Activity: Problem 1 and Problem 2

Submitted by Jim Brennan, adopted from Massachusetts professional development workshop for the Standards for Mathematical Practice.

A second student is asked to complete problem 1. The student takes a different path (knowingly or unknowingly, even if I have to get in their way so they choose a different path.) Student two finishes the problem, gets a short round of applause, and I thank both for their efforts.

Short class discussion about how both students solved the problem; they took different paths to solve the problem but they got to the same finish. Maybe one was a more direct approach, maybe one is more creative (clownish is fine too);

Next comes problem two. A page marked "Problem 2 Start" is placed on the floor; a third volunteer is selected. They watch me pick up the "Problem 1 Start" and "Problem 1 Finish" pages, and they are asked to finish problem 2. They have no way of knowing that I had hung the "Problem 2 Finish" page on the bulletin board near the Math/Science office. I ask them to finish problem 2; we discuss what happens;

What to look for:
• That the student moves at all, which is great that they realize that they know that they are not done, and that they have to try something;
• The student may look toward me for visual clues as to what to do, or if they had moved they may look for signs that they are on the right track; they get no feedback from me; what they know is that if they go back they are no closer to finding a solution than when they started, so they should not go back; The general discussion point is that sometimes you select a path and you see if it is reasonable, maybe you can't tell if you are on the path to a solution, but if there is no indication that your are not on a solution path then why not keep going.
• In both classes I did this with both students went to the location where "Problem 1 Finish" had been; this was awesome, since often we want to solve a new problem by looking at the solution to a problem that we have already solved. I could not have scripted this better.

File: Start-Finish.pdf

• The four-page PDF contains starting and ending points for two problems. Placing them in plastic sheet protectors or laminating them makes them reusable; This is good to use one time per class per year;
• Using this activity at the beginning of the year is a good idea for referring back to the outcomes and drawing connections to other activities.

• Practice 1: Make sense of problems and persevere in solving them.
  Big Idea: Identify entry points to a solution
  Big Idea: Monitor Progress, change course if needed

• Practice 3: Construct viable arguments and critique the reasoning of others.
  Big Idea: Use Previous Results