3 New Desmos Activities: Talkers & Drawers

Goals of the activity:

Students will:
  • Begin to recognize characteristics of linear, quadratic, or periodic functions.
  • Generate a need to use proper vocabulary around linear, quadratic, or periodic functions.

Specific recommendations:

  • The “talker” cannot use their hands and should keep them behind his/her back. This will help the student be careful and direct the language they choose to describe the graph.
  • The “drawer” cannot talk.
  • Set a time limit. Possibly 3-4 minutes for the “talker” to describe the graph to the “drawer” with the goal to reproduce the graph.
  • Consider having all the “drawers” reveal the graphs at the same time for dramatic effect.
There are three different versions of the activity based on topic
Links to the three activities:

What the student experiences:

Once students choose a role tell them “Talkers, your goal is describe the graph perfectly to the drawer. Drawers, your goal is to listen carefully and without talking try to match the talkers graph. You will have 3 to 4 minutes for each graph.
When the time is up, tell all the drawers to click the REVEAL button at the same time to see how close your sketch was.
 

What the teacher experiences:

While students are describing and sketching take time to listen to the words they use. Store these words for later in the class so you can link them to the proper names.
Example: 
You heard Jose Adem Chain say, “The pattern starts at 2 and goes up…” If most students are using the phrase “starts at..” We can introduce the term y-intercept.
Or on the periodic function version:
A student might say, “…it does that and then repeats 4 units later” You now have a gateway into introducing the period of the function.
After each round use the Teacher View to showcase some student graphs to the class.
Consider restricting the students to the current sketch and move from sketch to sketch as a class.
Last question.

The words generated on this slide will most likely be informal. As a class discuss the informal use of the word and then introduce the more formal words relating to the topic.
Inspired by Brian McBain and also the team at Desmos

Two Trains…

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! 

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).

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

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

 

 

Promote Struggle – A Hero’s Journey in Math Class

While in Miami for the Apple Distinguished Educators Institute we saw a speaker from Pixar (I can’t recall his name) discuss the aspects of Story. More specifically he spoke about the Hero’s Journey. That talk really hit home for me. Below is how I interpreted his message and how it relates to my classroom.

A Hero’s Journey

All of these characters take a hero’s journey….

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Since I’m a math teacher describing the Hero’s Journey is best done with……a graph (English teachers will know it’s shown as a cycle).

On a time vs. Tension graph the Hero’s Journey looks like this: Time is the length of the journey….or story. The tension is felt by the audience. 

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In the beginning the hero is introduced, the main conflict is introduced, his/her world starts to change. As the story continues the hero must battle the forces of evil & go through struggle. They must experience conflict. It’s the conflict that the hero learns about themselves. They learn their strengths and weaknesses. It’s the struggle that makes the ending awesome. Its the struggle that make the hero see the solution. It’s the lessons they’ve learned in the struggle that let’s them go aha! I know what I need to do! The story would mean nothing to the hero and the audience if the climax was much earlier in the timeline. As the story ends the character returns to a NEW normal. They take their learning and come out stronger on the other side. 

This curve we see above is nothing new to us. This curve is what learners go through. It’s a Learner’s Journey too.

Now, if we take a look at our traditional math classrooms we have a format much like this:

Photo credit: Kyle Pearce

Photo credit: Kyle Pearce

Let’s look at that structure on the Time Tension graph. 

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After we take up homework, we introduce the new lesson or topic or problem to work on. It’s unfamiliar so tension in our students starts to increase.  But what happens is that as the tension rises it immediately falls back down. And my good buddy Kyle Pearce mentioned to me that the tension doesn’t fall all the way back to the axis….a good number of our students feel that tension permanently. 

Why does the tension fall immediately?

We make that happen. We relieve students of their pain by immediately telling them HOW to solve the problem.

Screen Shot 2015-11-17 at 9.59.24 PMIt’s Our examples & solutions. Students don’t get a chance to struggle & discover, Therefore the math formula, strategy or algorithm means nothing to them! The memorizers will memorize and do ok, and the non-memorizers lose again. The ideas and strategies have no real value to them. 

I think students should feel the need for the math they learn. They should experience struggle ….just like the hero.Screen Shot 2015-11-17 at 10.20.30 PM

Let’s take the old model of our lessons and change it to match the Hero’s Journey. It’s the struggle that adds value to their learning. Let’s move the reveal of math rules etc farther in the timeline. Let’s let the students productively struggle through problems. The reveal of the “math” will mean so much more after students see and/or feel the need for it. 

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An example in my class this week came when I wanted to teach students how to determine an equation of a quadratic function when given some key points.

I gave them this simple Desmos Activity Builder slide.

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Students already knew about vertex form of a quadratic function so I knew they could put in most of this equation. It’s the “a” value that they really didn’t know how to get efficiently. So I saw a lot of this…

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Students used trial and error to find -1/4 as the right “a” value. But we then asked “How do we know that’s the right one?” We then discussed plugging in a point to check to see if the right side equals the left side. They had a few more slides just like this but with different points. By the end of the last slide you could see that they really wanted a more efficient way of determining the “a” value than guessing and checking. This is where I stepped in and we discussed the idea of using one of the points and the equation to solve for the “a” value. Everyone was on board! They all had struggled before we discovered an efficient strategy. They all wanted it. If I had started class by showing them the first slide and then just telling them how to do it, I would see lack of understanding of why and bored faces.

It’s the struggle that makes the math worth it! Let’s let our students be Heroes. How are you promoting struggle in your classroom? I would love to hear of your ways. Leave a comment below.

Click here to grab the Desmos Activity Builder Activity I showed above.