MCF3M

Pumpkin Time-Bomb Activity

by Jon Orr

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?

Screen Shot 2015-10-24 at 6.34.42 PM

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.

Screen Shot 2015-10-24 at 4.54.15 PM

Click here to grab a copy of the prediction 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.
Screen Shot 2015-10-24 at 2.48.38 PM
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.
Screen Shot 2015-10-24 at 5.14.57 PM
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.

Screen Shot 2015-10-24 at 5.17.17 PM

So Kristen would predict that if her circumference was 90.5 cm then it will take 272 rubber bands to blow up the pumpkin!

Screen Shot 2015-10-24 at 6.28.55 PM

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.

[Updated] – You can grab a copy of the spreadsheet to save in your Google Drive. From here you can modify. 

Access the Form

Access the Data

From Oct 30. 2015

A few pumpkins from 2014 & 2015

Sneaking in Factoring

by Jon Orr

I started a series of new warm ups for my MPM2D class today. My goal is to sneak in factoring as warmups throughout the semester. By the time we need to learn it (like when we need to factor to solve equations) we will have mastered it already. I also previously snuck in multiplying binomials when we tackled quadratic patterns as Mary Bourassa did in her 2D class.

So today I gave them this slide and said I want you to solve a puzzle!

Screen Shot 2015-09-29 at 9.04.00 PM

They broke out their iPads and used the Algebra Tile app to put together the rectangle. The kids worked away and you could see them trying to put tiles in a way to make the rectangle

….and they soon found out that they had to fit a certain way!! 
On take up we made sure everyone had either my rectangle or a rotated version.

Then we did this one…..

Screen Shot 2015-09-29 at 9.04.25 PM


After we were done I asked the class: “If the combination of squares and rectangles makes up the area, what are the dimensions of the rectangle?” They had a little bit of a hard time here, but finally could see the x + 4 and the x + 2 as the length and the width. I then wrote …

 And then I heard some “aaah”s. We had previously seen both versions of the quadratic expressions and discussed why the factored form helped us out quite a bit if we wanted to find the x-intercepts.

We stopped there….It only took us 15 minutes. Tomorrow we will do a few more…..always writing the factored form after. I will also try to get students to notice efficient strategies to make the rectangles.

  • Why did you put 4 x terms along the width and 2 x terms along the length?
  • How does that relate to the number of singles?

Where I hope to go with these warm ups is to factor all types of trinomials:

  • Perfect Squares

    daum_equation_1443575324234

    This time…..make a square

… and get this…

IMG_1503

  • Trinomials of the Type ax^2 +bx + c


IMG_1504

  • Completing the square too!!!!
IMG_1508

This time…make a square




IMG_1506
We’ll be definitely working our way out of the app and onto paper with area diagrams…

IMG_2988

Factoring

 

IMG_2990

Completing the square

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Completing the square

I think working with these puzzles for the next few weeks first will give us a strong base when it’s time to factor to help solve equations and then complete the square. I think I’ll track all the warm ups we do like this and I’ll post them all!

Lollipop Lollipop oh la la Lollipop! — & Rates of Change

by Jon Orr

Last year on twitter I saw that Alex Overwijk and Janice Bernstein with their grade 12 advanced functions classes did this lollipop activity!

I knew that I wanted to give this a try for this semester! What I especially love about this activity other than students experiencing rates of change is that this is an activity that can span multi-grades!

Here is what we did,

Generating Curiosity

I found this video on YouTube and asked the class to think of great questions we could ask about what we see!

FullSizeRender-1Great questions from the kids and we all agreed to look at

  • How does the sucking time affect the radius, circumference, volume, and surface area?
  • How long will it take until the lollipop is all gone?

Let’s investigate those relationships starting with the easy to measure (circumference) and also estimate how long it will take until the lollipop is no more!

We had guesses : ranging from 10 minutes through to 35 minutes.

Gathering Data

I handed out one lollipop per pair of students, along with some dental floss for measuring circumference. We set our timer for 30 seconds and began sucking and capturing data!
We recorded the circumference every 30 seconds up to 7 minutes like Al’s and Janice’s instruct in their lesson Plan.
FullSizeRender
They also have a great handout for tracking the circumference over the 30 second intervals. Screen Shot 2015-09-18 at 2.22.08 PM

Analyzing the Data

So we first looked at the Time vs. Circumference and Time vs. Radius relationship
Linear - Lollipop

Screen Shot 2015-09-18 at 2.27.24 PM
We discussed its linearity and why. Students predicted with more accuracy when their lollipop would run out.
Up to this point this task is great for grades 7, 8, 9, or 10!! (Just edit the file to exclude the average and instantaneous rates of change).

  • Grade 7 & 8: Practice plotting points and reading/interpreting graphs.
  • Grade 9 & 10: Find lines of best fit and first differences.

We found the average rate of change for each 30 second interval and discussed what this meant. We used the last column to talk about narrowing the interval down to estimate the instantaneous rate of change, and noticed that it’s about the same for all values. Why does this make sense???

7Yar2VXD

 

We moved on to looking at Time vs. Volume and Time vs. Surface Area

Screen Shot 2015-09-20 at 9.33.23 AM

Great talks around how Volume and Surface aren’t deceasing at a constant rate! It changes! Students can see these changes and see in their tables where the volume is changing the fastest.

Overall a great intro activity to get students thinking about narrowing intervals to approximate instantaneous rates of change.

Next up: We’ll relate what we did here with the tables to the graphical interpretation of rates of change (secant and tangent lines) and then on to the algebraic!

Screen Shot 2015-09-20 at 6.23.18 PM

 

Speedy Squares

by Jon Orr

Last week I attended the annual OAME (Ontario Association of Mathematics Educators) in Toronto. It was so great to finally meet some of the people I’ve been tweeting with.

I was pumped to attend Mary Bourassa’s double session on great classroom activities. One of the activities that I’ve seen on her blog, but not used in my own classroom was Speedy Squares. So when I had an opportunity to try it, I jumped on it!

There is something special about doing the lessons yourself while learning about a lesson at a conference.

Read about the lesson:

You can read about the lesson on her blog here part 1 and here part 2.

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The big question: We want to determine how long it will take to build a 26 x 26 square out of link cubes.

More Curious

While actively building the squares I had a great idea to make the introduction to the activity a little more curious! So when I got back to my classroom I broke out the cubes and created this….

Maybe before the time trials of building the squares, we can dive into generating questions and wonderings first.

  • What is he making?
  • How many squares will he use?
  • How long will it take?

Now that we have generated questions….we can then move onto Mary’s awesome two day lesson.

Once students have got an answer to how long they would take to build the 26 x 26 square, you could show the video of me building it!

I’m really interested to see if elementary teachers can use this in their classes and what they come up with!