##### Ontario Alignment By Overall Expectation

## Real World Applications of 3D Measurement

### Proportional Reasoning With Volume of a Cylinder and Sphere

In this 3 act math task, students sharpen their **proportional reasoning** and **3D-measurement** skills as they try to determine how many packages of gumballs as well as how many gumballs (individually) will it take to fill the cylindrical jar. The learning goals for this task include:

- calculating the volume of a cylinder and applying their knowledge;
- calculating the volume of a sphere and applying their knowledge;
- applying their knowledge of proportional reasoning to solve problems.

## Act 1, Scene 1: Introduce The Problem

Show students the following video or this photo:

Ask students to talk to a neighbour and come up with some possible questions.

This task will focus on two questions:

Q1 – How many packages of gumballs will it take to fill the jar?

Q2 – How many gum balls (individually) will it take to fill the jar?

You might want to show the students the following video before or maybe even after they discuss with a partner and make a prediction:

## Act 2 – Give Students Some Information

After students make a prediction, have them discuss with their partner what information they need to make a more accurate prediction.

Then, show this video clip or show these photos:

- Download Photo 1: Jar Height

- Download Photo 2: Jar Diameter

- Download Photo 3: Gumball Diameter

At this point, students should be able to improve their prediction of how many individual gumballs it would take to fill the jar by calculating the volume of the jar and volume of a gumball.

You can also challenge them by telling them how many gumballs on average are in each package:

## Act 3 – Reveal the Solution

Once students have shared out their work, updated their predictions based on their calculations and some good ‘ol debating happens in your classroom, show them these two clips:

## Knowledgehook Gameshow

Check out the matching Knowledgehook Gameshow:

Make a clone of the Gameshow so you can edit to your liking here.

## Resources

Just added some more resources including a Keynote Slide Deck fully loaded and ready to rock in your classroom!

- Entire Lesson Slide Deck (incl. Sequels) [KEYNOTE]
- Act 1, Scene 1 [VIDEO]
- Act 1, Scene 2 [VIDEO]
- Act 2 [VIDEO]
- Act 3, Scene 1 [VIDEO]
- Act 3, Scene 2 [VIDEO]

## How’d It Go?

If you use this task in your classroom, please share your experiences in the comments section! Always appreciative of any improvements that can be made including resources you might want to share for inclusion.

## 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!

## Share With Your Learning Community:

## About Kyle Pearce

I’m Kyle Pearce and I am a former high school math teacher. I’m now the K-12 Mathematics Consultant with the Greater Essex County District School Board, where I uncover creative ways to spark curiosity and fuel sense making in mathematics. Read more.

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I am trying to think of a way to help my students understand that simply dividing the volume of the jar by the volume of the gum ball will not get an accurate number because of the empty space created by the arrangement of the gum balls in the jar. How would you suggest I show them that. I was thinking about using water to fill the empty space and then find the volume of the water and subtract that to help remove that from the gum ball number. Suggestions?