Sunday, January 13, 2019

The Crow and the Pitcher Rate of Change


The Crow and the Pitcher is based on an Illuminations lesson. I used it as the introduction to linear functions to demonstrate a real-world rate of change for my students. The lesson is based on Aesop's Fable, "The Crow and the Pitcher." I began the lesson by reading the fable to them. You can also show this video from Sesame Street if you do not have the book. In looking for a video of the book, I came across this experiment. I showed only the first experiment and their minds were blown! So much so, that as they collected their data, I let the video play out. 




I borrowed graduated cylinders and beakers from the amazing science teacher on my team. The "pebbles" were rocks from the Dollar Tree. So not a lot of supplies were needed. The handout for the Illuminations lesson went a little deeper than I needed but leave it to Math=Love to have just the right one! You can find it here in her post about this same lesson. I followed the Illuminations lesson more than hers because it had more structure which I thought my students needed.



Students were in groups of two to three. I think two was the magic number for this activity. We discussed the variables that were in the fable and decided which was independent and dependent. They used height of the water as the dependent variable and the number of pebbles as the independent variable. They filled their graduated cylinder with 80 mL of water and we discussed what our first data point would be.





Students added one pebble at a time and then put a data point on their table. They continued adding pebbles until they filled up the table. 


I like the way this group would predict how much the water level would rise before they dropped the pebble in. 



Once they added seven pebbles, I had them share how many it would take to get to 100 mL. A couple of strategies they used were to extend their table and to see how many times they needed to add two to get to 100. We then talked about rate of change as the change in the dependent variable divided by the change in the independent variable. I used the Greek symbol for Delta and they immediately recognized it from our Greek Week when they memorized the Greek Alphabet. So all I had to do was define it as "the change in" and they were set!


Most groups' data was a rate of change of 2 mL/pebble. But for the few that were different, we had great discussions about why. Especially this group who sorted their pebbles and wanted to do the trial again because it had to be the "color of the pebble that messed up their data!" 

          

The Illuminations lesson continues to fill the container with more marbles to determine domain and range. I let my students do it for fun! 


Turns out, they taught me about water displacement, which they had learned in science! Showing, once again, that lead learner is a way better description than teacher of what I do each day! As with all real-world math labs we do, I hope that it gives my students something concrete to anchor their learning.  



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