# Cup Stacking #MFM2P #3ActMath

This activity is another one that stems from one by Al Overwijk, but a bit more directed than his. In Al’s activity, he opens it up to any model of cup stacking which results in relations that are linear, quadratic & beyond. Maybe my class can come back to this later in the course & do it that way. For now, we stuck to a nested cup model that I knew would result in a linear pattern since that was my learning goal for this activity.Also different from Al is we used a stool simply because we don’t have enough solo cups to get to the height of a person when they’re nested inside each other 😦

The Scenario:

Act 1: Notice, Wonder & Estimate

 What do you notice (facts)? What do you wonder (Q’s)? What is the height of the chair The cup is way smaller then the stool How many cups do you need to get the same height Each picture has more cups How many cups does each picture have there more than 1 cup. why do you have only 3 chairs? Each picture has different number of cup How many cups that can be same hight with the chair there’s more cups in each picture how much cups does it Stool and cups How many cups we need to put together so that they have the same height with the stool? What’s the height of the chair The number of cups increase Why are there cups – There are a different number of cups in each picture. – The stool is much taller than the stacked cups. – The only thing that changed is the number of cups – How many cups will it take to stack it as high as the stool? More cups in each picture How many cups do we need to cover the hight of the chair cups what is the volume of each cups? The number of cups is increasing How many cups would it take to be the same height as the stool 3 stools, cups is increasing How many cups it will take to reach the height of the stool In each picture there is a certain amount of cups The chair is always the same How many cups it increases at a time

Act 2: Collect data & solve

Each group received 8 cups and were instructed not to share their cups with any other group. They quickly grabbed rulers & began measuring. They made tables of values on their boards to record their measurements. But quickly most groups began to look for patterns after taking 2 measurements & then continued their tables based on their assumptions of how it will continue to grow. But I let them continue with that thinking for now. Here were there boards:

I then asked them to take one of the equations for line of best fit that they’d found in their group and go to their boards to solve for the number of cups needed to match the stool’s height:

Act 3

We stacked the cups as a group next to the school and the actual answer was 73! We discussed possible reasons for differences between our first answers, our answers after using Desmos & the real answer.

A third day was spent practicing two skills that had been assigned via Khan Academy over the previous days of work:
Graph from slope-intercept form
Slope-intercept equation from graph

The entire activity is available here.

– Laura Wheeler (Teacher @ Ridgemont High School, OCDSB; Ottawa, ON)