Subtract Before You Add

I’ve been reading Dan’s posts for a while now and this is one series that has stuck with me…..  “You Can Always Add. You Can’t Subtract.” Ctd . Here is one small way I used this concept today…

Here is the original problem from EQAO

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My applied students in previous years have struggled on problems like this.  I simply “whited out” some….

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That pic is what I start with. It’s amazing what happens! With the original problem students immediately are turned off….it looks tough, and confusing. It’s got a few things going on!  With this new one… are voicing their thoughts on a bike priced at $175. They’ve got lots of ideas on this statement. They start sharing stories and are comfortable! It’s pretty awesome that this “subtraction” strategy has changed the tone in my classroom. It’s more inclusive……more safe!

I then reveal a little more….

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We had another discussion on what this means…..but most students jumped right to finding that percentage (we calculated percentages last day). Kids were engaged! just because we started with that small simple statement.

I then revealed everything once they had calculated that percentage.

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Again, they were off and working…..I had a student put their solution on the board and we discussed it. It was awesome to see that there were not intimidated on this problem! It was also awesome to see that they could apply their knowledge when we saw another problem like this!

thanks Dan!

Using the Internet to create Proportion Problems

We used this image today to create our own proportion problems. Shown here is how much data is generated at each company after 1 minute. I took the screen shot from this site

Here was my example of a proportion problem: “If there are 48818 apps downloaded in a minute from Apple, how many in one day?”

My students then designed their own problems to solve……..we then wrote them on the board and everyone picked some to solve….here are a couple:

My kids were engaged and wanted to solve each others problems ……just to see how crazy the data was. We then voted on which piece of data was the most shocking! That gave us a purpose for the practice!!! The consensus was how many Netflix hours were watched each minute!!!!

My first Lesson with Pear Deck


Today we gave PearDeck a try. It was awesome….. so far here are the best features:

  1. When I asked students to: “Place a moveable dot on the point where the function gives a value of 40″. On their own screen they see just their dot, but on the projector screen they see everyone’s. — on this particular example the class was split on the two points where the volume is 40. This was awesome because we could all see that there are two solutions. I then asked “Now place a dot where the function gives a value greater than 40″ Again they could see in live time everyone’s responses……but it was great for explaining that there are infinite solutions to that question (Our lesson goals were to solve inequalities using graphs)!!!
  2. It worked on all devices!!! It worked on their phones, iPads, tablets and computers…..this was great. I didn’t need to book a lab or for everyone to have an iPad with a specific app! It’s web/cloud based so they just need to access a webpage.
  3. Works with Google Drive….load files right from the Drive….it also saves to the drive. When kids join the class they are asked to sign into their google drive account. So on the dashboard I can see their name!

Some Feedback

Noticed that I had to switch between projector view and dashboard view so that we could see the entire class’s responses to the drawing questions. It would have been nice to see their drawings overlapped just like when you place a dot!

More to come. Totally worth the subscription fee though!!

Modelling in Clash of Clans

Here is a task I’ve been playing around with lately. Let me know what you think!!!!

Thinking of using this task with my grade 11s functions class/ or more advanced functions classes. I have recently been playing Clash of Clans and if you have played you know that you have to wait for items to be built/upgraded, etc. The time to wait changes based on the your progress and cost of the item/upgrade. You do have the option to SKIP the upgrade wait time by using gems. What has me wondering is that the amount of gems needed to skip an upgrade. What’s the relationship between upgrade time and gems? Our task is to see what that relationship is.

Act 1 : I’ll show this short video to my students:

I’ll ask for any questions the students had from watching the video and settle on —How many gems would it take to upgrade the town hall? — which will take 2 days.

Get the students to make some guesses…..

Act 2 :

Then get them discussing what other info we will need. I want them to come up with the idea they need more instances of upgrade times vs. gems. I can start to show them some pics…..was thinking of revealing each “point” at a time and getting then to guess!


Here comes the modelling time…….plop these down in Desmos. We’ll start to select a model based on the data we see:

Screen Shot 2014-09-24 at 11.04.31 AMpremade desmos page with some sliders built in for each type of model.

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Have them decide which model they like best for the answer…..use the model to come up with an answer. My guess is that students will assume linear and come up with an answer that is too high (I’ll update later after I use it with students). ……and then we can have the big reveal……

Act 3

Watch the video ….

Or use the image..




Find the cost of upgrading immediately… much wait time can you skip with $20?


Head on over to to download the files.

To edTech or Not?

To edTech or not???

This was my lesson today where I used some technology….

In our Volume of Cylinders & Prisms grade 9 applied lesson we started out grabbing an Explain Everything file from our Google Classroom.

Our first problem embedded within the file was You Pour, I Choose from Dan Meyer. We watched the Act 1 video and then students filled out a google form embedded right in Explain Everything. The form asked them what questions they had after seeing the video.


The next slide showed the forms responses in a google sheet!


The students got to see live what each other were asking. Most kids had the same question…..Which had more or do they have the same!!

We then made guesses using a form……and saw each others guesses.


After, we set out to work deciding what we needed to know before answering the problem……mades some guesses along the way and then solved the problem!

I’ll admit that we had some internet connection problems accessing google forms and every time we do I seriously think that it wasn’t worth it……but today it seemed worth it because it gave some of those shy kids a voice in my class. I’ve worked on problems like this and when I ask students share their questions….guesses…..usually the “brave” kids make their voice heard and the shy ones are left out (unless I ask them specifically). The tech today even though was spotty……served a purpose……its for small reasons like this that I keep trying out edTech in the class!!


The Need for Speed!

Here was our lesson today on Instantaneous rates of change/slope of a tangent line

Yesterday we completed the awesome Desmos activity Function Carnival!! Some students were extremely competitive when trying to match the motion of the cannon shot to their graph…..some students not so much……here are their graphs

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After showing the kids this picture we talked about the motion of the guy and how it relates to the graph…..Questions we had

  1. When would he be travelling the fastest? How do we know?
  2. When would he stop? How do we know?
  3. What happened after the parachute opened?

My goal here was to get talking about the speed of the guy. I asked:

If the guy was carrying a speedometer or a GPS…..what would his speed read out the moment before his parachute opened?

We stopped and made some estimates based on our intuition.

We talked about how to determine instantaneous speed from our knowledge of average rates of change, average speed, and slopes of secants lines.

We finally came to the conclusion that we could calculate the average rate of change between two points REALLY close together!!!!!! BINGO.

So I said let’s drop this image in Desmos! (we came to a decision that the cannon ball guy’s max height could have been around 9 metres).

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We looked at the graph and decided that it was HARD to estimate two points really close together.

So we added in some transformations to a basic quadratic function and fit the curve to the graph.Screen Shot 2014-09-12 at 8.44.11 AM

I had pre-loaded some “extra” info in the sketch to demonstrate graphically the idea we were coming up with……the idea of looking a the slope of a secant line and as one point gets closer to the next the slope of the secant line approaches the slope of the tangent line.

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After looking at it graphically…..we used the equation we came up with to algebraically calculate the slope of the tangent line (the instantaneous rate of change).

We then practice that calculation using other points the students were interested in knowing about.

That was our lesson on Instantaneous Rates! Thanks Desmos!!

Guess Who!!!

One of my kids’ favourite game is Guess Who…..remember this one?



You remember it! I wanted my students to practice recognizing characteristics of polynomials without having to just complete questions out of the text book… I thought this game could work great! When you play this game you ask characteristic questions about the person you have picked and try to narrow the choices down…..all before the other person has guessed yours!

Perfect for characteristics of functions!!! Could also be great for my grade 9s who will later learn characteristics of linear relations.

I put this “board” together for the possible choices.

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And kids will use dry-erase markers and “paper protector” sheets so they can re-use the Game boards.


Here are some pictures of my students playing the game

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Math is Like…. [first day]

An activity I have done every semester since I started teaching is one I call “Math is Like….”

After going through all the course mumbo-jumbo, we talk about creativity!

Then the activity starts like this….

Here is your chance to get creative!! Take your Post-It and write Math is like….”

I then give the students some examples from previous years. The idea is that they are to complete the statement with their own thoughts.


Some students write funny things, some negative things, some insightful things! I let them know they are allowed to write whatever comes to mind as long as its school appropriate.

I have found that this gives students an “airing- out” of past experiences and we get a fresh start!! My grade 9 students have all come from different backgrounds in math….some great…..some not so great! So I tell them that if you have had a negative experience in math in the past, part of my goal this year is to help them change those beliefs about math

Here are some of this years Math is Like ….. statements. [I've got my work cut out for me!!!]







Minnie’s Juice Cup [3actMath]

Here is a 3-Act Math problem I’ve been working on. My first unit in the fall is measurement and I wanted something to do with volume.

Minnie’s Juice Cup!

Act 1:

Question: How many juice boxes will fit in the cup?

Act 2:

Make them guess for each of these measurements.



I am open to suggestions on how to handle the two different diameters. I tried averaging them and came up with a pretty accurate answer.



Act 3:


R2D2 – Post-It Note Art!

I loved Nathan Kraft’s Van Gogh Post-It Note art on his windows. If you haven’t seen it…check it out.

I wanted to do something similar for a while now (like @mr_stadel’s File Cabinet Problem) and found some time now that school is over! Following Nathan Kraft’s instructions with Excel I created my own Geek Art…

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Grabbed some Post-Its and got to work…..I also created a time lapse video so I can make a 3 Act math problem for my students (Coming soon!).


Info for 3 acts
Each Post-It is 2″ by 1.5″
The board measures 42″ by 43.5″
I actually used 609 Post-Its!!