Wednesday, November 23, 2016

#bottleflipping 2 day Desmos Lesson

After reading about water bottle flipping and a Desmos activity being created on it:

I took a look at a few teachers experiences with it including  the blogs of Elizabeth Raskin, Jon Orr, and Trish Poulin.

I decided to merge some of the ideas, with the first day using Mr. Orr's hook by trying to throw to flip a full water bottle and experience failure in front of the whole class. They screamed, "too much water, you need it to the third line!"

I showed them activity builder Mr Orr made with the 4 choices, and most selected I believe it was yellow. I asked them how we could figure out the best amount of water to have? Some suggested measuring with a ruler, and others said measure the water in it. So, having graduated cylinders that filled up to 100 milliliters, we used those. They made a table of 100% down to 0% with 10% increments. I asked them how we could see how much water for 90% full.

The water bottle is labeled with 16.9 ounces and 500 milliliters. I asked students what they would rather use. They said milliliters because it's a round number.

They said take 10% of 200 milliliters, and subtract it from 500. That left them with 450 mL. Then they'd pour another 50 mL out for their next trial. They would do 10 trials of each and record their successful flips in the data table of the activity builder.

As they complete the table, the points appear on their graph. So, seeing their small sample, the activity asks what it would look like for the whole classes data? Here's their predictions:

2ND PERIOD
GASPARD MONGE
It's gonna look like a decreasing straight line.
PIERRE DE FERMAT
It stays at zero until 30 % and then gradually declines.
CHRISTIAAN HUYGENS
the class is gonna look like a little hill
ARCHIMEDES
it will increase then decrease
ARTUR AVILA
It will start at around 5 and decrease slowly then increase a little bit. Then it will decrease and then very slowly down to 0.

3RD PERIOD
JAMES MAXWELL
It will be mostly a straight line but between the 20 to 40 percent filled the chart will peak up.
ATLE SELBERG
It will look similar because it most likely people will have more flips when the water bottle is less full and less flips when the water bottle is full for everyone.
SOPHIE GERMAIN
I think it would look like this where there are zero flips in all percentages of water instead of smaller amounts such as 20,30, and 40%.
DOROTHY VAUGHN
Stacey: I predict that at first, the graph will increase, then start decreasing. Sebastian: I predict that the most flips will occur between about 20-40% full Zurin: I predict that the graph will increase upwards a little when it has 50-20% of water and decrease to 0 again. Kaitlyn: I predict that the graph will increase similarly during 30-40% full.

5TH PERIOD:
ALAN TURING
We think there will be more successful flips in the middle region
TERENCE TAO
First it will start to increase than decrease .
SHIING SHEN CHERN
I think our class´s data will look like a zigzag since that´s how our group data looked like.
MARY ROSS
I think it will gradually increase after 80% full and it will be highest at 30% because it is not too full or too empty.
JEAN-PIERRE SERRE
we think that the data would be low because, the chances of a bottle flipping and landing on the bottom is slim.

DORIS SCHATTSCHNEIDER
Around the 50%-40% mark, that's where you're most likely to land more flips than any other percent.

& interpreting their data after seeing the whole classes graphs:

2ND PERIOD
GASPARD MONGE
View Graph
Around 30% the bottle is able to be flipped the most.
PIERRE DE FERMAT
View Graph
Mostly everyone got the most flips when the water bottle was 30% full.
CHRISTIAAN HUYGENS
View Graph
This is how I expected it to look, because it looked like a little hill. It was more flat though.
ARCHIMEDES
View Graph
when it got to 50% full, people started to land their bottles WE LOVE MATH ❤

ARTUR AVILA
View Graph
The highest number of flips is 31 at 30%. The lowest number of flips is 0 and the graph increases, decreases, then stays at 0 then increases and lastly it decreases and stays at 0.

3RD PERIOD:
JAMES MAXWELL
View Graph
The class did well in the first half compared to the last half in the experiment.
SOPHIE GERMAIN
View Graph
Conclusions we can draw are that they get a lot of flips at smaller percents. Though it is surprising that people landed the bottle at higher amounts such as 60% and up.
DOROTHY VAUGHN
View Graph
More flips occurred around 20-40% full but there were a few times when there was a success over 50% full.

5TH PERIOD:

ALAN TURING
View Graph
we thought that the middle of the graph would rise
SHIING SHEN CHERN
View Graph
The amount of water is the dependent variable in this experiment, and that the less the water, the higher chance of getting a perfect flip.
MARY ROSS
View Graph
we thought that the 30 would be the only one that would move up
JEAN-PIERRE SERRE
View Graph
most people got the bottle to flip correctly on the last ones
DORIS SCHATTSCHNEIDER
View Graph
The number of flips increased around the 40% mark and starts to decrease after 50%.

Here are their whole class graphs in order of 2nd, 3rd, and 5th period:

In each class there appeared to be some outliers at around 80%. Though you can't deny that 30 or 40% is always the highest, usually 30%.

On day 2 we had a competition where students switched off flipping bottles for a minute. They had 3 trials. I asked them what we could do with their trials to represent their overall performance. They said to find the average. So, they explained to add up all the successful flips and divide by the number of trials, 3.

Then I borrowed ideas from other math bloggers and asked how many could they land in 1.5 minutes? Make a table and graph their average if they continued flipping at a constant rate for various amounts of minutes. Write an equation. How many lands in 10 minutes? How long to make 100 lands? And if you were given a 10 land head start, how long to land it 200 times?

It was a great opportunity to revisit proportional relationships.

The highest average in each class was in a final flip-off at lunch, with all participants in the finals getting a donut, with 1st through 3rd place getting more than 1 donut.