Objective: To be able to write and solve a system of inequalities and equations with a creative twist. This will also be an introduction to linear programming.

Materials Needed:

• Graph paper (at least two sheets)
• Ruler
• Candy (or something to hypothetically hide on the graph)
• Clean sheet of paper

Background Information: Slope-intercept form of a linear equation is y = mx + b.

Length of Activity: You should allow at least two class periods working in groups of two. 

Procedure:

1. Divide the class into groups of two.



2. Give each student their candy or object to hypothetically hide on their graph.



3. Each group will “hide” their candy somewhere on the coordinate plane.
   1. Determine the grid point where you have hidden your candy.
   2. Write a system of three inequalities on a clean half sheet of paper where the solution will be a small area surrounding the hidden candy.
   3. Write a system of two equations on the other clean half sheet of paper where the solution is the exact location of the candy.


4. Groups 1 and 2, 3 and 4, 5 and 6, etc. will exchange their system of three inequalities.



5. When groups receive the system of three inequalities, give them sufficient time to graph the system on their own sheet of graph paper.



6. Once the time limit has expired or groups have successfully graphed the system, groups will receive the system of two equations from the same group they received the system of inequalities.



7. Groups will try to successfully graph the system of equations to determine the exact location of the hidden candy.



8. If Group 2 finds Group 1’s candy, then Group 2 gets Group 1’s candy.



9. If Group 2 does NOT find Group 1’s candy, then Group 2 does NOT get Group 1’s candy.



10. If Group 2 finds that Group 1 has made an error setting up their system of three inequalities or system of two equations, Group 2 gets Group 1’s candy.