Chapter 11: Cup Stacking

This week in class, we looked at a seemingly simple question...

How many cups tall am I?

The thing I loved about this question, is how many ways a student would be able to look at this question, and how many ways an educator can facilitate the activity according to the information they provide. 

For instance, giving them absolutely no information, you could ask students what they would need to know to solve the problem. I would expect that they would want to know things such as:

-the teachers height

-the height of a cup

-how they are stacking them

You could then given them all of that information, however it still isn't enough to solve the problem if they are to stack the cups conventionally (see the image below).

         https://crazedmummy.wordpress.com/category/useful-for-teaching/

Concluding to the class that the cups must be stacked conventionally, you could then ask, what further information would you need to solve this problem? This conversation should lead to the height of the base and the lip of the cup. Given this information, students should be able to work through the problem, either numerically, graphically, or using a data table. Regardless of how the students solve the problem (assuming they are correct), they are exploring linear relations.

This is only ONE approach to the problem. Another great approach would be providing students with the height of two different stacks of cups. At this point, they would have to find the slope of a line using two points to solve the problem. Or, you could extend the problem by having students use different size cups. Or, you could actually just give the cups to the students and have them test their answers. Or, you could given them only a few cups and have them develop a solution on their own....

There are so many different ways this question could to presented, all of which should result in a unique learning experience. I find that as mathematics students/educators, we tend to value math questions based on their complexity, however, "seemingly simple" tasks such as this allows students to become more invested in the math. Stacking cups is tangible, and its "within reach" of students regardless of their academic achievement levels. They are not scared of the question. I think this is the key to unlocking the potential of students that identify as being "bad at math". 

Thanks!