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Guessing Gumballs Sequel

Real World Applications of 3D Measurement

Proportional Reasoning With Volume of a Cylinder and Sphere

In this 3 act math task, students will extend the proportional reasoning and 3D-measurement skills used in the previous task, Guessing Gumballs, to determine whether the gumballs from the short and wide jar will fit into the tall and thin 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: 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.

The question I’m looking for here is:

Will the gumballs fit into the tall and thin jar?

Prompt students to make a prediction and be prepared to backup their prediction by discussing with a partner. Will all the gumballs fit? Will it overflow? Will there be a lot of extra space? Will it be a perfect fit?

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:

At this point, students should be able to improve their prediction after using the dimensions to calculate the volume of both jars and determine how much volume the gumballs could “theoretically” occupy.

Act 3 – Reveal the Solution

Once students have shared out their work, updated their predictions based on their calculations, show them the solution:

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!

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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