3act Math

Two Trains…

by Jon Orr

How many of you have seen a problem like this one?

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I’m a fan of taking a problem like this, one that you would assign for homework (in the “application” section of the exercises….and one that very few students even attempt….and someone will ask you to take it up next class) and bring it to the start of my lesson. I’ll teach our concept/idea through this problem. But we can’t just throw this problem up on the board and say “Let’s solve it”……because no will want to. There is no drive for any of us. Like Dan mentions here….who cares!

Who cares about the trains travelling…who cares that they are even trains….they could be bicycles, or cars playing chicken….but is changing the context really going to change how engaging the problem is to students? Dan argues no. I agree.  Before you read about this lesson check out this post on Real vs. Fake world….and the Circle Square lesson on 101qs.com which was an inspiration for changing the Two trains problem around.

Here’s my go at this one:

Show them this video:

ask What do you notice? What do you wonder?

Have students guess WHEN the two dots would meet?

Give some more info

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Have them guess on WHERE the dots will meet?

Have a discussion on what will be needed to determine the times and distances. Spend some time here on speed. Go over the relationship between distance, time, and speed.

Show them this image and have them makes some guesses on where the dots are now.

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then reveal

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Calculate the speeds of the dots. Have students go back to their original guess on time and find how far each dot would travel.  Who in the class is closest? Did anyone guess right?

Now help them generalize…

Create the equations

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If our lesson is on solving this using an algebraic technique we can teach them that here. Or maybe we want to show them the graphical solution. Either way we have taken the tougher question from homework that no one cares about and used it to set up and teach a skill.

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and finally,

I’m sharing this lesson now (before I teach it) with you hoping to get some feedback. Writing these lessons here also help me work out the details. This is week 4 of the #MTBos blogging initiative and its focus is lessons. I won’t get a chance to teach a lesson this week. Our school had final exams and then PD days in preparation for second semester. Good luck to all those starting up again!!

 

Catch the Spiral! 

by Jon Orr

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).

[aio_button align=”center” animation=”none” color=”blue” size=”medium” icon=”star” text=”See the plan” relationship=”dofollow” url=”https://docs.google.com/spreadsheets/d/1O6xynI57e9iza6YTP9nEIu6DnbaEeL-KztV5js9xkwg/pubhtml?gid=0&single=true”]

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

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

 

 

Angular Velocity, Trig Whips & Elmo

by Jon Orr

The #MTBOS is an amazing group of dedicated generous teachers!! This lesson came together because teachers are happily sharing what they are doing!

Generating Curiosity!

Dan Meyer has a series of blog post on Developing the Question you need to read. In one example he uses this video below to spark student wonder and start a fight. I copied his plan on how to use the video to generate discussion on speed.
Show this video

Pause the video before the bike is revealed and have students wonder “What is going on here?, What could the dots be?” Let the video play and then ask them to rank the dots from fastest to slowest. This is where wonder will happen. Are dots B and C moving at the same speed? What do we mean by speed anyway? Enter angular velocity vs. linear velocity.
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An Example for Linear Velocity vs. Angular Velocity

Show them this video obviously fake but fun video to generate some discussion.

Main Question we looked at together:How fast is the top swimmer moving when he hits the water? How fast is his angle changing? Before we calculate any of these we’ll go and experience the difference between the two.

Experience the Change

Bob Lochel has a great activity called Trig Whips where in groups of 4 students will experience the difference between angular velocity and linear velocity. Read about it!
A few pics and videos of our class Trig Whipping!

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Whole Class
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Consolidate

We came back in and summarized our findings from Bob’s handout. We made it clear that everyone had the same angular velocity but we all had different linear velocities. We turned our attention back to the diver video and determined the angular velocity and linear velocity of the top diver.

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That’s where class ended! Tomorrow we’ll start off with….

Andrew Stadel’s Elmo Problem!

See all the resources from Andrew here
Tomorrow we’ll find Elmo’s ending position after the 1 minute, angular velocity and linear velocity.

Fast Clapper

by Jon Orr

One of my favourite lessons to do with my grade 9 applied students is the Fast Clapper! I first saw it on Nathan Kraft’s virtual filing cabinet! My main goal here was to solve proportions through algebra.

We started class like this:

ME: Hey guys get ready…..I want you to clap as fast as you can……Ready…..Set……..GO!

Class: They clapped. Some students gave it their all….some not so much.

ME: Ok….That’s enough. Now let’s make a competition out of this! I want you to clap as fast as you can for 10 seconds….count how many claps you make! …Ready —– GO!

Class: This time all of them gave it their all!!

ME (after 1o seconds): STOP! Great job! Quick, write down how many claps you made in those 10 seconds. Who thinks they had the most.

James: I did….I had 37 claps

Josh: Nope, I’ve got that beat……48 claps.

Shylynn: I did 56

Class: Whoa!!

ME: OK….now find how many claps you made in 1 second!

They did this pretty easily and we went around the room again….still seeing Shylynn with the highest!

ME: Great job…..now watch this guy….

Hayden: Wow!!! that guy can clap

ME: I know….Let’s watch again. This time watch the video and try to see something you didn’t before.

We watched a few times. Each time students would notice something different. We noticed:

  • He closes his eyes
  • The record is 721 claps per minute — “I wonder if he’ll beat the record”
  • He clapped 58 or 60 times in the video
  • The video only showed the first few seconds

ME: Let’s take the suggestion to discover if he beats the record. Who thinks he’ll beat the record? Who thinks he’ll tie the record? Who thinks he won’t beat the record?
We took a vote and recorded it.
ME: In order to see if he beats the record we’ll need some of that info from the video…..but we better be exact. Why?
Janice: If we’re off by a clap in the first few seconds….it could be huge after a minute.
ME: Ok, let’s be exact.
Jake: We could pause the video on the last moment to see.

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Judy: He claps 63 times in 4.6 seconds.

ME: OK….go for it. Work together to see if he beats the record.

They got going and I needed to work with a few groups to discuss how to get started. “IF you could find how many claps in 1 second how could that help?”
After some time I stopped them and showed some students’ solutions

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We then showed the rest of the minute!

We moved into re-solving the problem using ratios and proportions. I went through slides to show how to set up the proportion and how to solve it with algebra.

I’m a strong believer in letting the students struggle and persevere through problems. I want them to use their prior knowledge to solve the problem in any way they can, any way that makes sense to them. I can see their understanding when they have to explain their thinking to me and the class. After they solve the problem in their way…..I take what they have done use it to explain the “math teacher” way.

Today one of my grade 10 academic students was solving a problem and I could see some good thinking on the page….but he also wrote: I don’t know how to start this. I asked him right there why he wrote that when he had almost a full answer on his page. He said “I know that’s not the way you want me to solve it!” I jumped on that quick and said….”I want you to solve problems that make sense to YOU. Just show me your thinking” He went on to solve the problem with in a great way.

We need to build our students confidence up. We need to promote and value their solutions instead of forcing our solutions on them.

So, back to Fast Clapper: I used their solutions to help explain why the math teacher way also makes sense. Here is a silent version of the slides I used.

We moved on from here to solve Dan Meyer’s Sugar Packets problem and the Smart Car Smash to practice solving proportions with algebra.

And then used a Knowledgehook gameshow to practice some more…go ahead, give it a shot.