I gave the following Illustrative Mathematics task:
Quickly during break, I did a cut and paste and created this:
Eventually, I hope to make the differences between my 1st and later periods less extreme...this reflection blog should help.
Here are a few more observations about this activity:
- My students either never learned how to add and subtract on a number line, or they have since forgotten (due to lack of usage, I'm sure). Most groups chose to assign a number value to a and b in order to answer the question. For example, they would say that letter a is positive because it's about 1 1/2, and 1 1/2 - 1 would still be positive 1/2. Similarly, for question b, they said 1 1/2 - 2 would get you into the negatives. Most groups did not look at using the number line to "jump" one or two places to the left.
- Question c allowed great conversation! There was confusion and blown minds...it was great! Most groups said -b would be negative, but a few figured out the idea that it would be the opposite of b (or a positive).