Pumpkin Time-Bomb Activity

For the last few years  I’ve 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.

[Update] – October 2018 – The form now has over 500 entries!!

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.

SPARK Curiosity

Play this video which shows Jimmy placing rubber bands around a pumpkin.

NOTICE & WONDER

Using a notice & wonder strategy, have your students record anything they notice and anything they wonder from the video.

ESTIMATION:

Steer you class’ wonders toward the questions: 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.

If you’re looking for your lesson goal to be around estimation then show the act 3 video next, but if you’re looking to go further and tackle a learning goal around Using scatterplots, lines of best fit, or linear regression jump down the post.

Show the Act 3 Video

Using Scatterplots & Trends to Improve Your Prediction.

Alternatively, to Spark Curiosity you could use this pre-made Desmos Activity! which allow you and your class to follow a Curiosity Path.

WITHHOLDING INFORMATION to create ANTICIPATION:

Use the PAUSE tool on the activity to lock their screens while you show your students the video on your main screen. Encourage your kids to discuss what they notice and wonder from the video! In pairs, I have my students TALK first and then TYPE second when collaboratively working on a Desmos activity.

ESTIMATION:

Consider pausing the screen again while you use the snapshot tool to grab student responses! This will lead into predicting how many bands will make Jimmy’s pumpkin explode. Have your students TALK first and TYPE second on screen 2 to make a prediction. Again, share students predictions using the conversations tools Desmos provides.

FUEL SENSE MAKING – IMPROVE YOUR PREDICTION:

Bring your students down the curiosity path a little more. Ask them about how we can improve our predictions? What other information would you like to know about the pumpkin or the bands?

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?

Using the PACING tool in Desmos move your students few the next few screens to make a scatterplot prediction of the relationship between the diameter of a pumpkin and how many bands will make it explode.

Screen 5 shows a scatterplot of pumpkins that have already been blown up and the relationship between diameter and bands (or non relationship). Have your students move the orange point to a place that helps them predict the number of bands. What placement would be wrong?

The next few screens ask your students to do that all over again while looking at the relationship between the height of the pumpkin and the number of bands.

Finally, reveal the answer after students have improved upon their predictions.

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. Where will YOUR pumpkin fit on the scatterplots shown in the Desmos activity?

If you are not planning on using the Desmos activity then you can use the original activity post from October 2015.

FUEL SENSE MAKING – Making A Model

Throw out the question: “What about the pumpkin do you think affects how many rubber bands are used to make it explode?” 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.

FUEL SENSE MAKING – Analyzing Data

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.

For example:
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 lesson. It includes only data for Diameter and Circumference.

Access the Form

Access the Data

From Oct 30. 2015

A few pumpkins from 2014 & 2015

Gaining Insight

As the year closes down I think back on 2017.  I was curious about some of the stats on this site and was blown away at some of the numbers. I never thought that when I started sharing what goes on in my classroom that I would have over 150000 views in a single year! Amazing….and thats all because of you! I dug a bit deeper and found the three most popular posts from this year.

At first glance I thought, “Yeah, those top 2 posts make sense. Their kinda gimmicky and fads. We search for those relevant topics our students are into; games and bottle flips! I’m sure if I wrote a post on fidget spinners it would be up there too.”But after thinking back on those activities and comparing them I think both their value come from being able to gain great insight into student thinking. And it’s that ability to assess our students deeper thinking here that teachers are drawn to.

Take the Angry Birds lesson for example, the creativity that is embedded  throughout the lesson is everything. Students get to choose how their flight paths look and act. There’s a story behind every arc they put into their activity. Their thinking can’t help but spill out all over, and I get to use that knowledge I gain to help push them along. Take away the angry birds and you still have a great creative lesson.

Replace it with a drawing, or trace of a picture or even a marble run and students experience the exact same creativity and learning goal expectations. The activity still allows me to have those insightful conversations.

The bottle flipping activity is a formative assessment gold mine. Again take away the bottles and replace with paper balls or card tossing and this lesson is identical, and I have just as much success at seeing into my students thinking.

It’s this insight that we all want. It’s this insight we need. Insight allows us to what Kyle Pearce and I have been calling ignite our moves. Seeing how a students thinks in live time allows us to act. We may act to address a misconception. We may act to push learning further. We may act to plan our next lesson. We may act to change our planned lesson into something that the students need at that moment. Lessons that allow insight into student thinking must be our norm.

This fits with the 3rd top resource. Spiralling Grade 9 Math. The file found on this post give us a day-by-day to teach with lessons just like the ones above. Not gimmicky lessons —  Lessons that spark curiosity! They are lessons that provide great insight so I can ignite my moves and fuel my students sense making. And fuelling sense making has to be our main purpose.

Have you used any of these resources? Comment below to share how?

3 New Desmos Activities: Talkers & Drawers

Goals of the activity:

Students will:
• Begin to recognize characteristics of linear, quadratic, or periodic functions.
• Generate a need to use proper vocabulary around linear, quadratic, or periodic functions.

Specific recommendations:

• The “talker” cannot use their hands and should keep them behind his/her back. This will help the student be careful and direct the language they choose to describe the graph.
• The “drawer” cannot talk.
• Set a time limit. Possibly 3-4 minutes for the “talker” to describe the graph to the “drawer” with the goal to reproduce the graph.
• Consider having all the “drawers” reveal the graphs at the same time for dramatic effect.
There are three different versions of the activity based on topic

What the student experiences:

Once students choose a role tell them “Talkers, your goal is describe the graph perfectly to the drawer. Drawers, your goal is to listen carefully and without talking try to match the talkers graph. You will have 3 to 4 minutes for each graph.
When the time is up, tell all the drawers to click the REVEAL button at the same time to see how close your sketch was.

What the teacher experiences:

While students are describing and sketching take time to listen to the words they use. Store these words for later in the class so you can link them to the proper names.
Example:
You heard Jose Adem Chain say, “The pattern starts at 2 and goes up…” If most students are using the phrase “starts at..” We can introduce the term y-intercept.
Or on the periodic function version:
A student might say, “…it does that and then repeats 4 units later” You now have a gateway into introducing the period of the function.
After each round use the Teacher View to showcase some student graphs to the class.
Consider restricting the students to the current sketch and move from sketch to sketch as a class.
Last question.

The words generated on this slide will most likely be informal. As a class discuss the informal use of the word and then introduce the more formal words relating to the topic.
Inspired by Brian McBain and also the team at Desmos

Polygon Pile Up

When it comes to angles involving parallel lines, triangles, and other polygons I’ve always assumed my grade 9 applied students “get this”. I’ve felt that angles were an easy topic. I guess I thought this because most students seem pretty happy when solving angle problems and for the most part being doing pretty well on assessments. However, this year I noticed two inadequacies that I am trying to address.

1. Most of my students didn’t actually know what an angle measurement of 65 degrees really means.
2. They have a hard time determining what information is needed when solving multi-step angle problems. Lack of a good strategy.

When having students determine angles in triangles almost all of them knew that all three angles should add to 180 degrees. The trouble came when I saw some answers like this (from more than one student).

What bothered me was the location of the 40. I wondered why outside the triangle? I pressed this student for more info. I asked him to draw me any right triangle and label the three angles.

Hmmm…I asked him to point to one of the angles. He pointed to where he labeled the 85. What I found is that this student was mixing up length measurements with rotational measurements and he was not alone.

I found a great activity to hit this head on. Laser Challenge from Desmos worked wonders to get my students to understand and experience rotational measurements. Students have to enter values to rotate the laser and mirror to hit targets.

My students “felt” what 60 degrees is. Experiencing that rotation made all the difference to clear up what we were actually measuring. When second semester rolled around and my new crop of kids came in we started with this activity right away.

Most of our students struggle with solving complex problems where they have to think of a strategy. Before I gave them something like this,

I wanted to them to experience what information would be useful to know first. I decided to turn the problem around and inside out.

I gave them this.

I wanted them to think backwards….just like we need to do sometimes when solving longer problems. On the “easy” side most filled in 3 angles in the quadrilateral. What was great was that prepared them to think what we could leave out for the harder one. This simpler diagram challenged my class to think, plan, and strategize!

It was great to do this before we introduced this puzzle Jim Roesch, Kristyn Wilson, and myself created:

[There is a video embedded here — Can’t see it? Click through to the post page]

Here is the puzzle