes: Kleenex boxes, gift boxes, shoe boxes, etc.
  • Toilet paper rolls, cylinders (empty food cans), cones, balls (spheres), etc.
  • Rulers with centimeters.
  • Glue and/or tape. You may need both.
  • Aluminum foil (one large container is enough).


  • Introduce the basics of surface area and volume. I say basic, and I mean basic. Introduce the unit and do some practice problems just to get pupils into the idea of what surface area means, and review the idea of area (especially if the area/perimeter unit was previously taught).
  • Introduce the challenge; explain the parameters and the materials.
  • Students then select the materials they will use, and set about designing their structures.
  • Next, have them calculate the surface area and volume of their structure (to the nearest square centimeter, and note this carefully). Stick to simple structures for those pupils who struggle with math.
  • Remember that they will need to subtract any areas that are covered by an object. This is something that you will want to make sure to cover beforehand. At this point, students take their calculations to the teacher to check for accuracy. (It’s a good idea for kids to write the actual surface areas right on the structures; this will be covered by foil later on anyway.) To protect their structures, they will receive the exact amount of aluminum foil they have calculated and "ordered" from the teacher.
  • They apply the aluminum foil to complete the structure. Then they complete the report and turn it in to the teacher. They must also turn in the pages they used for their calculations.
  • If someone miscalculates and doesn’t have enough foil to finish their project, you have the option of allowing pupils to negotiate for more foil. However, you can also choose to be strict and not allow for more foil. This approach will stress the importance of making accurate calculations. It's up to you, the teacher.
  • Set aside a time at the end of the project for the class to share their projects, critiques, realizations, etc.     

Important note: This particular lesson as presented was intended for GATE 5th graders, consisting of some pupils who were relatively unfamiliar with anything beyond standard perimeter and area, as well as others who had been working with the circumference of a circle, and also area and perimeter of more advanced shapes. It worked beautifully for all of them. With some simple modifications, it would absolutely work well in a class of struggling mathematicians.

As you will quickly realize, it is very easy to adapt this for almost any grade level by simply adding or deleting a few words. Obviously, with ELL’s, you will need to provide oral explanation, and/or have the sheet(s) translated. But honestly, once you’ve finished reading this, you will realize that the concept of the project itself is really quite simple: you need to build a structure, figure out the surface area and volume, and cover it completely with aluminum foil.

Helpful Worksheets to Successfully Complete this Activity:

Building a Zarcon-Proof Home-Activity

Building a Zarcon-Proof Home: Report

Formulas for Surface Area and Volume of Various Shapes