Begin to recognize characteristics of linear, quadratic, or periodic functions.

Generate a need to use proper vocabulary around linear, quadratic, or periodic functions.

Specific recommendations:

The “talker” cannot use their hands and should keep them behind his/her back. This will help the student be careful and direct the language they choose to describe the graph.

The “drawer” cannot talk.

Set a time limit. Possibly 3-4 minutes for the “talker” to describe the graph to the “drawer” with the goal to reproduce the graph.

Consider having all the “drawers” reveal the graphs at the same time for dramatic effect.

There are three different versions of the activity based on topic

Once students choose a role tell them “Talkers, your goal is describe the graph perfectly to the drawer. Drawers, your goal is to listen carefully and without talking try to match the talkers graph. You will have 3 to 4 minutes for each graph.”

When the time is up, tell all the drawers to click the REVEAL button at the same time to see how close your sketch was.

What the teacher experiences:

While students are describing and sketching take time to listen to the words they use. Store these words for later in the class so you can link them to the proper names.

Example:

You heard Jose Adem Chain say, “The pattern starts at 2 and goes up…” If most students are using the phrase “starts at..” We can introduce the term y-intercept.

Or on the periodic function version:

A student might say, “…it does that and then repeats 4 units later” You now have a gateway into introducing the period of the function.

After each round use the Teacher View to showcase some student graphs to the class.

Consider restricting the students to the current sketch and move from sketch to sketch as a class.

Last question.

The words generated on this slide will most likely be informal. As a class discuss the informal use of the word and then introduce the more formal words relating to the topic.

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.

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.

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:

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.

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.

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

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?

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.

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.

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?

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.

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.
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.
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.

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

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).

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