desmos

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

Trashketball – A Spiralled Lesson!

by Jon Orr

This was our multi-day, curriculum-spiralled, activity this week!

Day 1 – Filling the Bin!!

Let’s get curious!!…..I showed this video from Andrew Stadel, and took questions & wonderings:


We settled, (I chose) on the question on how many paper balls would fill a bin! They made predictions, too high, too low and right on!

They made paper balls and found their diameter. We agreed that each ball could be different so we recorded everyone’s diameter and averaged them to give the “average ball size”

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Function Matching – Down the Desmos Rabbit Hole!

by Jon Orr

Before our break I created a set of challenges for students to investigate translations of different functions. I had a few goals in mind:

  • Introduce a few basic functions that we will work with in this unit (square root, rational, cubic, quadratic).
  • See how certain points on the function are translated.
  • How does affecting the values in the equation affect the graph of a variety of functions?
  • Use function notation to represent translations.

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