Describing Relationships – Active Learning

We have started discussing graphing relationships in my grade 9 class.

Our lesson goal was to

I can…

describe a situation that would explain the events illustrated by a given graph of a relationship between two variables

I have loved and wanted to incorporate them…and some of Dan Meyer’s graphing stories …into my lessons! This is the perfect place…’s how we did it.

Day 1: We start with an estimation…..

I play the video (Poor quality) about 6 different glasses filling up with coloured water.

I pause it after a few seconds and ask: “Which glass will fill up the fastest? Draw the shape of your winning glass on your whiteboard” We take some guesses from the class…..then watch some more video. About 3/4 of the way through I pause again. “Anyone want to switch glasses?” Some of them will switch and some stick to their original guesses. After watching the final result…..I get some boos and “You tricked us”. We discuss why they filled up at the same time….which leads us into saying Volume of all  = Same and comparing the volume of the glass vs. time……which leads us to discuss the rate at which the glasses are filling = Also Same!

From there we jump right into and the WaterLine Activity.

This is one of the most engaging tasks on this topic I’ve seen. The predictions of height of water vs. time and the ability to self correct is amazing! As the kids work through the activities I always take time to discuss their answers to:


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We have a great discussion on how this new graph looks and I get them to draw one one on their whiteboards. (wish Desmos could add that prediction/check into the activity!).

WaterLine and its discussion takes the remaining of the period to complete.

Day 2: Graphing Stories & Distance Time!

We begin by watching and drawing different graphing stories from Dan Meyer (Elevation, Distance vs. Time). Check them out and download them! (He doesn’t even charge $4.99 for them!).

We then use Vernier’s LabQuest2 and the motion detector (borrowed from Science). Students walk in from of the detector and the rest of the class watches in real time how their distance changes vs. time. We get the kids to walk slow….then fast, walk away/towards….so they see how the graphs relate to real motion!




Lastly….. The kids are to create their own video graphing story and have peers draw the graphs to match.IMG_2664-0.JPG

  1. They pick a card that has some sort of motion described: “student walks fast away….then backs up slowly”
  2. They create a video that shows that motion. They use their phones or our iPads to capture that motion.
  3. They trade that video with another group and then they have to draw the graph to match!
  4. They keep trading and graphing different relationships!

The first time I ran through this series of activities I freaked out after because we just used two days and the kids didn’t solve/answer any problems from the textbook/worksheet! They don’t have anything written in their notes!!!!


IMG_2667.JPGEvery year I realize that there is great thinking and reasoning going on here! We have great discussions on what the graphs should look like. We need less notes and more active learning!! The kids are completing problems because they created them! They lived them! I feel they have understood the main concept at a deeper level!

anyways……thats all for now!









Pumpkin Time Bomb – Data Collection

I was watching Jimmy Fallon on the Tonight Show last week and saw this…

After wanting to try it myself (I did on the weekend with my kids – messy) I had a “wonder question.” I wondered would it be possible to predict accurately the number of bands to destroy any pumpkin?

After a few tweets:


I decided to gather some data…..maybe other math teachers out there would blow up a pumpkin and send me the data. I put together a form/activity for people to fill out. See the form below.

So….when the data files in I will send out a spreadsheet so teachers can analyze the data with their class. Hopefully we will see some relationships….and be able to predict how many rubber bands to blow up pumpkins next Halloween!

Here are some videos so far….


Please contribute to the data

Fill out the form

Kyle Pearce (@mathletepearce) has written on his blog about this activity. Check it out!

Here is the open spreadsheet with all entries so far

Here is a desmos file showing some relationships (or non-relationships)

This is my class and our result —- 407 bands


Pattern Talks

I was blown away by my grade 9 class today. They have been so insightful and brave when sharing their strategies when solving problems!!!

On Thursdays we have been starting class with Fawn’s site Visual Patterns. Today we were working on this one….

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How many boxes will be in the 100th frame?

Here is one solution from a student:


ME: “Tell me how you’re right”

KID A: “I saw it was growing by 4 and knew to multiply the frame number by 4…..but it didn’t give me the right number… i adjusted it by adding 1. So in the 100 frame I multiply 100 by 4 and then add 1….gives me 401″

Honestly,  this is how I expected everyone to do it…… here is the next one I saw (2 students had this solution).




ME: “Tell me about this”

KID B: “I noticed that one the first one there is 1 box on each corner of the middle box. And on frame 2 there are two boxes on each corner…and on frame 3 there were 3 boxes on each corner. So I knew that on frame 100 there would be 100 boxes on each corner…..thats 400 and add the one in the middle”


I was so surprised……I loved that these students looked at the pattern that way! It was refreshing that they used a strategy that worked for them and not waited for the teacher to show them how to do it!

Here is another one from the same class….




ME: “Tell me about this”

KID C:”Well, you are adding 4 every time…..if you forget about the first frame and imagine that block of 5 removed from the second frame….then you have 4 then you are really just adding 4 99 times……4 X 99 = 396. Then just add the original 5 back on to get 401.”

I’ll admit I was blown away with not only the solutions but the courage the students had to get up and share their methods. (oh…..We haven’t “formally” discussed Linear Relations YET—-just warm ups for now)

If you haven’t already checked out Visual Patterns… better…..they are great warm ups or warm ups that turn into full periods!

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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