I’m sure we have all seen students flipping bottles in school and sometimes the sound is enough to drive me crazy. Over and over and over again! I questioned often whether I could turn this into a math task and then I came across this post from Dan Meyer titled : **#BottleFlipping and The Lessons You Throw Back**. Oh no! Dan Meyer tried it and didn’t like his lesson – does that mean there isn’t one that I could do?

I approached a colleague of mine, Jean-Louis Frado, while at a conference and we got to talking. We talked about it for two days and we knew we had to be onto something. We even sent PMs to Dan Meyer and he thought we were onto something. This was enough to motivate us 🙂

While we were messaging Dan Meyer and planning our activity, Jon Orr tweeted out his activity using the bottle flip and we actually pulled from his lesson to make ours. Therefore, I guess we could consider this lesson an extension or « a leg » of Jon Orr’s **Flippity Flip, Bottle Flip!**

So here is the idea : * CAN WE FIND THE BEST FILL HEIGHT FOR ANY BOTTLE?* Is it proportional? Is there an ideal ratio between height of water to height of bottle? Is it volume of water to volume of bottle? Is it…? you get the idea – our minds were racing and we were excited.

We planned the activity during a PD day and tested out the lesson during an open house for Grade 8 students at the school. We know that these students are flipping bottles all the time and we knew the entry points were at a good place for these students.

I teach at a French school and so here’s the lesson plan (in French) : **Faire flipper**

We had students answer the two first questions from the **DESMOS activity** in the same way Jon Orr started his activity

When students explained why they put the line there, the answers were :

You can’t have too much and you can’t have too little.

It has to be less than half but not too low.

So, we let them flip using their idea of the optimal amount of water. Before flipping, we talked about how many trials they required and how many needed to be successful to say they have the optimal amount. Most of the time, they decided 3 out of 5 was enough and 3 in a row was ideal!

They flipped and they flipped and they flipped…they adjusted water height, they measured bottles and they kept going until they were sure they had it.

We had them go back to the DESMOS activity and adjust the line following their experimentation. Now, we had this!

There were still a couple groups sticking to their lines but a few groups had adjusted their lines and met at the same place. We wanted to talk about **what this place could be and if we could describe it**. So, we asked them to do this using DESMOS. Here are the answers :

This time instead of describing too much, too little and giving ambiguous answers, we were seeing some math. We were seeing fractions, we saw percentages (not shown above), we saw ratios…we were onto something 🙂 … Maybe!

Ok, so now the kicker! * Will this ratio be maintained no matter the size of the bottle?* We asked, they answered :

So, we got back to experimenting and we let groups choose the bottle they wanted to work with.

This is where we really saw the math and the measuring start to happen. They wanted to create equivalent ratios and keep up the proportion to test their hypothesis.

They flipped and flipped and flipped! They felt pretty confident that they had found it and they estimated the ideal height of water to be 1/4 of the bottle height – they veered away from the 1/3 here because it was too heavy. This is where we able to talk about the difference between 1/3 and 1/4 when then the whole is larger. In the small bottle, the difference is almost negligeable but in a larger bottle, it changes everything.

**Now it was time to take out the BIG BOY!**

We went outside for this one and we flipped it! The ratio worked and the flip was successful.

Here is a video of the students **flipping BIG** and of **us having fun on our PD DAY** while planning the activity.

We observed #mathtalk during the entire activity. We also observed reasoning, reflecting and modeling! We had students asking some interesting questions or making observations that would allow for extending questions. To be honest, we could probably flip bottles for a week!

Examples were :

Is there a stronger ratio between the diameter of the base and the height of the water?

Is the weight of the water more important than the height?

If the base is large and the amount of water small, will it still flip?

Did we really find the optimal amount?

Does it depend on who is flipping the bottle? Does it depend on the style of flip?

**Student engagement was at a maximum here and our follow up will be proportional reasoning, part-whole talk, proportionality, equivalent ratios…**

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