Stacking Cups

I did Stacking Cups by Dan Meyer again.  I haven't done it in a few years and I think my intro made it more successful this time.  I let the students lead themselves to the problem.

I just held up a cup and asked them about it.  They talked about how it could hold water and food.  I shared that they were pretty dirty because many other students had touched them.  They were less eager for food and drinks then :)

Eventually they started talking about how you could stack cups and I asked for them to keep listing different ways to stack them until the stacked them inside of each other.  Then I set a small stack next to my water bottle and had them estimate how tall my water bottle was.  We discussed how even though the the cups stacked halfway up my water bottle, we would need more than twice as many.  I take a few estimates and then we calculate.  I set it up by asking what else we could measure and three (of four) classes decided to measure me :)  The other class chose a particular student and I went with that.  I actually think that was the most fun!

I also gave them some guiding questions based on standards we've been working on.  Here are the questions I asked them to answer in their groups:

1.  Identify the independent and dependent variables.  Select a letter to represent each.
2. How tall is one cup?  How tall are two cups?  Three?  How could you organize this information?
3. Write an equation to model the situation.  Check to make sure it matches the values that you stated in [2.]
4. What is the slope?  Interpret the meaning of the slope in the context of the situation.
5. What is the y-intercept?  Interpret the meaning of the y-intercept in the context of the situation.
6. What is your estimate for how many cups tall Mrs. Freed would be (closest without going over)?  Explain how you determined your estimate.

The next day we discussed as a class.  I compiled all of the equations groups had created and we talked about how they related to the cup.  We discussed how precision was important in order to calculate a correct estimate.  Some groups had calculated an estimate and then put their actual estimate down because I said closest without going over.

This is the class that decided to measure how many cups tall this student is.

After discussing we measured and then I had them complete an individual reflection on google classroom.  I asked them about an equation I had made up.  The questions I asked were very similar to the ones in their group.

What surprised me the most was how much more willing to do the math they were when they made up the question.  And they were so surprised when they saw that I knew they were going to come up with that :)

-Kathryn