A major understanding in today's lesson is that at any step in solving an equation the solution set should remain consistent. This requires students to slow down and be more precise than usual in their thinking (MP6). In slides 2 and 3 of Solving and Justifying Equations, students verify what they had learned in a previous lesson showing that a value substituted in for the variable will make the equation true after a term has been added to each side or each side has been multiplied by a non-zero constant.
(1) I will allow students to experiment with adding/subtracting a term of their own choosing. I want to remind students that the term that is added or subtracted could be a variable. Also, I remind students that the emphasis is not on isolating the variable, rather it is on verifying the equivalence of the two expressions after manipulating each side of the equation.
(2) "Multiplying" by a non-zero constant could also mean multiplying by a fraction with 1 in the numerator which would be the same as dividing by the denominator of that fraction. You also have the option of changing the statement above to multiply or divide by a non-zero constant depending on the terminology you choose to use with your students.
While students are working, I will try to pinpoint a few students who chose to manipulate the problem in an interesting way. I then have a handful of students (3-5) put their work on the board. I intentionally pick different approaches such as adding variables, integers, subtracting integers, etc. (Adding two different integers will not really show the variance in possibility).
Увидев эту цифру, Бринкерхофф испытал настоящий шок. 999 999 999. Он ахнул. Миллиард долларов. Соблазнительный образ Кармен тут же улетучился.