# Chocolate Mania [3 Act Task]

This post and task was written and created by both Jon Orr and Kyle Pearce.

For about a year now Kyle Pearce and I have been travelling to schools and districts across North America sharing our techniques on how to Make Math Moments That Matter for our students.

In those live workshops we’ve been using a task without a name. On the first anniversary after creating that task we wanted to share it here with you and give it a name.

We’re all about creating tasks and then thinking about how they might be modified for use across a variety of grade levels. With a few modifications, you can successfully run this task in classrooms from K through 10. In particular, you could address the following expectations:

• building estimation skills;
• building multiplicative thinking and proportional reasoning using arrays;
• building multiplicative thinking and proportional reasoning using double number lines;
• making connections to the inverse relationship between multiplication and division;
• connecting double number lines and ratio tables to creating and solving proportions through algebraic reasoning;
• highlighting the value of the constant of proportionality (i.e.: unit rates) so students can “own” every problem possible in a proportional relationship;
• determining rates of change;
• representing linear relations in various ways;
• solving problems using the four representations of linear relations; and,
• many more.

Here is Chocolate Mania:

## Act 1: Sparking Curiosity

Ask students to create a notice/wonder table or you can use one that we built for our online workshop Making Math Moments That Matter.

Ask your students to write down anything they notice and anything they wonder while viewing this video:

Note: There is no audio. Can’t see the video because you’re viewing this post in a rss reader? Click here to go to the post page.

Here are possible notice and wonders from our workshop participants and also some from our students:

• They’re both wearing plaid.
• The video is in reverse.
• How many chocolates will they eat?
• Did they get sick?
• How long did it take to eat all the chocolate?
• It looks like they’re spitting it out.
• Kyle is eating Kisses.

At this point the students’ responses are listed on the board during the class discussion.

After capturing all the notice and wonders on the board steer the class to working on the problem:

### “How many chocolate did Kyle eat? How many did Jon eat?”

Have your students estimate how many each of us ate. What is too high? What is too low? Your students may be feeling uneasy about their estimates; that’s okay! The point here is we don’t have enough information. To help with estimates at this stage we disclose that all the wrappers of all the chocolates we ate are showing in the image above.

We encourage you to record many of the estimates in a chart as a class. This will put some pressure on making those estimates carefully.

## Act 2: Revealing Information to Fuel Sense-Making

To avoid rushing to the algorithm we’ll push down the curiosity path some more. Instead of just handing over all the necessary information to solve a problem ask the students what they want to know more about. This process is key; student anticipation of what is needed is a gold mine for understanding where they are in their thinking. By having them ask for information they have to start problem solving!

Students may ask for the time it takes for the whole video and you as the teacher can then say, “And what would you do with that if I gave it to you?” Listen to how they answer this. You’ll gain valuable information about where that student is on this problem solving journey. You will know after that answer if the student is thinking proportionally or not.

Here is some information to share:

Ask students to share what this series of photos tells them. What do they notice? What do they wonder? Then share this photo. It reveals the total amount of ml each of us consumed.

At this point students will have enough information to determine how many pieces of chocolate each of us ate. Let them go at it!

## Fuel Sense-Making to Consolidate Learning.

Note: You or your students may want to work with more familiar numbers compared to what you see above. For example, to get a close prediction to the actual number of chocolates each of us ate a student may round the 111.8 ml to 110 ml and similarly round the 17 ml for 3 chocolates to 20 ml.

Depending on the grade level or skill level of your students we can expect to see some of these strategies

• Counting with familiar numbers;
• Using arrays;
• Number line counting;
• Tables of value counting;
• Long division;
• Unit rates;
• Solving Proportions;
• Creating and solving equations.

Here are some of those strategies:

### Counting Up Chocolates and ml.

Students may count up 17 ml every 3 pumpkins until they reach close to the total amount of ml. If they go over the total amount they may want to subtract a cup of chocolates so they can get more accurate.

Here’s that strategy in action

### Working with Fractions:

To get more precise answers we can encourage students to work with parts of chocolates in decimals or fractions. Many teachers would be inclined to stay away from fractions because they feel it may “de-rail” the lesson. We say use this context to reinforce fraction work and understanding.

### Counting/Multiplying/Dividing Using Arrays:

Students may organize their counting strategy in a double array model. Simultaneously counting in groups of 3 pumpkins and 17 ml will allow them to see that they will need just over 6 cups of pumpkins, while showing the proportional relationship between the pumpkins and volume.

### Double Number Line:

Students who solve the problem with a proportion will benefit from seeing it laid out on a double number line. By showing how to solve a proportion on a double number line we take a familiar concept (counting on the number line) and extend it to work multiplicatively. Students who solved the problem with an additive strategy will see the benefit of greater precision of using a scale factor.

### Unit Rates:

Many students may use a unit rate to help solve this problem.

Note: This student will benefit from a conversation on notation, units and order of division.

### Linear Relations:

You may choose to use this problem to either introduce or practice linear relations. I used this task to link the idea of finding the unit rate to determining the rate of change (slope) in a linear relation and then use it to build an equation to help solve the problem.

### Reveal the Answer:

After consolidating the learning goals you wanted to bring out into the open for discussion with your class show them this reveal video of the actual number of chocolates each of us ate. Be sure to go back and validate those students who estimated the closest early in this task.

## Is there a Volume relationship?

We want to leave you with some thinking here. We chose these chocolates for a very specific reason. In fact we hunted down the spherical chocolate that has the same height and diameter of that Hershey’s Kiss.

Your Task: What volume relationships can we pull from this image?

Did you notice the relationship between the amount of chocolate by volume Jon ate versus Kyle?

Look for an upcoming post on how we used this task to teach volume. But before we do that we want to know how you see a lesson on volume forming with this information. Use the comment section below to share your ideas, questions, comments, or even just snippets of what a lesson could look like.

Download the videos, animated gifs, and other resources to make sure that this 3 Act Math Task can spark curiosity to fuel sense making in your classroom!

## New to Using 3 Act Math Tasks?

Download the 2-page printable 3 Act Math Tip Sheet to ensure that you have the best start to your journey using 3 Act math Tasks to spark curiosity and fuel sense making in your math classroom!

# 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.

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.

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

# Magic Rings

A good friend of mine Brian McBain showed me this construction with two paper rings taped together. I had two of my daughters predict what would be made from cutting down the middle of both rings. Watch below.

They also wanted to make a survey to see what you would predict. Can you do us a favour? Watch the start of this video. Pause the video and make a prediction. Enter your prediction on the google form below. Then watch to see what is created! Have fun.

Can’t see the video or survey? Click through to the post

The Orr team thanks you for participating. If you teach a class go ahead and share this with them. We would love to see what other kids predict.

# Fast Clapper

One of my favourite lessons to do with my grade 9 applied students is the Fast Clapper! I first saw it on Nathan Kraft’s virtual filing cabinet! My main goal here was to solve proportions through algebra.

We started class like this:

ME: Hey guys get ready…..I want you to clap as fast as you can……Ready…..Set……..GO!

Class: They clapped. Some students gave it their all….some not so much.

ME: Ok….That’s enough. Now let’s make a competition out of this! I want you to clap as fast as you can for 10 seconds….count how many claps you make! …Ready —– GO!

Class: This time all of them gave it their all!!

ME (after 1o seconds): STOP! Great job! Quick, write down how many claps you made in those 10 seconds. Who thinks they had the most.

James: I did….I had 37 claps

Josh: Nope, I’ve got that beat……48 claps.

Shylynn: I did 56

Class: Whoa!!

ME: OK….now find how many claps you made in 1 second!

They did this pretty easily and we went around the room again….still seeing Shylynn with the highest!

ME: Great job…..now watch this guy….

Hayden: Wow!!! that guy can clap

ME: I know….Let’s watch again. This time watch the video and try to see something you didn’t before.

We watched a few times. Each time students would notice something different. We noticed:

• He closes his eyes
• The record is 721 claps per minute — “I wonder if he’ll beat the record”
• He clapped 58 or 60 times in the video
• The video only showed the first few seconds

ME: Let’s take the suggestion to discover if he beats the record. Who thinks he’ll beat the record? Who thinks he’ll tie the record? Who thinks he won’t beat the record?
We took a vote and recorded it.
ME: In order to see if he beats the record we’ll need some of that info from the video…..but we better be exact. Why?
Janice: If we’re off by a clap in the first few seconds….it could be huge after a minute.
ME: Ok, let’s be exact.
Jake: We could pause the video on the last moment to see.

Judy: He claps 63 times in 4.6 seconds.

ME: OK….go for it. Work together to see if he beats the record.

They got going and I needed to work with a few groups to discuss how to get started. “IF you could find how many claps in 1 second how could that help?”
After some time I stopped them and showed some students’ solutions

We then showed the rest of the minute!

We moved into re-solving the problem using ratios and proportions. I went through slides to show how to set up the proportion and how to solve it with algebra.

I’m a strong believer in letting the students struggle and persevere through problems. I want them to use their prior knowledge to solve the problem in any way they can, any way that makes sense to them. I can see their understanding when they have to explain their thinking to me and the class. After they solve the problem in their way…..I take what they have done use it to explain the “math teacher” way.

Today one of my grade 10 academic students was solving a problem and I could see some good thinking on the page….but he also wrote: I don’t know how to start this. I asked him right there why he wrote that when he had almost a full answer on his page. He said “I know that’s not the way you want me to solve it!” I jumped on that quick and said….”I want you to solve problems that make sense to YOU. Just show me your thinking” He went on to solve the problem with in a great way.

We need to build our students confidence up. We need to promote and value their solutions instead of forcing our solutions on them.

So, back to Fast Clapper: I used their solutions to help explain why the math teacher way also makes sense. Here is a silent version of the slides I used.

We moved on from here to solve Dan Meyer’s Sugar Packets problem and the Smart Car Smash to practice solving proportions with algebra.

And then used a Knowledgehook gameshow to practice some more…go ahead, give it a shot.