Provide each small group of three or four students a worksheet containing systems of equations where they must rewrite one of the equations into the proper format and substitute it into the second equation. For example with a system of equations where “x + y = 11” and “3x – y = 5,” the group could rewrite the first equation as “x = 11 –y” and substitute it into the second equation to read “3(11 – y) –y = 5.” Students in the group talk through the steps of the activity and complete the assignment, asking for teacher input where required.
Provide a group of students with story problems they must write as an algebraic equation and solve for the variables, using substitution. Here's a story-problem example: “One pitcher and two bowls hold 8 cups of milk. One pitcher minus one bowl holds 2 cups of milk.” From that example, the group would determine that the system equations should read: “x + 2y = 8” and “x – y = 2.” Rewriting the second equation provides a substitution of “x = y + 2.” When the substitution is applied, the first equation appears as “2 + y + 2y= 8.” Solving for “y” results in a value of 2 and allows the group to determine that the value for “x” is 4. The group determines the pitcher holds 4 cups of milk and each bowl holds 2 cups of milk.
Assign students into groups of four, and provide each group with eight problems. With each problem, one student must create the first substitution equation, a second student solves for the first variable, the third student solves for the second variable -- and the last student checks the two equations to verify that the ordered pair works in both equations. With each system of equations, the students switch roles until each student experiences solving each of the four steps twice.
Divide the class into four groups. Display a system of equations on the whiteboard or smartboard. Allow the team to work quickly to solve for the variables, using substitution. The first team to correctly supply the constant values of both variables sends a team member to the board to demonstrate the solution using substitution. Teams receive points for correct answers and correctly demonstrating the solution.