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I play a game in class called guess my dice right before we do factoring. I made this up when I taught a low level Algebra 2 class. I roll two dice that have more than six sides. (I started with six siders and then very quickly went to a local game store and bought some 8,10, and 12 sided dice.)
I tell my students that my dice add to 19 and multiply to 88 and ask them to guess my dice. I try to play this at the end of class for a week or two as I have time leading up to factoring. Then when they discover how to factor this dice guessing skill is very helpful. They always realize what I’ve done and think I’m really tricky.
Level 1: Two dice – For each level progress to higher sided dice.
Level 2: One red and one yellow (any colors) – The red die is negative. (don’t tell them)
Level 3: Two dice – Both dice are negative.
Level 4: Two dice – mix Levels 1-3. Sometimes give “fake” numbers with an impossible solution. When they give up or say it’s not possible, ask how they know they have exhausted all possibilities. – suggestion from a comment on Dy/Dan by Timstudiesmath.
Level 5: I just came up with a possible level 5. — Create a table of all the possibilities for sums and products and the corresponding values that my dice would be.
Another option but not really a level: Once students “get how to play” they can play in groups of four with one player as the dice roller.