Estimation

Is Lego Gender Biased?

by Jon Orr

Here was how our conversation in math class (MFM1P) went…..How many pieces make up this Star wars Lego ship? Screen Shot 2015-02-23 at 3.28.54 PMWe started with that picture and had a great conversation around Lego.

Then I showed this one.

Does the pool/hot tub have more pieces/less pieces/ or the same? This turned into “boy” Lego vs. “girl” Lego. My personal opinion is its all great…. My 3 daughters are just as excited to play with Yoda as they are with Disney princesses. Girls in the class agreed that they didn’t need their own line of lego!!!

I moved our conversation a little forward with asking Which costs more? And which should cost more?

Screen Shot 2015-02-24 at 5.46.05 AMAnswers: Continue reading →

The Power of Match My Graph

by Jon Orr

I was checking out twitter last week and ran into this from Dan Meyer:

— Dan Meyer (@ddmeyer) February 19, 2015

and I had a concept coming up that I have always had a tough reaction to. I threw it out there.

To get students to be interested in it I wanted them to be “dying” to figure it out.

I thought about putting them in a place where they had to struggle— I wanted to open up the middle!
Michael Fenton has a series of Match my Parabola challenges and I thought of those. I modified his challenges a bit to include those examples from my tweet.

Screen Shot 2015-02-24 at 9.58.19 AM

Click to access Desmos page

Continue reading →

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:

Screen Shot 2014-11-27 at 7.29.45 PM

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!!!

IMG_2794.JPG

 

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.

Screen Shot 2014-11-26 at 7.09.50 AM

 

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.

Screen Shot 2014-11-26 at 7.13.32 AM

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!