Author: Jon Orr

Describing Relationships – Active Learning

by Jon Orr

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 Graphingstories.com and wanted to incorporate them…and some of Dan Meyer’s graphing stories …into my lessons! This is the perfect place…..here’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 Desmos.com 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!

 

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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!

[UPDATE: April 2015 ] – Read the modifications for Day 2 — the inclusion of a gallery walk. 

anyways……thats all for now!

 

 

 

 

 

 

 

 

Pumpkin Time Bomb – Data Collection

by Jon Orr

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

Results

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

by Jon Orr

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:

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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…..so 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).

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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”

ME: “WOW”

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….

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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…..you better…..they are great warm ups or warm ups that turn into full periods!

Subtract Before You Add

by Jon Orr

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…..kids 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!