MFM1P

Spiralling grade 9 applied math

by Jon Orr

So, I’m going to spiral the grade 9 applied course! I’m a little hesitant because I’ve taught this course with a units approach for the last 10 years. But I’m also exited!!! It seems so awesome that everyday we will solve problems; Alex Overwijk says

“learn to uncover curriculum instead of cover curriculum“

Instead of “boring up” the first day with paper and expectations, and policy, etc, etc we talked about being curious, collaborative, creative, and embracing challenge!

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So….we dove right in to this.

Act 1: Showed this:

 

 

  Continue reading →

Projects from 2013-2014, iTunesU, iBooks

by Jon Orr

I feel like since I started using Twitter for Pd and following the #MTBos my learning curve has been steep! As a result, when I look back at resources I have created I find myself wishing that I had done it “this way” or “that way” or used a different task here or there.
This is no problem for creating lessons, activities, tasks to use with MY students because I can always modify, change, manipulate!
My regrets show up when I’m involved in a project that gets published or shared out beyond my reach and afterwards my thinking has changed by seeing a great blog post, or a new activity, or by just having a discussion with a colleague. I wish I had all the time in the world to keep everything “up to date”

Our blogs, Google Drive Folders, Dropboxes are easily update-able and where are current lessons are!

Here are a few of those projects that I hit publish and find it hard to keep up to date: Each of these has lots of stuff I’m proud of, and some stuff I wish I could find the time to “update”

ITunesU Course – MPM1D (created April 2014)
Last spring I created an iTunesU course for my school board (Lambton-Kent).
Purpose: To share some digital resources I have used, or, are using in my grade 9 Principles of mathematics course.

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https://itunes.apple.com/ca/course/principles-mathematics-public/id946920145

iBook – Measurement (created July 2014)

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Whatcha Thinking – independent use of 3 Act Math Tasks for MFM1P

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iBook – Linear Relations (created July 2013)

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Filling it up!

by Jon Orr

In our grade 9 applied class we are finishing off linear relations and moving into solving equations. I want an activity that is hands-on, engaging, and shows a purpose to solving linear equations.

Here is some thoughts on an activity I want to try. Let me know what you think. Any feedback would be greatly appreciated.

Here it is: Filling it up!!

Show them this picture….

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Let them wonder, let them ask what that thing in the pitcher is.

ME:

“How many would be too much?”

“How many would be not enough?”

“How many is just right?”

Have them record the guess. “We’ll compare our answer to our guess”

Next,

ME: Let’s find out how many.

Organize them into groups of 3.

ME: What are we going to need?

We’ll need volume of the pitcher, volume of the cup, and volume of the weight.

Have discussion on:

What shape is the cup? …..is it more like a cylinder or a cone? Which is it closest to? What formula for volume will you use? Will you be right?

What shape is the pitcher? What shape is the weight?

Choose 1 member of you group to find the volume of the cup; choose 1 member for volume of the pitcher; choose 1 member to find volume of the weight.

Have the items around the room like stations:

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IMG_2772Each member will find the volume of their object and bring it back to the group.

Allow the students to work

Here are some scaffolding questions I can use (Please feel free to give me some more)

  • What’s changing as you fill up the pitcher?
  • Does it start with zero volume? What volume of the pitcher is already taken up?
  • What volume is left after the weight?

Here is a possible solution….

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My idea is this could be great context for introducing solving equations using opposite operations! Use their technique  and show how the volume grows as the cups increase. Use Desmos and relate it to y = mx + b.

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show them how their strategy is the same as solving 5562 = 1511 + 335x. Boom! Context for solving equations!

My ideas for extensions would be to put objects like….

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in the pitcher. Count how many cups to fill the pitcher now. Use our equation to solve for the volume of the car. [Corresponding Grade 9 Academic learning goal: Find the y-intercept (initial value) of a linear equation given the slope (rate of change) and a point. ]

What do you think?? Think it would work? I would love some feedback!

Stacking Cups!

by Jon Orr

So we did Dan’s Meyer’s stacking cups lesson in class today!!!  I first saw this activity from Andrew Stadel in his 3-Act math collection. Not sure who first came up with it though. But thanks to both of you!

I started class by stacking the cups up in front of them…..allowed them wonder what was going on. They had questions like

“What are you doing?

“Are we having Hot Chocolate?”

“Are we going to use them to drink something?”

“What are your doing?????”

“How many cups do you have?”

and “How tall are you in cups?”

and bingo there we go!

I told them that is our task for today…To discover how tall I am in cups! I then had them estimate how many cups it would be! They were uncomfortable to start. They wanted to guess perfectly so they wanted to know how tall I was. They tried to put cups next to me as I walked around. They wanted me to lie down! I said just make an estimate to start off! I wanted them to guess so we had something to compare their final answers to. I wanted them to continually checking their work against their initial guess.

After a few minutes of estimating one group asked: “Are we stacking them like this…..

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or like this…..

IMG_0965.JPGAwesome!!!! I said “Does it matter?” and they all yelled yes!!! So we then agreed that we had TWO problems to solve. So we put up two sets of estimates!!! We decided to stack them like the second picture first!

Estimates

Estimates

I then asked:

“Did you need anything from me?”

they asked for: Rulers, my height, and Desmos!

I gave them all of those things…….everyone wrote frantically when I said I was 183 cm tall!!!

They worked! I saw groups stacking cups, recording values in Desmos, and measuring!

Almost all groups realized that the stack height was only changing by the lip amount and I saw a lot of this…

IMG_2730.JPGwhich had me excited!!! It gave me a chance to say: “Tell me about this, why do you think this is correct?” It was so interesting to hear their responses…..they were convinced they were right so I said let’s plot this in desmos and see if the equation matches the table

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Oh!!

They knew they were wrong…..but what was awesome is that they knew how to fix it!!!! Desmos is awesome for this. It’s like a visual self correction machine! We discussed that the start of the line didn’t seem to match up with our points. Then the ahaa! happened.

“We didn’t use the zero row for our start value.” They fixed it and were visually rewarded with a correct answer.

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After our equations were in desmos, the kids dragged their finger along the line until they reached a height of 183 cm and read off the number of cups! For the kids who seemed ahead of the game this was my chance to introduce solving equations by using opposite operations!

Finally we stacked the cups to verify.

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Round 2: Stack the cups end to end.

Most groups divided my height with the height of 1 cup…..21 cups….give or take….So great! It gave us context when we discussed opposite operations when solving equations.

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I found it was great that we had two problems in one! We are discussing how to distinguish between partial variation problems and direct variation problems. And here is one scenario where we got to look at each!!! Such a valuable activity!

Oh……did you want to know my height in cups (overlapped)??? —–> 128!

[UPDATE: April 2015]

As an extension use the videos from Andrew Stadel to teach solving linear systems graphically! Access his task here

Below are the list of Ontario Curriculum Expectations covered in this activity—-> Look at them all!!!!

  • pose problems, identify variables, and formulate hypotheses associated with relationships between two variables
  • carry out an investigation or experiment involving relationships between two variables, including the collection and organization of data, using appropriate methods, equipment, and/or technology (e.g., surveying; using measuring tools, scientific probes, the Internet) and techniques
  • describe trends and relationships observed in data, make inferences from data, com- pare the inferences with hypotheses about the data, and explain any differences between the inferences and the hypotheses
  • compare the properties of direct variation and partial variation in applications, and identify the initial value
  • express a linear relation as an equation in two variables, using the rate of change and the initial value
  • describe the meaning of the rate of change and the initial value for a linear relation arising from a realistic situation
  • determine values of a linear relation by using a table of values, by using the equa- tion of the relation, and by interpolating or extrapolating from the graph of the relation.