Group Work, In-Class Activity (also can be used as Homework)

Time Required: 30 minutes

Materials: regular graph paper

Objectives:

• Solve systems of equations
• Accurately plot points and graph lines
• Interpret the relationship between the solution to a system of equations and the corresponding graph
Prerequisites: Solve a system of two equations and two unknowns graphically and algebraically.

Description:

This activity reinforcse the relationship between the solution to a system of equations and the intersection of their corresponding graph. Generally, students begin to solve systems by using graphing and then algebra. Once a student learns to solve the system by algebra, they often forget the connection to the graph. Hence in this lab, they will use algebra first and then graph their answers.

The situation is one where the student is asked to determine where an animal trail intersects with an access road. Given linear equations which represent the placement of the access roads, assign each person/group one or more equations representing an 'animal trail'. They will then determine where their trail intersects each of the two roads. This represents the spot where they will lay their have-a-heart trap. (A have-a-heart trap is one which is baited with food and catches the animal alive without hurting it.) After solving the systems, a graph is drawn to determine if the placement of the traps is accurate.

This lab is a good summative activity to reinforce the connection between the algebraic and geometric representation of a system of equations.