Mainly what I am worried about here is that question 2 will go awry and students will go overboard and way far away from equation types they know about. And I also don't know whether that would be a good thing that students and teachers can just roll with, or if it's going to present challenges that are too much for too many people.
So, if (and only if) this fits in with your plans, please try it out and let me know how it goes! Thanks in advance!
Okay here's the task:
1. Here are some equations that all have the same solution. Explain how you know that each equation has the same solution as the previous equation. Pause for discussion before moving to the next question.
x = -2
x - 3 = -5
-5 = x - 3
500 = -100(x - 3)
500 = (x - 3) ᐧ -100
500 = -100x + 300
2. Keep your work secret from your partner. Start with the equation -5 = x. Do the same thing to each side at least three times to create an equation that has the same solution as the starting equation.
3. Write the equation you ended up with on a slip of paper, and trade equations with your partner. See if you can figure out what steps they used to transform -5 = x into their equation. When you think you know, check with them to see if you are right.