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

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.

R2D2 – Pear Deck/Desmos Mash Up!

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… how the video will be displayed on the projector and not on each individual device!!!


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… 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.



Revealing the dimensions….


Students are ready to solve….



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!


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).

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!

Link to the Desmos Activity

Guess Who & Polygraph Lines

As we come to the end of the semester review days are here. To help grade 9s review properties of linear relations we played Guess Who. Last September I ran Guess Who with my grade 12 Advanced Functions class with great success. I made up a new sheet for grade 9 with a variety of linear relations (graphs, equations, and tables).

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Guess Who game sheet

The students played a few rounds each! The questions coming out were pretty good! I overheard lots of “Does is show direct variation?”, “Does it have an initial value?”, “Is your graph decreasing?”
All great terminology I love hearing from my grade 9 applieds!!

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After a few rounds of “low tech” Guess Who, we broke out and “high tech” Guess Who —– Polygraph – Lines

Students use a class code to access the game. Round 1 is playing the orginal guess who with pictures of people against the computer. 
The system then links you up randomly with another student in your class. You take turns each choosing a graph and asking questions to guess your opponents graph! 

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Again, great questions and discussions here! I could see the deep thinking about what questions to ask to eliminate options. Desmos once again out does it! Linking up digital resources while keeping learning social!

These students have been great to teach this semester! I’ll miss them next year!!

Show what you know in Gameshow!

IMG_3350Last week, Kyle Pearce wrote a post on running GameShow by KnowledgeHook. I was drawn to this idea mostly because of review time coming up and wanted a nice way to practice EQAO multiple choice type questions. GameShow is great for that. I love that it works on any device. Students can use their phones, iPads, laptops, etc to submit their answers.

Today I created a custom GameShow to practice simplifying algebraic expressions with my students. KnowledgeHook has a bank of questions already to go…..I just did some picking and choosing of questions I wanted to tackle and added them to my newly created custom gameshow.

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I stressed to my students to not worry about any time in the game. These multiple choice questions are not about speed. Let’s make them about accuracy. They played in teams of two with whiteboards beside their devices. I asked them to show full solutions on their whiteboards.


What was awesome while playing our GameShow today was that once students submit their answer they can upload a picture of their work!!!


On the teacher side, I could see how many solutions were uploaded for each answer option.Screen Shot 2015-06-03 at 12.22.07 PMAs a class it was great to choose correct answers and analyze them. All answers are anonymous until the teacher clicks the reveal.  It was equally rewarding to analyze the incorrect answers and talk about how we can make them better!!! Students seeing each others’ solutions is powerful! 


Since I asked for all solutions to be uploaded the students started putting more effort into their answers! I find when we use other software like this, putting in an answer is like a game. “How fast can I get it in” Uploading slows it down and puts an emphasis on the solution! Like it!!! That’s the way a gameshow should be played!!!!

This program is super new so head on over to . It’s free. And has content build right in. Even if you’re not from Ontario you can have access to the free bank of Ready Made gameshows or create your own. You actually don’t even need to teach math to make use of the gameshow!!!

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