Flippity Flip, Bottle Flip!

How are all these middle schoolers/grade 9s landing these bottle flips?


Before today I hadn’t seen any of our students doing this bottle flipping thing! But I had a feeling they had all done it before. Today we started an activity with watching trick shots of bottle flips and will end with us creating and solving linear equations.

I showed this video:

My students wanted to argue that some of the tricks were fake…. but they were glued to watching. They all had tried flipping bottles before and some said they were amazing at it.

I had a full water bottle with me and asked if I could flip this. They all shouted that it was too full. I tried flipping and it was a no go. So I cracked it open and drank a few gulps. “Nope….you still won’t be able to flip that Mr. Orr — too much water still.” Again, I tried flipping it and nope. Still not even close. “Mr. Orr you probably won’t be able to flip it even if it had the perfect amount of water.”  So I took a few more swigs. “Still no good sir.” As I was chugging….someone yelled out for me to STOP! I did…..then flipped that bottle…. and…..Boom! The class was blown away!

I had them log into a simple Desmos activity that asked them to choose which bottle would be ideal for flipping.

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Almost everyone had chosen yellow.

The next slide had them moving a line to show the water level and then having them estimate how many ml would be ideal.

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Students were estimating between 100 and 200 ml.

“I think it’s 125 because that would be a quarter of the bottle. I think a quarter is the perfect amount of water.”

“I think it’s not 250ml because it has to be less than half…..but I think it’s not exactly half of that….so half of 250 is 125….but I’ll say 150ml.”

I shared all of their guesses:

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They kept asking if they were going to get to flip any bottles?? I said, “This is math class….do you think we flip bottles in math class?”

Then I broke out the bottles.

Here is the plan. We are going to have a bottle flipping contest. Rules:

  • Draw a line on your bottle where you think the ideal amount of water should be. Determine how much water to put into it in ml.
  • When you know how much water you need record it on our chart….put exactly that much water in there.
  • You must use your bottle for the contest.

Here are some pics of them working on this first part.

img_2250 img_2248 img_2247 img_2243 We had just enough time in this class to determine our volume, fill the bottle to verify it met the line, and practice flipping for about 10 minutes.

Part 2: The Contest

Students complete in five one minute trials. Recording how many “lands” they get each trial. screen-shot-2016-10-07-at-1-37-07-pm

We average those five trials to develop your “Landing” equation! Who was the winner? What does their graph look like?

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We use that equation to solve some problems. How many after ____minutes? How long will it take to make 100 lands? What does the equation look like if you have a head start of 5 lands?

I’ve modelled this lesson structure after this Paper Tossing activity and ultimately after Alex’s Card Tossing activity.

Featured Comment:

Mason:

 Well I am a middle school student and I go to chesnee middle school and I think that I just might show this to MY math teacher even though I don’t like math but you just made me want to like math. I’m in the sixth grade.

Pumpkin Time-Bomb Activity

Last year around this time I shared out a Google Form for classes to record measurements around their pumpkins and make them explode! I shared that form on Twitter so that we could crowd source as many pumpkins as we could to make the sample size large enough. I was pretty shocked at how many schools from North America took on Pumpkin Time-bomb. By the time Halloween was over the spreadsheet had over 90 entries. That’s over 90 pumpkins exploded in the name of math and data collection.

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This coming week let’s add to the data and use the it in our classroom to discuss: Scatterplots, Trends, Correlation strong, weak, no-correlation, lines of best fit, correlation coefficient, etc.

Here’s a sample lesson you could use on the day you make your pumpkin explode.

Generate Curiosity

Play this video which shows Jimmy placing rubber bands around his pumpkin.

How many rubber bands will make the pumpkin explode?
Have students write down a guess that is too low. Too high. Then estimate their best guess.

Show the Act 3 Video

Now Bring out your pumpkin for the class to see! Have them predict how many rubber bands it will take before it will explode. Repeat the estimation process. Have them save their guess till the end of class.

Making A Model

Throw out the question: “What measurements of the pumpkin changes how many rubber bands are used?” Let your students brainstorm a list of variables. Have a discussion on variables & relationships. Write all the variables on the board they come up with. Narrow down the list to items that are measurable with the pumpkin we have in the class. What affects the explosion the most? Height, diameter — circumference, thickness of the wall?

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Have them choose a variable that they feel should have a relationship with the number of rubber bands. Fill out the prediction part of the handout.

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Click here to grab a copy of the prediction handout

As a class measure all variables needed. Write them on the board for all to see.

Analyzing Data

Give students the link to the spreadsheet of all the pumpkins to date (You should copy and paste the data to your own sheet so you can filter/sort the results and share that sheet out to your students.)
Discuss with your students the lack of consistency in the selection of rubber bands from all over the country. How can we minimize this variable skewing our results? Filter the data with your students(or before hand) showing one type of rubber band (Most common is a rubber band of length 8.65 cm). This will only show all the pumpkins that have been destroyed using that type of band.
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Get your students to grab the data that relates to their relationship.

For example:
If Kristen chose the relationship Circumference vs. Rubber bands she should copy and paste the circumference column and the rubber bands column into a new sheet side by side. Then copy and paste all that data into the pre-made Desmos File.
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She can adjust the scale in Desmos as needed. Have her move the movable point and drop it where she thinks your class’ pumpkin will lie. Or you can have her find the line of best fit to help predict how many rubber bands it will take. Either way we want her to predict with more accuracy.

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So Kristen would predict that if her circumference was 90.5 cm then it will take 272 rubber bands to blow up the pumpkin!

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Now if Kristen chose a variable that it was clear there is no relationship then you get to have a discussion about correlation vs. no correlation. Have her choose new variables to predict on.

Once everyone in the class has a new prediction start wrapping bands around that pumpkin (You may want to start this as early as possible).

Watch your pumpkin explode and give congratulations to the student who predicted closest to the actual number of rubber bands.

Don’t forget to enter all your data to the sheet by filling out this form (you can also use the form to show the videos to the class).

[Updated] – You can use this Desmos Activity Builder Activity to facilitate the lessson. It includes only data for Diameter and Circumference.

[Updated] – You can grab a copy of the spreadsheet to save in your Google Drive. From here you can modify. 

From Oct 30. 2015

A few pumpkins from 2014 & 2015

Knot Again!

I am loving Alex Overwijk’s Knot activity more and more.
Go ahead and read about it!

Ropes of Different Thickness & Equal Lengths

I’m a huge advocate for having kids get their hands dirty and try things out. This one is particularly awesome because students get to experience how the rope length changes. They get to feel and create that change.

For those of you who don’t have ropes….or use this after the activity as part of a consolidation.
Problem 1- Solving a linear equation.
Act 1



Knot Again! Act 1 from jon orr on Vimeo.

Act 2
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Act 3

Continue reading

Popcorn Pandemonium

My afternoon grade 9 applied class (as a group) is very outspoken, loud, and restless (maybe it’s because it’s the afternoon and they have been sitting at desks all day). They have been a challenge to keep on task. So….I  am trying to find opportunities for them to be outspoken, loud, and restless.

A few weeks ago I came across this post by John Berray. Using/eating marshmallows to compare rates of change. I loved his idea of “experiencing rate of change” I decided to re-purpose his lesson to meet our goal of—> “I can solve a linear systems of equations by graphing.” I also took his recommendation of using popcorn instead of marshmallows…..and it paid off!!

Here is the low down…. we start the “Math Dial” off low.

ME: OK you are going to have a good o’ fashion popcorn eating contest!

Start with this video:



Ask for questions:

Here are a few from math tweeps

here are a few questions we can address with this problem.

  • When will Tim and Don eat the same amount as Jon?
  • Who will eat the most when the minute is up?
  • Will there be a time when Tim and Don eat the exact same amount?
  • When would Don eat more than Tim?

ME: Ok lets figure out who will eat the most in the 1 minute. But I want to recreate the video with you guys.

So I made a giant bowl of popcorn. (Don’t have time to make enough popcorn? — have kids give high fives to a timer instead)

Arrange groups of 2 or 3 and everybody grabbed some popcorn to start!

Round 1:

In each group kids are to choose who to mimic, Jon, Tim, or Don. They are to eat just like them! Allow them to ask about how fast each person is eating….or how much did each start with, etc.

Show Act 2 to answer those questions:


Tell them to get their timers ready….because they will eat just like one of those guys. Ready…..all you Tims and Jons eat your starting amount … Set….Go!

Start the timers and eat!

Question 1:
After they are finished, have them work out on their whiteboards who would eat the most in a minute.

Question 2:
When would Tim & Don eat the same as Jon if ever? (Great potential here for integer solutions talk).

Question 3:
During the minute, at anytime did Tim and Don eat the same?

If there was no time limit find when Tim & Don would eat the same?

Used this handout so they could create tables of values. Had them graph in Desmos!

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The awesome thing was that my students were desperately trying to find the equations to match their graphs….they didn’t want to plot all the points. I visited each group helping them find the equations if needed. Once the equations were in desmos they knew where to look.

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Act 3 – The reveal of who ate the most in a minute
 


Round 2: Do it all over again with new eating patterns!
Here are two possible eating pattern cards to give out:

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Students who finished early worked on our Crazy Taxi  vs. a new Insane Cab

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(@mathletepearce has a nice write up on using the Crazy taxi problem in class.)

Next day! Solving Multi-step equations…..will solve this systems of equations algebraically.