This title became obvious to me this past week as I listened to my student discussions. I did an activity with my Algebra 1 classes where groups of three students had to make a 4 by 4 with playing cards, so that the all rows and columns add to 25. When that was accomplished, I asked them to now make all rows and columns add to 31 (if they completed that, I had them go to a 5 by 5, sums to 31). Many groups just put down cards and forced it to work. Some groups thought it through and started with a pattern. Before they attempted the sum of 31, I asked how they got 25 and could they use what they learned to get 31. I suggested they look for patterns. Again, some groups just started over. Most of the groups replaced one card at a time until they got it to work. One group discussed for a long time and JUST REPLACED A DIAGONAL to complete the sum of 31 by increasing each card in the diagonal by 6 (WOW). This would not work if the diagonal were larger card values, but they originally started by putting tens on the edges. GREAT DISCUSSIONS!
After the activity we debriefed and I explained that I was more interested in their discussions and the approaches they took. We finished the class by talking about “Growth Mindset” vs “Fixed Mindset” people. This will really lend itself to the mathematical practices discussion later.
In my Honors Algebra 2 classes I started with a 5 by 5 getting a sum of 31. The number of groups that started with a pattern was much larger and the discussions were much richer. I then asked them to think about increasing the sum to 35, but without actually doing it. This got better thought and discussions than if they just did it. AWESOME ACTIVITY.
Next up…VRG and VNPSs….I explained to my classes that I had way too much whiteboard space for me and I would need their help filling them with math next week.