Solving a System of Linear Equations: Escape from the Tomb

From NCTM "Illuminations".  Detailed lesson plan for hands-on activity that can be solved experimentally and by solving a system of linear equations.  Two bowls are suspended from the ceiling by springs. One bowl is lower than the other. In one bowl, you can only place marbles; in the other bowl, you can only place bingo chips. Students must determine how many items must be placed in each bowl so that the heights of the bowls are the same.  Requires some setup and materials.  Resource includes instructor materials and well-designed students worksheets to accompany the project. Students represent the problem physically,symbolically and by using a table. Exact solution requires solving a system of linear equations.

Standards & Objectives

Learning objectives: 

Students will:
Solve a system of linear equations.

Lesson Variations

Blooms taxonomy level: 
Understanding
Extension suggestions: 
  • Change at least one of the items so that students have to solve the problem again, this time not using both bingo chips and marbles.
  • As students test their solutions, begin a discussion about human error and uncertainty. Talk about the fact that not all the individual objects weigh the same, or about how measuring the distance to the floor can attribute to calculation errors.

Helpful Hints

Materials:

  • Springs (or Slinky® Jr.)
  • Two small paper bowls
  • Bag of bingo chips
  • Bag of marbles
  • String
  • Scissors
  • Tape measure
  • Calculator
  • Escape From the Tomb Activity Packet 

References

Contributors: