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# Draining The Pool

## How long will it take to drain the pool?

No Expectations/Standards Selected

## Making Predictions With Scatter Plots in the Real World

This Real World 3 Act Math Task will have students making predictions via interpolation and extrapolation using scatter plots and a line of best fit.

## Related Math Topics:

Data management of two-variables including:

• making predictions between two-variables,
• creating scatter plots,
• classifying correlations as positive/negative and strong/weak, and
• interpolating and extrapolating using a line of best fit.

This task can be extended to linear relations and equations by having students determine an equation of the line of best fit or alternatively, non-linear regression to find an equation of a curve of best fit.

If you haven’t already, I recommend using the Candle Burning 3 Act Math Task prior to using this task, as the data appears to have a stronger linear correlation.

## Act 1: Introducing the Problem

Show students Act 1:

After showing the video clip, I have students discuss with their group some questions that come to mind. Sometimes, I have students focus on two types of questions:

1. The first question that comes to mind; and,
2. a unique question you don’t think someone will come up with.

This tends to differentiate the question responses rather than seeing a ton of the most obvious one. We discuss these options, then settle on our first question:

How long will it take to empty the pool?

Then, we move on to Act 2.

## Act 2: Reveal Some Useful Information

I personally don’t ask too many questions about what information they want, as most tend to know where this problem is heading.

Show them Act 2:

Although I try to avoid fading out my videos to ensure the information doesn’t go away, here’s a screenshot of the last frame, for your use:

Feel free to save the image.

At this point, students can head off on their merry way. I find most of my students tend to go straight for a scatter plot and extend a line of best fit, while others might choose to try to leverage the initial value/y-intercept and estimate a rate of change/slope to create an equation. At midterm and beyond, I’m hoping that the second option becomes more attractive to my students since we have been working with linear equations quite a bit. If no students head in that direction, I would introduce it during the consolidation of the problem as a potential strategy for future use.

If you’re beyond students drawing scatter plots and want to do something more advanced with this problem, consider using Desmos as a way to manipulate and interpret data.

Click the image below to grab a shared Desmos graph with all the data points plotted from a table of values with regression line/curves:

## Act 3: See The Answer!

Once students have updated their prediction based on their mathematical thinking, we can show students Act 3 so they can cheer (or cry) based on what really happened:

Here’s a screenshot of the last frame, if you’d like to use it for some of your consolidation:

## Sequels / Extensions

• What do you predict the depth of the pool would be after 17 hours of draining? (interpolation)
• What would be a reasonable drain rate for this pool assuming the trend is linear?
• What would be a reasonable equation for a line (or curve) of best fit?

Please comment to let me know how it worked 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!

## Share With Your Learning Community:

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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