##### Ontario Alignment By Overall Expectation

## Using Real World Rates and Proportional Reasoning

The following 3 act math task shared by Nathan Kraft (@nathankraft1) involves **proportional reasoning** with opportunities to address learning goals around rates, proportions, rates of change and creating equations.

Jon Orr and I have used this task in presentations a number of times over the past few months and many have asked us to share our slide deck and other resources with a summary. So, here we go!

## Act 1 – Sparking Curiosity

Show the following video:

*Note that this is an edited version of Nathan’s video where I have blacked out the number of claps. You can always add. You can’t subtract.

I typically give students a prompt to jot down what they notice or wonder. Giving a minute of rapid writing in point form or otherwise can be a great opportunity for students to get sucked into the problem.

Students might notice:

- A timer
- he claps fast
- we saw about 4.5 seconds worth of clapping
- current world record was 721 claps in a minute
- …and so on

Students might wonder:

- Why is he clapping?
- are those “legal” claps for a world record?
- how many years of practice does he have?
- will he break the record for claps in a minute?
- …and so on

While we will engage in a healthy amount of discourse around these noticings and wonderings, my main focus is to pull out the question:

Will he beat the current record?

I’m then going to ask students to make a prediction. Will he beat the record? How many claps per minute do you think he’s going to get based on what you saw? I might even show the Act 1 Video a few more times to give students an opportunity to use a mathematical strategy to help with their prediction.

We will record student predictions up on the board next to their names for an opportunity to celebrate later.

## Act 2 – Climax: Raising the Tension

Show Nathan’s video:

I am very explicit with my words after showing the video. I say something like:

Do you think you can improve your prediction?

The reason I do this is so that every student has an entry point to the problem. I don’t necessarily care about the exact answer the “math” says you should get. I’m happy with a student using friendly numbers to help them get closer. I’m happy with students using some sort of strategy we might have seen in the past (proportions or maybe trying to create an equation from previous years). The best part by doing this is everyone can get closer to the expected actual result.

What do you think? Will he beat the record?

Here’s one question from a Knowledgehook Gameshow that could be used to support this task:

## Act 3 – Conclusion: What Really Happened?

Allow students to check their solutions:

## Additional Resources

Additional resources can be downloaded from the download link and the Knowledgehook Gameshow can be grabbed here to modify and edit.

How are you using the problem? Please share in the comments and be sure to thank Nathan for sharing on his blog or on Twitter.

## 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

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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 - M1, 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 - M1, 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 - M1, 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.2, 3.NF.3, 3.OA.1, 3.OA.5, 3.OA.9]

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

Grade 5 [5.MD.1, 5.MD.3, 5.MD.4, 5.MD.5, 5.NBT.2, 5.NBT.3, 5.NBT.6, 5.NBT.7, 5.NF.1, 5.NF.2, 5.NF.3, 5.NF.4, 5.NF.5, 5.OA.1, 5.OA.2, 5.OA.3]

Grade 6 [6.EE.1, 6.EE.2, 6.EE.5, 6.EE.6, 6.EE.7, 6.G.1, 6.G.2, 6.NS.1, 6.NS.3, 6.NS.6, 6.RP.1, 6.RP.2, 6.RP.3]

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

Grade 9Practice [MP.1, MP.2, MP.3, MP.4, MP.6, MP.7]

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

Hi Kyle.

I have a Windows PC. What is the best way to open the Fast Clapper materials?

Thanks, Chris

Hi Chris – which materials in particular? The videos should open on any platform. However, if the keynote file is in there, that is only useful for MacOS / iOS devices.