Projects from 2013-2014, iTunesU, iBooks

by Jon Orr

I feel like since I started using Twitter for Pd and following the #MTBos my learning curve has been steep! As a result, when I look back at resources I have created I find myself wishing that I had done it “this way” or “that way” or used a different task here or there.
This is no problem for creating lessons, activities, tasks to use with MY students because I can always modify, change, manipulate!
My regrets show up when I’m involved in a project that gets published or shared out beyond my reach and afterwards my thinking has changed by seeing a great blog post, or a new activity, or by just having a discussion with a colleague. I wish I had all the time in the world to keep everything “up to date”

Our blogs, Google Drive Folders, Dropboxes are easily update-able and where are current lessons are!

Here are a few of those projects that I hit publish and find it hard to keep up to date: Each of these has lots of stuff I’m proud of, and some stuff I wish I could find the time to “update”

ITunesU Course – MPM1D (created April 2014)
Last spring I created an iTunesU course for my school board (Lambton-Kent).
Purpose: To share some digital resources I have used, or, are using in my grade 9 Principles of mathematics course.

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https://itunes.apple.com/ca/course/principles-mathematics-public/id946920145

iBook – Measurement (created July 2014)

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Whatcha Thinking – independent use of 3 Act Math Tasks for MFM1P

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iBook – Linear Relations (created July 2013)

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Popcorn Pandemonium

by Jon Orr

DOWNLOAD THE TASK & RESOURCES

Download the videos, images, and resources by clicking download below

DOWNLOAD

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.

DOWNLOAD THE TASK & RESOURCES

Download the videos, images, and resources by clicking download below

DOWNLOAD

Let’s Start with the Easy Ones

by Jon Orr

Here’s how I taught students how to solve trigonometric equations in our grade 12 advanced functions class.

Started with this Ferris wheel problem

From 101qs.com find it here

What has been working well is starting our “math” at a very low level…..like on a dial…..then we slowly turn the dial up….adding more “math” in. Read more about the Math Dial from a comment on Dan Meyer’s blog here.

Starting with this video the math on the “math dial” is very low.

I asked: What questions do you have after seeing this….

Answers:

How fast is it spinning?

What’s the radius?

What’s the period?

Where will the red dot be after 3 min?

And that last one is the question we studied.

Act 2:

From 101qs.com

Almost all kids solved this problem using proportions! They kept the dial in the low position still!  They realized that it takes 5 seconds to travel from dot to dot. Therefore it takes 40 seconds to go all the way around. They divide 3 minutes up into 40 second sections and get 4.5 rotations. The dot will end at the top of the Wheel!!  But the Trigonometry in me was screaming to get out……I asked, “Did anyone create a trig equation to model the height?” — cue crickets!

So we cranked the math dial up a tad!

I said:
When I go on a ferris wheel I always look for my house.” We talked about how high that might be in relation to Dan’s problem….we settled on about maybe 40 feet.
My question: How long will it take to get to that height?

Guesses? Will it be a nice number? No? Why not?
Crank it up a bit more …
Let’s create an equation for the height in terms of time (we had already learned how to do this and it was no problem for the class) .daum_equation_1417134251422

Now, to solve our question we have to solve this equation!

daum_equation_1417134353017

Student: That looks super hard!
Me: It does doesn’t it!

Let’s make that our goal!
We don’t want the math dial going up too quickly!

Let’s start with the easy ones, like this:

Screen Shot 2014-11-27 at 7.27.23 PMGotta keep the math dial low for a bit more…

Screen Shot 2014-11-27 at 7.29.22 PMWe solve this as a class, then another, and another, slowly building up our skills; slowly bringing the dial up. We stop at the end of the class. I assign a few more like the ones above. “Let’s get good at these so we can do the super hard one… Practice these for homework….”

Next day:
We take up the assigned questions then get back on track! We then solve these:

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We have a discussion on how many solutions there are here… and plop down a graphical solution in Desmos

Screen Shot 2014-11-27 at 7.30.00 PMThe math dial is getting up there…

Me: “Are you ready to try the big one?”

We do it! And everyone is into it….they have been waiting two days to see the answer! And the dial is pretty far up there!
After:
One student says: “That was pretty awesome! ”
That was my highlight of the day! Best compliment for a teacher!

We then show the graphical solution in Desmos. IMG_2795.JPG

Oh…..and we started class playing Pictionary (It’s our Wednesday thing) there was a tie and we have a good o’l match of Rock, Paper, Scissors to declare the winner. It was Intense!!!

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Many Many Volumes

by Jon Orr

In our senior math classes (advanced functions & calculus) we come across a problem like this….Screen Shot 2014-11-26 at 7.00.47 AM

I really like these problems, they have great potential but not really in this form. Let’s jazz it up and spend an entire class with this

Start with this video:

Ask What questions do you have about this?

Them:
What size is that rectangle?
Why are the corners cut?
Is volume always the same?

Etc,

My question:

What size of that square do we cut out so the box has the biggest volume?

Play the video again and have them yell out when they think the box has the largest volume.

Have them guess
What is too small?
What is too large?

Have them take their guess for the size of the corner and find the volume of the box

Draw a picture of the “card board” label the dimensions.

Draw the squares to cut out. Optional (Cut them out) make the boxes.

IMG_2790.JPG

What’s the new length?
What’s the new width?
What’s the height?

What’s the volume?

Is this the max?
How can we check?
Have them do another? And another.

Have them come up to your computer and enter their height and volume in the Desmos page for each box.

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Now, let’s generalize!
This time let your guess be x and find an expression for the volume.

What’s the new width? Take 8 and subtract twice your guess. (8-2x) Now the length? What is the height now??

Put that expression into Desmos and let them see the function, let them point to the maximum.

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For calculus: have them find the maximum using derivatives!

Show them this video to check their guesses.

From here we can solve problems like our original textbook question. The kids are invested now and they are ready to use the equation to find the value of x where the volume is say 24 cubic units.

Further reading: Jonathan Newman’s volume of a box Activity 

Credits: Algebra in motion for the Geometers Sketchpad file. Dan Meyer – this lesson mimics his Circle Square lesson.

UPDATE [Nov. 27, 2014]

Luke Walsh created a Desmos Sketch that seems super useful!