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Match My Graph & Crowd Sourcing Challenges

by Jon Orr

Here’s a quick synapsis of an activity from my Advanced Functions class with transformations of trig functions.

We used a Custom Polygraph from Desmos to generate talk/discussion on key properties of trig functions (Students have previously dealt with trig functions in grade 11).

I overheard students asking questions about x-intercepts, period, and amplitude. Awesome!

We took a note on key properties of the sine function and cosine function (We ran out of time for Tangent). 

Let the struggle begin!

Students were then asked to work through this Match My Trig Function Activity built using Desmos’ Activity Builder.

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Each slide is set up as a challenge. They are to write a sinusoidal function that “overlaps” the black target function. Students will have to use their memory or trial and error to discover how the parameters change the graph.

Watching the dashboard I can ensure their struggle is productive. I can jump in with feedback when I see they need it.

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Here’s the best part, once they completed all 12 challenges they created their own trig function matching challenge and shared it out on a Padlet board. We had crowd sourced a bank of challenges to work through!  The students didn’t hold back either… They wanted to create hard ones to push their friends.

See the challenge – Live Board Below

Can’t see this board? Click here

That’s where class ended. When we came in the next day  and they all choose at least 5 peer challenges to complete…. And that’s when the taunting began!

To end it off we took a note based on their discoveries of how the parameters changed the graphs.

Click here to create your own Custom Activity Builder or here to create your own Padlet board.

 

 

Sneaking in Factoring

by Jon Orr

I started a series of new warm ups for my MPM2D class today. My goal is to sneak in factoring as warmups throughout the semester. By the time we need to learn it (like when we need to factor to solve equations) we will have mastered it already. I also previously snuck in multiplying binomials when we tackled quadratic patterns as Mary Bourassa did in her 2D class.

So today I gave them this slide and said I want you to solve a puzzle!

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They broke out their iPads and used the Algebra Tile app to put together the rectangle. The kids worked away and you could see them trying to put tiles in a way to make the rectangle

….and they soon found out that they had to fit a certain way!! 
On take up we made sure everyone had either my rectangle or a rotated version.

Then we did this one…..

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After we were done I asked the class: “If the combination of squares and rectangles makes up the area, what are the dimensions of the rectangle?” They had a little bit of a hard time here, but finally could see the x + 4 and the x + 2 as the length and the width. I then wrote …

 And then I heard some “aaah”s. We had previously seen both versions of the quadratic expressions and discussed why the factored form helped us out quite a bit if we wanted to find the x-intercepts.

We stopped there….It only took us 15 minutes. Tomorrow we will do a few more…..always writing the factored form after. I will also try to get students to notice efficient strategies to make the rectangles.

  • Why did you put 4 x terms along the width and 2 x terms along the length?
  • How does that relate to the number of singles?

Where I hope to go with these warm ups is to factor all types of trinomials:

  • Perfect Squares

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    This time…..make a square

… and get this…

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  • Trinomials of the Type ax^2 +bx + c


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  • Completing the square too!!!!
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This time…make a square




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We’ll be definitely working our way out of the app and onto paper with area diagrams…

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Factoring

 

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Completing the square

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Completing the square

I think working with these puzzles for the next few weeks first will give us a strong base when it’s time to factor to help solve equations and then complete the square. I think I’ll track all the warm ups we do like this and I’ll post them all!

Desmos Challenges in iTunesU, Multi-Touch Book, and Web Version

by Jon Orr

For many years now my classes have been completing a course wide project on Picture Modelling. Before Desmos (B.D.) I use to send home copies of Geometer’s Sketchpad for students to generate a picture using only functions.Screen Shot 2015-08-28 at 12.41.47 PM
After Desmos showed up it was now super easy for students to generate art and access graphing software from any device.

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The project has been so successful at engaging students to learn about various functions and their transformations I extended it to all grades! For the last few years the project spans grades 9 through 12. Each year learning new functions and creating art.

Screen Shot 2015-06-10 at 1.49.50 PMThis summer while at the Apple Distinguished Educator Institute in Miami I started a project that would create a digital resource that would link the Modelling Functions with Art Project with function challenges created by Michael Fenton, Dylan Kane, and myself.

If you are in an one-to-one iPad room or have access to iPads the resources are in an iTunesU course and multi-touch book for iPad  otherwise they are linked on this site for any device (see below).

Each chapter starts with linking patterns, tables, graphs and equations in pre-made Desmos graphs or in pre-made Desmos activities made using Activity Builder.Screen Shot 2015-08-17 at 7.49.53 PM
Following that, activities ask students to match functions to specific criteria like Michael Fenton’s Match My Line or in my Match My Trig Function. Again the teacher can choose to use the activities in the Multi-touch book or from the pre-made Desmos activity.

Every so often in the challenges students are asked to show their thinking by uploading a picture of their work on a Padlet page. Students can crowd source different ways to solve the same problem. 

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Finally, at the end of each chapter students are to create a working piece of art and share it on a Padlet gallery page! Students can see each others work and comment.

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Each chapter covers different functions but many chapters can be done in the same course:

Ontario curriculum suggested chapters:

  • Chapter 1 – Linear Functions  – grade 9 & 10
  • Chapter 2 – Quadratic Functions – Grades 10 & 11 & 12
  • Chapter 3 – Various Functions (function notation, cubic, square root, reciprocal, non-functions).  – Grades 11 & 12
  • Chapter 4 – Trigonometric Functions  – Grades 11 & 12
  • Chapter 5 – Exponential & Logarithmic Functions – Grades 11 & 12 (Coming soon!).

The project page has more details on how to access the course, book, and web resources.

[aio_button align=”center” animation=”none” color=”blue” size=”medium” icon=”none” text=”Go to the Project page” relationship=”dofollow” url=”http://wp.me/P3az6g-14y”]

R2D2 – Pear Deck/Desmos Mash Up!

by Jon Orr

School is just right around the corner for us up here in Ontario and I can’t stop thinking about that first day. As for my grade 9 applied class’ first day I have ran the R2D2 problem in the past with great success.
Now, over the summer I’ve seen great improvements in Pear Deck and wanted to get into it! Also Desmos has been busy and released Activity Builder!! So let’s mash these two apps up with some R2D2!!

So here is the R2D2 problem presented with Pear Deck and an extensions with Desmos….

Act 1: The video

and this is what Pear Deck will show after you insert the video…..love how the video will be displayed on the projector and not on each individual device!!!

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I like using Pear Deck here for asking for wonderings and notices because it allows students who normally won’t shout out answers to have a voice in the room. Students get to input their responses and the teacher can show them on the projector.

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For generating estimates I absolutely love how they put our Too high and Too low guess on a number line…..it gives us the visual of where our actual estimates will lie.

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Act 2: Gathering the Info

In the new version here I get students to draw their estimates of the dimensions of both the board and the post it note…..this pushes them into drawing diagrams.

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Revealing the dimensions….

 

Students are ready to solve….

 

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Act 3: Revealing The answer

The Extension: How many rectangles can we make that have an area of 609 post it notes?
To extend I want students draw out different rectangles and label their dimensions! They can use Pear Deck’s white board!

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But then they can enter them into Desmos through a pre-made activity I created in Activity Builder. (the Pear Deck file links to the Desmos activity).

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For each rectangle the student can come up with they find the perimeter and plot the length vs. perimeter in the Desmos graph. The teacher on the projector can use the Overlay function and show all the different rectangles students are coming up with…essentially showing the pattern that emerges! Using the pattern students can read off the minimum perimeter!

 

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If you have a Pear Deck account Grab and download the file below!

[aio_button align=”center” animation=”none” color=”blue” size=”medium” icon=”star” text=”Pear Deck File” relationship=”dofollow” url=”https://drive.google.com/file/d/0B9g0jeaVwshveDVhWktzdTRudE0/view?usp=sharing”]

Link to the Desmos Activity