I begin this lesson with an equation in standard form on the board (3x +4y = 12) and complain that I can't put it into my calculator to graph it. I challenge my students to rewrite the equation in terms of x, so that the y variable is isolated and I can use my calculator to graph it. (MP1, MP2) This is a fairly simple challenge, but by putting it into a context my students understand and can relate to - using my calculator instead of having to graph by hand - I have better engagement. When everyone is finished, I randomly select three students to go to the front board to show how they rewrote the equation. I have three students instead of just one for two reasons. First, it reduces the pressure to be correct in front of classmates. Second, it gives multiple examples of how to work the problem, something I'm always trying to demonstrate for my students. We review the work as a class and I ask if there are any questions. This is an opportunity to see how strong my students skills at rewriting equations are, to address general areas of confusion, and to note which students may need additional support during this lesson. In particular I look for students who struggle with either changing the sign from positive to negative as they move 3x across the equal sign, or who forget to divide both 3x and 12 by 4.
You will need copies of the formula sheet and Game Time rubric for this section of the lesson. I tell my students that today they will be working in teams to create a game (like chutes n ladders or Trivial Pursuit) to practice rewriting formulas. I say they will be working with their front-partner and that I will be providing a list of formulas, but that they can use additional formulas if they choose, so long as the formulas are in common use. I tell them that they have 25 minutes to create their game, which must include the correct answers to each question, so that we have time for other teams to play them. I pass out the formula sheet and Game Time rubric and ask if there are any questions. (MP1) While my students are working, I walk around offering encouragement and redirection as needed. This is also my opportunity to make sure that the games being created actually meet or exceed the rubric, so that when it's time to play, all the games are good to go. My Twist It video explains why I chose to have my students create a game for this lesson.
After about 20 minutes I advise them that they need to finish their games and get ready to share them. I have each team pass their game rules and materials clockwise and tell them teams that they have about 10 minutes to play. I collect all the games at the end of this session so that we can use them again tomorrow during our review.
I ask my students to pair-share about the arithmetic they used to rewrite these equations. After a moment or two, I randomly select students to share what they talked about with the class while I summarize their comments on the board. This activity helps them recogize that we use the same kinds of mathematics to rewrite formulas and to create and solve equations; that mathematics is not a series of isolated processes but a network of options.