MEL3E Day 25

Our warm up today was writing a cheque! 

Students were to fill out a cheque to me! I’ve definitely thought that these were given skills that we all would know, but the class reminds me that is not the case. I didn’t learn these money skills while in school. I picked them up along the way. My students, most of whom are 17, haven’t seen these skills yet. I’m so glad we offer this class to students! It’s too bad not all students get to take this class. I know some of my senior advanced function students could benefit from it.

We picked up finishing the On The Map Desmos activity. Some students who were away yesterday were here today so I worked with them to get caught up on drawing routes, estimating distances, and  using the scale to determine the route distance.

Pentomino Puzzles

A few years ago I was introduced to a series of activities (through my then districts math consultant) that builds a driving need for students to createscreen-shot-2016-09-30-at-8-14-39-am, simplify, and solve linear equations. I used the activity for a few years in a row while I taught grade 9 academic. Since then I had forgotten all about it (funny how that goes) UNTIL NOW!

The activity ran as a series of challenge puzzles around Pentominoes and a giant hundred grid chart.

Activity 1: Explore

Ask students in groups to choose this tile and place it on the hundreds chart so that it covers a sum of 135. The task seems so simple to start but unpacks some great math.

Allow them to determine this sum anyway they like.


I circulate and listen to their strategies. I give them very little feedback at this point. After a few minutes I choose some of those groups I heard interesting strategies to share..then let any other group share out their strategy.

img_2198Activity 2: Keep Exploring

I have them use the same tile and try again. Place the tile so that it covers a sum of 420. Listen to those strategies! Most groups that didn’t have a strategy before will try to adopt a strategy they heard last round. At this point most students will catch the strategy “If I divide the sum by 5, being like the average then I should have the middle number in the shape.”

This is where I stop and have a formal discussion as to why dividing by 5 here works? Will this always work? Will this always work with other shapes? What other shapes will this work with then?

We formalize the strategy.

Our big problem to start is not knowing where to place the tile. Let’s say I label the middle square n. What will the square immediately to the right of n always be? The left? The top? The bottom? Have them check this out by placing the tile repeatedly back on the grid.

Now let’s add all of those expressions up


The middle square must be a multiple of 5!!! I have them try this strategy out by throwing out another sum and have them place the tile.

Look at another tile!


We go back and outline that we could have chosen a different square to label n. Which results in a new equation and solves for different value…..but results in the same placement of the tile!!


We continue by me having them select different tiles, giving them sums, having them create equations and solving them. I love how hands-on this lesson is. Holding the tiles adds some “realness” which I feel drives the need to solve these equations.


this year when I remembered this activity I wasn’t sure I still had the tiles kicking around (I found them later). I immediately made a digital version with Explain Everything.


The digital version gives each student their own copy and while working in groups can chat about what strategy worked and what didn’t. Before on the paper version….only one student could hold the tile. Also, when students have to voice their strategy through Explain Everything they have to have careful thought. They think about the words they want to use. We this careful thought they get to make their thinking visible for me!

One new addition to the activity I get to make here is that they can create their own pentomino…..and then their own puzzle to share with their classmates.



Since then I also created the activity with some help from the team over at Desmos


Click to access and rune the activity

I love their new conversation tools….I get to pause the class and discuss when needed!


Students can even sketch their new tile and create an expression to match! screen-shot-2016-09-30-at-9-24-03-am


Desmos even added some nice extension questions. Love it! screen-shot-2016-09-30-at-9-24-23-am


In the future the next time I explore this lesson I see a blend of hands on tiles with digital support. I think having the best of both worlds here can pack a powerful 1-2-3-4-5 punch!

Pick your favourite!

Download the Explain Everything Pentomino Puzzles .xpl file. 

Access the Desmos Activity



Catch the Spiral! 

Last May I shared my day-to-day planning spreadsheet for my grade 9 applied course. On that sheet I recorded the topic, tasks, and resources for each day of the semester. I used that as a resource for myself when teaching 1P through a spiral this semester. I found that having that sheet to go back too was super helpful and a time saver. This semester I followed that timeline except with a few tweaks here and there.

Since that sheet was so handy to have I made one similar for my MPM2D class. It was my first time spiralling that course and I wouldn’t go back to teaching through units again.

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I heavily relied on Mary Bourassa’s blog….she is amazing. She shares her day-to-day plan as posts on her blog and also shares all of her resources and handouts. Thanks so much Mary!!!

Spiralling in Academic vs. Spiralling in Applied

I struggled initially with deciding to spiral the MPM2D course because of my experience with MFM1P. I had previously taught the 1P course through activities and 3 act math problems so it was a no brainer to just mix up the order of the problems and tasks. It was an easy transition since I had all the resources. For the 2D course though, it had been a while and I had not taught it with a task/activity approach.

What I found to work best in the academic class was to learn all new ideas/topics through activities and productive struggle with some direct instruction thrown in as a consolidation. Unlike the 1P course where I switched tasks/topics daily, I stuck to a topic/idea for a few days or a week in the 2D course. Once, for example, the class was comfortable with transformations of quadratics we would switch to trigonometry for a week, then analytic geometry for a week, etc.

I felt that through spiralling and teaching through productive struggle my students were better problem solvers. They were not just waiting to be told how to solve a problem. They were always actively thinking about which ideas they had learned could apply to solve a particular problem. That confidence I saw allowed us to go more deeply into the content than ever before. We just didn’t skim the surface of the processes, algorithms, and algebra needed, we solved problems!!

If you wanted to spiral the 2D course or a similar course I thought I would share out my plan to help out. Here is my day-to-day plan with links, resources, Desmos activities, 3 Act tasks, assignments, homework, etc from my spiralled MPM2D course. (It’s not fully complete for every day but you’ll get a sense of how the class ran).

Most files are either Smart Notebook, Apple’s Keynote, or PDF.

Get Apple’s Keynote on your Mac or on iOS.



Match My Graph & Crowd Sourcing Challenges

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.