Match My Graph & Crowd Sourcing Challenges

by Jon Orr

Here’s a quick synapsis of an activity from my Advanced Functions class with transformations of trig functions.

We used a Custom Polygraph from Desmos to generate talk/discussion on key properties of trig functions (Students have previously dealt with trig functions in grade 11).

I overheard students asking questions about x-intercepts, period, and amplitude. Awesome!

We took a note on key properties of the sine function and cosine function (We ran out of time for Tangent). 

Let the struggle begin!

Students were then asked to work through this Match My Trig Function Activity built using Desmos’ Activity Builder.

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Each slide is set up as a challenge. They are to write a sinusoidal function that “overlaps” the black target function. Students will have to use their memory or trial and error to discover how the parameters change the graph.

Watching the dashboard I can ensure their struggle is productive. I can jump in with feedback when I see they need it.

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Here’s the best part, once they completed all 12 challenges they created their own trig function matching challenge and shared it out on a Padlet board. We had crowd sourced a bank of challenges to work through!  The students didn’t hold back either… They wanted to create hard ones to push their friends.

See the challenge – Live Board Below

Can’t see this board? Click here

That’s where class ended. When we came in the next day  and they all choose at least 5 peer challenges to complete…. And that’s when the taunting began!

To end it off we took a note based on their discoveries of how the parameters changed the graphs.

Click here to create your own Custom Activity Builder or here to create your own Padlet board.

 

 

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.

Reading Relationships – Literacy & Math

by Jon Orr

Friday last week was a PD day for us here in Chatham. We spent the day going over our OSSLT (Ontario Secondary School Literacy Test) results from last year and discussed how departments can make a difference. We came to a giant conclusion through the data that although OUR students could read…..they struggled with comprehension.

The OSSLT is a giant beast and most schools say “Literacy is a whole school issue.” I agree….but it can seem daunting to take on as a whole. Each of our departments decided to narrow their focus. Departments would choose a type of reading activity and incorporate that type into their lessons on a regular basis. We would own that type of reading assessment and use the data/results in June to see if we made a small difference.

In math we chose reading informational texts and answering multiple choice questions based on those readings.

Here is one sample lesson plan our math department created to do in our grade 9 & 10 classes.

Generate Curiosity

Show students this Estimation180 challenge.

How many pages in this book?

Day 99 http://www.estimation180.com/day-99.html

Have them guess too high, too low, best guess (Grab Andrew’s tracking sheet)

And the answer.

I zoomed into the passage on the answer picture and asked students to read the passage silently to themselves and raise their hand when finished.

We discussed that different people read at different speeds. Students made sure to point out: “Just because I read slower doesn’t mean I understand less.” Connor wanted to go as far as saying that maybe if you read slower you will understand more.

These were great observations and I said let’s explore this more.

I had them guess how fast they read in words per minute. To help make this guess we counted up all the words in the passage above (51) and asked them if they thought it took a minute to read that passage. Some students agreed and predicted they read 50 words/min, some predicted much higher at 300 words/min. They all recorded ther prediction on their whiteboard.

Let’s discover our reading speed! We’ll explore the relationship between words read and the time taken.

Predicting

Using the handout students predict what the relationship between time read and words read will look like.

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Finding our Speed

A great reading resource is the series  Critical Reading Series. 

Screen Shot 2015-10-28 at 6.34.54 PMAll articles are of appropriate length with questions that are of the same variety as the OSSLT. The key for us is the book also shows the number of words per article!!

I gave each student an article titled Jackie Chan Actor & Stuntman (1006 words) I also asked them to get out their phones to time how long it takes to read.

After reading, students are to answer questions based on the reading. We’ll take up and compare our score vs. Speed later.

They read, recorded their times and calculated words/min on the handout.

Explore the Relationship.

We used this rate to introduce direct variation. We filled out a table showing words in 1 min, 2 min, etc. We showed it was linear and introduced terms initial value, rate of change, and direct variation.

I stole parts of Kyle Pearce’s template for our task Flaps for this handout

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We went on to use our equation to answer the following…

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Lastly after students answered the follow up questions from the reading we graphed our reading speed vs. our score on the reading. We’ll repeat this lesson again and again, each time adding to this graph…..trying to see if Connor’s statement — “does reading slower result in better understanding?”  —  true or false.

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Run this lesson in your class:

Grab all Files Now 

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.