Graphing Functions Water Lab

The math department at my school is top notch at collaborating and coming up with innovative ways to reach kids. One of the Algebra 2 activities they developed is a water lab for introducing nonlinear functions. It is a great activity for the beginning of the year or really anytime functions are being introduced. By the end of the first class students are already talking about "fast to slow" and "slow to fast". It's awesome!

This activity can also be used with younger kids as a way to practice measuring and data collection. The shapes of their graphs will open up great discussions about what happens when we pour water into bottles that are wide or skinny.

Bottles of different shapes*
plastic water bottles (bigger than I show here-- I didn't have a bigger one)
small plastic cups
food coloring
graph recording sheet

*As an aside, my husband and I joke about how ironic that beer glass is with "#1 Dad". Also, we don't use beer glasses in school. We use Chemistry glassware in this lab. But I'm home this year so I raided the cabinets!

Each station has a glass bottle, a bottle of colored water, a ruler and a marked plastic cup (see below). 

Students pour colored water into the plastic cup to the tape mark. The lower the tape, the more accurate the graph will be (and the more time students will be at each station). 

They then pour the measured water into their glass bottle...

Again and again, measuring each time...

And recording the heights.

This bottle is skinny at the bottom and wider at the top and the graph reflects this in how it increases fast at first then more slowly. 

If I had placed the tape lower on the plastic cup I could have caught that little flare at the glass's bottom.

This post is super short! So if you have any questions about the setup, please post them below or send me an email at

UPDATE: Teacher Ms. Pottie emailed to let me know that Desmos has a digital online version of this lab called Water Line! Cool!

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  1. Replies
    1. It's a great activity! Thank you for your comment!

  2. Don’t the bottles have to have the same volume?

    1. Not at all. Any curved botles are great to use for this lab.