Last year around this time I shared out a Google Form for classes to record measurements around their pumpkins and make them explode! I shared that form on Twitter so that we could crowd source as many pumpkins as we could to make the sample size large enough. I was pretty shocked at how many schools from North America took on Pumpkin Time-bomb. By the time Halloween was over the spreadsheet had over 90 entries. That’s over 90 pumpkins exploded in the name of math and data collection.
This coming week let’s add to the data and use the it in our classroom to discuss: Scatterplots, Trends, Correlation strong, weak, no-correlation, lines of best fit, correlation coefficient, etc.
Here’s a sample lesson you could use on the day you make your pumpkin explode.
Play this video which shows Jimmy placing rubber bands around his pumpkin.
How many rubber bands will make the pumpkin explode?
Have students write down a guess that is too low. Too high. Then estimate their best guess.
Show the Act 3 Video
Now Bring out your pumpkin for the class to see! Have them predict how many rubber bands it will take before it will explode. Repeat the estimation process. Have them save their guess till the end of class.
Making A Model
Throw out the question: “What measurements of the pumpkin changes how many rubber bands are used?” Let your students brainstorm a list of variables. Have a discussion on variables & relationships. Write all the variables on the board they come up with. Narrow down the list to items that are measurable with the pumpkin we have in the class. What affects the explosion the most? Height, diameter — circumference, thickness of the wall?
Have them choose a variable that they feel should have a relationship with the number of rubber bands. Fill out the prediction part of the handout.
As a class measure all variables needed. Write them on the board for all to see.
Give students the link to the spreadsheet of all the pumpkins to date (You should copy and paste the data to your own sheet so you can filter/sort the results and share that sheet out to your students.)
Discuss with your students the lack of consistency in the selection of rubber bands from all over the country. How can we minimize this variable skewing our results? Filter the data with your students(or before hand) showing one type of rubber band (Most common is a rubber band of length 8.65 cm). This will only show all the pumpkins that have been destroyed using that type of band.
Get your students to grab the data that relates to their relationship.
If Kristen chose the relationship Circumference vs. Rubber bands she should copy and paste the circumference column and the rubber bands column into a new sheet side by side. Then copy and paste all that data into the pre-made Desmos File.
She can adjust the scale in Desmos as needed. Have her move the movable point and drop it where she thinks your class’ pumpkin will lie. Or you can have her find the line of best fit to help predict how many rubber bands it will take. Either way we want her to predict with more accuracy.
So Kristen would predict that if her circumference was 90.5 cm then it will take 272 rubber bands to blow up the pumpkin!
Now if Kristen chose a variable that it was clear there is no relationship then you get to have a discussion about correlation vs. no correlation. Have her choose new variables to predict on.
Once everyone in the class has a new prediction start wrapping bands around that pumpkin (You may want to start this as early as possible).
Watch your pumpkin explode and give congratulations to the student who predicted closest to the actual number of rubber bands.
Don’t forget to enter all your data to the sheet by filling out this form (you can also use the form to show the videos to the class).
[Updated] – You can use this Desmos Activity Builder Activity to facilitate the lessson. It includes only data for Diameter and Circumference.
From Oct 30. 2015
A few pumpkins from 2014 & 2015