##### Ontario Alignment By Overall Expectation

Grade 4 [Number Sense and Numeration - NS3]

Grade 5 [Number Sense and Numeration - NS3]

Grade 6 [Number Sense and Numeration - NS1]

Grade 7 [Number Sense and Numeration - NS3]

Grade 8 [Number Sense and Numeration - NS3]

MFM1P [Number Sense and Algebra - NA1]

MPM1D [Number Sense and Algebra - NA2]

## Sparking Curiosity to Promote Conceptual Understanding of Multiplication

This **3 act math task** was inspired by work we are doing at my district around fractions, measurement, and proportional reasoning.

In this real world math task, we’ve attempted to create a task that is accessible by students in Kindergarten and primary grade levels, but could be extended into the later grades by simply asking more complex questions with intentionality.

So let’s get going!

## Act 1: Sparking Curiosity

Show students this video.

While I typically have students do a rapid write of what they notice and what they wonder, if we are in a kindergarten through grade 3(ish) class, it’s likely that students are sitting with you on the carpet. In that case, it might make more sense for them to think of what they notice and wonder in their minds and then share out with their partners through a **think, pair, share**.

While Yvette Lehman and I were leading this task in a grade 3 classroom recently, we intentionally told students that they could notice and wonder ANYTHING and EVERYTHING that comes to mind with a big BUT…

When sharing with your neighbours, **do not share any numbers** that you might have noticed or wondered. We were lucky that this pre-planned instruction came to mind right before we led the task, because otherwise, some students may have immediately came up with “9” as an answer and then the task as well as the sense making would likely be dead.

Here’s some of the “everything and anything” students noticed and wondered on chart paper (remembering that nothing with numbers would not be shared yet):

- I notice hot chocolate.
- I notice a glass.
- I wonder if the hot chocolate is already made in the container?
- I wonder if someone is making hot chocolate?
- I wonder if that is YOU in the video.
- And many others…

At this point, we hadn’t landed on any particular wonder yet.

## Act 2: Reveal More Information

We then said… let’s watch this video to see if we have any more noticings and wonderings.

After watching this clip, students had more noticings and wonderings:

- I notice more glasses.
- I wonder if the person is going to make more hot chocolate?
- I wonder how many scoops they’ll need. I think I know!
- I wonder who is going to drink the other hot chocolates?
- And many others…

At this point, we took their wonders and said:

I think this person is going to be making 3 whole glasses of hot chocolate!

Why don’t we start by thinking in our minds about how many scoops we needed for the first glass and then how many scoops we’ll need for ALL 3 GLASSES?

BUT – we don’t just want to know how many. We want you to convince us of how many in any way you want.

Manipulatives are on your tables, so with your partner head to your stations and try to make a plan of how you’re going to convince us of how many scoops were needed in total to make 3 hot chocolates.

And, they were off to the races.

The materials on their table included:

- Connecting cubes.
- Square tiles.
- Integer chips (or “circles” with one colour on one side and another on the other).
- Large paper.

We would have liked to have relational rods on the table as well, but there were none available in the manipulative kit we were working with. Bummer.

## My Challenge to YOU: Fuel Sense Making

What do you think the students might do with this task?

My challenge to you is to leave a comment below anticipating what you think students might do in a grade 3 class.

You can also anticipate what would students in YOUR class do to convince you of the total number of scoops?

How might you modify this task to work in your classroom with your diverse learners?

If you want to be bold, test what you’ve anticipated by doing the task in your classroom and come back to report your thinking in the comments.

If we have enough people taking interest in this task, I’ll update this post with some of the intentional ways we fuelled sense making in this particular situation and we will share student work

## DOWNLOAD THE TASK TIP SHEET & RESOURCES

Want to make sure this task goes off without a hitch?

Download the **media resources** and 2-page **Hot Chocolate 3 Act Task Tip Sheet** that you can print and have with you close by to ensure that you maximize your chances of Making a Math Moment That Matters for your students!

## Act 3: The Big Reveal

After consolidating learning using student generated solution strategies and by extending their thinking intentionally, we can share what really happened with this video.

I hope you enjoy the task!

Don’t forget to take on the CHALLENGES I’ve set out for you.

Looking forward to hearing from you ALL in the comments! Remember, we don’t learn if we don’t reflect.

## Extension Questions:

There are quite a few different directions you could go in after this.

Some you might consider are:

- How many scoops do you need for 3 whole glasses and 1 half glass of hot chocolate?
- Can you show your thinking using additive and multiplicative thinking?
- How many scoops do you need for 27 glasses?
- How many scoops do you need for ANY number of glasses? How would you describe this?

Cara had a great question about how we might ask a question that would illicit division, which had me thinking. Check out her comment and my suggestion here.

Can you think of others?

Post in the comments below!

## 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.

Access Other Real World Math Tasks

## Search More 3 Act Math Tasks

Grade 2 [Measurement - M1, Number Sense and Numeration - NS1, Number Sense and Numeration - NS2, Number Sense and Numeration - NS3]

Grade 3 [Measurement - M1, Number Sense and Numeration - NS1, Number Sense and Numeration - NS3]

Grade 4 [Measurement - M1, Number Sense and Numeration - NS1, Number Sense and Numeration - NS3, Patterning and Algebra - PA2]

Grade 5 [Measurement - M1, Measurement - M2, Number Sense and Numeration - NS1, Number Sense and Numeration - NS3, Patterning and Algebra - PA2]

Grade 6 [Data Management and Probability - DP3, Measurement - M2, Number Sense and Numeration - NS1, Number Sense and Numeration - NS2, Number Sense and Numeration - NS3, Patterning and Algebra - PA1, Patterning and Algebra - PA2]

Grade 7 [Data Management and Probability - DP3, Geometry and Spatial Sense - GS1, Measurement - M2, Number Sense and Numeration - NS1, Number Sense and Numeration - NS2, Number Sense and Numeration - NS3, Patterning and Algebra - PA1, Patterning and Algebra - PA2]

Grade 8 [Data Management and Probability - DP1, Data Management and Probability - DP3, Geometry and Spatial Sense - GS2, Measurement - M2, Number Sense and Numeration - NS1, Number Sense and Numeration - NS2, Number Sense and Numeration - NS3, Patterning and Algebra - PA1, Patterning and Algebra - PA2]

MAP4C [Mathematical Models - MM1, Mathematical Models - MM2, Mathematical Models - MM3]

MAT1LMAT2LMBF3C [Data Management - DM1, Data Management - DM2, Geometry and Trigonometry - GT1, Geometry and Trigonometry - GT2, Mathematical Models - MM1, Mathematical Models - MM2, Mathematical Models - MM3]

MCF3M [Exponential Functions - EF2, Quadratic Functions - QF1, Quadratic Functions - QF2, Quadratic Functions - QF3, Trigonometric Functions - TF1, Trigonometric Functions - TF3]

MCR3U [Characteristics of Functions - CF1, Characteristics of Functions - CF2, Exponential Functions - EF2, Exponential Functions - EF3, Trigonometric Functions - TF3]

MCT4C [Exponential Functions - EF1, Trigonometric Functions - TF3]

MCV4U [Derivatives and Their Applications - DA2]

MDM4U [Counting and Probability - CP2, Organization of Data For Analysis - DA2, Probability Distributions - PD1, Statistical Analysis - SA1, Statistical Analysis - SA2]

MEL4EMFM1P [Linear Relations - LR1, Linear Relations - LR2, Linear Relations - LR3, Linear Relations - LR4, Measurement and Geometry - MG1, Measurement and Geometry - MG2, Measurement and Geometry - MG3, Number Sense and Algebra - NA1, Number Sense and Algebra - NA2]

MFM2P [Measurement and Trigonometry - MT1, Measurement and Trigonometry - MT2, Measurement and Trigonometry - MT3, Modelling Linear Relations - LR1, Modelling Linear Relations - LR2, Modelling Linear Relations - LR3, Quadratic Relations in y = ax^2 + bx + c Form - QR1, Quadratic Relations in y = ax^2 + bx + c Form - QR2, Quadratic Relations in y = ax^2 + bx + c Form - QR3]

MHF4U [Characteristics of Functions - CF3, Exponential and Logarithmic Functions - EL2, Exponential and Logarithmic Functions - EL3]

MPM1D [AG3, Analytic Geometry - AG1, Analytic Geometry - AG2, LR1, LR2, LR3, MG1, MG2, MG3, NA1, Number Sense and Algebra - NA2]

MPM2D [AG1, AG2, AG3, QR2, Quadratic Relations - QR3, Quadratic Relations - QR4, T2, T3]

Functions [F-BF.1, F-BF.3, F-IF.4, F-LE.1, F-LE.2, F-LE.3, F-TF.5]

Geometry [G-C.5, G-C.8, G-C.9, G-GMD.3, G-GMD.4, G-GPE.4, G-GPE.5, G-GPE.7, G-MG.1, G-MG.2, G-SRT.11]

Grade 1 [1.NBT.4, 1.OA.1]

Grade 2 [2.NBT.5, 2.OA.2]

Grade 3 [3.NBT.2, 3.NF.1, 3.NF.3, 3.OA.1, 3.OA.5, 3.OA.9]

Grade 4 [4-MD.3, 4.MD.2, 4.NBT.6, 4.NF.3, 4.OA.1]

Grade 5 [5.MD.1, 5.MD.3, 5.MD.4, 5.MD.5, 5.NBT.6, 5.NF.1, 5.OA.1, 5.OA.2, 5.OA.3]

Grade 6 [6.EE.1, 6.EE.2, 6.G.1, 6.G.2, 6.NS.1, 6.RP.2, 6.RP.3]

Grade 7 [7.EE.4, 7.G.3, 7.G.4, 7.G.6, 7.RP.1, 7.RP.3, 7.SP.2, 7.SP.6]

Grade 8 [8.EE.1, 8.EE.5, 8.EE.6, 8.EE.7, 8.EE.8, 8.F.2, 8.F.3, 8.F.4, 8.F.5, 8.G.5, 8.G.7, 8.G.9, 8.SP.1]

Practice [MP.1, MP.2, MP.3, MP.4, MP.6, MP.7]

Statistics & Probability [S-ID.6, S-MD.4]

How many spoonfuls would we need for “our” class to each have a glass of hot chocolate?

What measurement of a spoon are we using? Is it an accurate measurement?

What would happen if we used a smaller measurement?

What do the instructions on the can tell us about how to measure the hot chocolate?

How many units (grams) are in the whole can?

How could we find out how many grams we use for one glass of hot chocolate?

Can you find a mug which has the same capacity as the glass?

About how many ml of water do you think is used for one glass?

How many glasses can be filled with one full kettle of water.

I love these, Bernadine. Thanks for sharing!!

Any others out there?

How could this task be made into a division problem? Or what questions could I ask to allow my students to see it as a division problem?

Great question! After act 1 and the notice and wonder, the beauty of a 3 act math task is you can take it wherever you want. You don’t necessarily need any photos or videos to support your questioning. Once they’re “in”, they’re “in”!

So, my thinking is… if you’re after division, you might say that in an entire container has _____ scoops. How many glasses can you make? This would be a quotative division problem.

Unfortunately, if you use the act 2 video where they see how many scoops per glass, then you wouldn’t be able to access partitive division. However, if you only showed act 1 and SAID that you made 7 glasses of hot chocolate and you used 21 scoops, how many scoops were added to each glass, you’d be attacking partitive division.

Hope this helps!

We’re using this tomorrow with teachers as a whole school 3 act math experience. Going to put out the challenge for every class to try. We will share more of the results after!

Can’t wait!! Let us know how it goes!

I did this question with grade 2 today. After video 2 I asked what might the math question be? Had some suggestions such as 1+2 =3 etc. kids eventually worded the problem from the task with math terminology included. Very exciting to open it to them. Also asked a grade 3 working on it to extend and create a new problem. His problem was how many did he need for whole class? He used a different math strategy to calculate his answer as well.

This is great to hear, Penny! So happy to hear you were able to make it into a grade 2 class and share your experience here! I had the pleasure of doing this task with a grade 3 class recently and a couple different grade 7 classes. It was fabulous learning.

Hello I am interested in how the task turned out with the Grade 7 classes. How did you get them to think deeply.

A colleague (Yvette Lehman) and I went into a number of grade 7 and 8 classrooms and extended the task asking students to determine how many glasses could be made if there were 55 scoops left in the container.

The key was stating they needed to convince us (saying an answer and showing nothing else wasn’t enough). We also said without a calculator. As you can imagine, some students could come up with say “18 glasses” but couldn’t show any conceptual understanding. This is where we introduced the double number line and had them use it as a tool for thinking.

Great fun and lots of learning!