Compare solving for a variable to solving a mystery. Show the clip https://www.youtube.com/watch?v=c6Vu-QzPgHU of the investigator “isolating” or identifying the guilty person. Stop the clip before the detective solves the mystery and ask students to try to solve the case based on the clues provided. Make the connection with “isolating” the given variable in the equation and “isolating” the guilty person in the clip. At this time, discuss as a class what the word isolate means to ensure that everyone understands the meaning. Good detectives use the same procedures every time. Good mathematicians use the same procedures to solve equations each time. Ask students to think back and explain how the detective was able to solve the crime in the clip we just watched. Explain to students that they will create a set of procedures to solve equations for a given variable.
Students will have one to two minutes to work alone on a problem (introductory problem; see attached) requiring them to solve an equation for a given variable. At the end of that time, the student will compare their work with their partner’s work. The teacher will then display the correct answer. At this time, instruct the students that each pair should work together to create a set of procedures explaining how they solved the problem. Allow students 5-10 minutes to do this, then as class let each pair share the procedures they created with the class. Each pair of students will then be given six problems to solve (worksheet; see attached), using the procedures they just created with their partner. Ask students to make a note if there are any changes that need to be made their procedures. Provide highlighters to each student and encourage them to highlight the variable being isolated as a further visual aid if they find it helpful.
Allow students to check their answers to the problems they just worked. Then, as a class, create one set of procedures for solving equations and isolating the variable in question. Each group should participate and help edit and improve the procedures until there is one document everyone can agree on. The teacher will write the procedures on poster/chart paper. The teacher will keep the procedures posted in the room throughout the year. If desired, the formal properties can be introduced in a subsequent lesson.
Conclude with an exit pass (attached) requiring students to solve for a given variable using the newly created procedures.