Thursday, December 14, 2017

And then what did you do?

In my experience, middle school students are often reluctant to try a problem they don't already know how to solve and uninterested in using alternative solution methods once they have one that works. Some middle school math teachers I worked with this week have found the same thing. So we considered how we might use techniques from improv to help students get started on a problem and possibly explore an approach they might not normally use. Improv techniques like the "Yes, And..." activity.

We decided to play it using this situation from Context for Learning Mathematics [CFLM] and a couple of starting choices.

Starting Steps:
1) First, I split up the dollar and the 25 cents and multiplied the dollar by 24.

2) First I doubled \$1.25 and got \$2.50.

We would make teams of three. Two people would engage in the "Yes, And..." activity while the third kept "numeric notes" that could be referred to after the activity.

Here's how it might work:

 Numeric Notes
First, I split up the dollar and the 25 cents and multiplied the dollar by 24.

Yes, and then I added back the 25 cents and got \$24.25.

Yes, and then I remembered there were 23 more quarters that I need add.

Yes, and I don't know what 23x.25 is so I did a quarter plus a quarter is a half dollar instead.

Yes, and that reminded me that there are four quarters in a dollar.

Yes, and that made me wonder about how many dollars there are in 24 quarters.

Yes, and I divided 24 by 4 and got 6.

Yes, and that means 24 times .25 is 6 dollars.

Yes, and then I added 6 dollars to the original 24 dollars.

Yes, and that means the total cost of the turkey is \$30.

Afterwards, the students reflect on the activity. This is an opportunity to observe their own thinking: what they did; why they did it; and how else they might have navigated the situation. I have done something similar with my college students, who finish up by writing a Metacognive Memoir about their experience.