I must start off today saying that I have never experienced such a fantastic start to the school year than I have this year.  The energy within our department is almost palpable, and I know that the students are catching on as well.  Here’s an email I got from one of my co-workers this morning:

I want to give credit to Teresa and Dianna because they were more of the driving force behind encouraging the use of Plickers.  I’m thrilled with the result nonetheless.

The group that impressed me the most today was my first hour, math recovery.  These are kids who have previously failed a math class and are recovering credit.  You can imagine the lack of math love in the room.  Here was their prompt:

SPOILER ALERT:  I’m going to reveal the answer so if you’d like to try it for yourself, stop reading.

I had them come up with ways they could make 37 using different amounts of numbers.  It seemed that we could get 36 using 10 numbers or 38 using 10 numbers but couldn’t quite get 37.  Then we tried getting 37 using 9 numbers or 7 numbers.  We had some good discussion about which strategy seemed the most useful.

One student in particular mentioned that he wanted to add some and subtract some but he felt he would always be short without a 2.  I had them share their results on the board and I was very satisfied with the effort I’d seen.

I was nervous about the answer reveal because as it turns out, it’s impossible to make 37 with 10 numbers.  What we were able to do is focus our attention on what we DID discover, rather than the fact that there was no answer.  We discovered that Odd + Odd = Even, Even + Even = Even, and Even + Odd = Odd.  Because there is an even number of odd numbers, an odd sum is not possible.  I was more pleased with this result than any single answer they could have given me.  I expected a backlash from a group of students used to answer-getting but found that they were able to embrace a learning activity that didn’t one final answer.  I’ll mark that class period in the win category.

1. Awesome. What’s a variation on this problem that you could give them next? What kinds of problems would they write if you asked them to each write a problem inspired by this one?

• Ooo, good question. I’ll have to ask them tomorrow! I want to explore multiplication patterns next 😉

2. Thanks for sharing this – and for your Nrich session in OK this summer. I’m going to try this exact one next week at some point because I want to test out a theory. Some of my Geom Students are frustrated that I have been asking questions that have more than one correct answer (such as – Segment AB is 10 units long. Its midpoint is at (3 , 7). What are the coordinates of A and B?) So, I’m interested in their response now if I ask a question that has NO correct answers.

3. Does everyone else know what grade this is or what age these kids are?

I think there should be an acknowledged difference between a problem and a puzzle. This thing is not a math problem. It is a puzzle, a very difficult and as it turns out hopeless puzzle but still a puzzle. In a puzzle you expect perversity, tricks, weirdness. But a problem should be sincere. It should be asked in good faith.

Seems to me like a weird way to take people failing in math and make them like math.

• I’m not sure it matters if it’s called a puzzle or a problem. The students elicited information from it beyond the question itself. Win in my book.

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