Today’s warm up we played the game of NIM. I started this off by saying “I’m the undisputed champion of Southern Ontario on the game we’re going to play. I’ll give $10 to any player who beats me!!” I put down the bill on the table!

Game of NIM in our classroom:

There are two players. There are 21 sticks in a pile. Players take turns. A player can choose to take 1 or 2 or 3 sticks from the pile. The player that takes the last sticks wins!

Easy enough game? My students thought so and were eager to win $10. I played 2 rounds each with a different student in front of the class. They couldn’t believe that I had won both times at such an easy game. I let them in on the secret so they could go off and play and win against their friends or parents.

If you can leave your opponent with a multiple of 4 …you win….so with 21 sticks you can always win if you go first.

Next up we are switching strands to Travel and Transportation. I started with having them split their whiteboard down the middle. On one half they wrote “I notice”. On the other side they wrote the heading “I wonder”.

I showed this short clip and asked them to write down anything they noticed and anything they wondered.

I gave them 2-3 minutes to write down their noticings and wonderings. Next they had 2 minutes to share that with their partners. Then they shared with the group. At first they were pretty shy to share with the group….but once we got rolling…….they wondered a lot!!

I explained that the “oh no” in the video was said because driving to SF looked super long! We had a great lengthy discussion about travelling by car. A few stories from me and also from them! The list of wonderings they generated will fuel our work for this part of the course! We will come back to driving costs and owning a vehicle costs next cycle…..this time around we’re going look at travelling by Air, Bus, Train. We’ll read schedules, learn about time zones, and read 24 hour clocks.

Today’s focus –and as it turns out Monday’s too– was on air flight. We broke out the iPads and looked up flights to SF. I handed out a recording sheet.

Most students hadn’t searched sites like Expedia or Travelocity before so we went slowly. We’ll resume this activity on Monday and we may get to doing some problems with the World Clock and the 24 hour clock.

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

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

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.

then reveal

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

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.

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!!

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.

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!

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.

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.

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.

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

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.