MPM1D

3 New Desmos Activities: Talkers & Drawers

by Jon Orr

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

Polygon Pile Up

by Jon Orr

When it comes to angles involving parallel lines, triangles, and other polygons I’ve always assumed my grade 9 applied students “get this”. I’ve felt that angles were an easy topic. I guess I thought this because most students seem pretty happy when solving angle problems and for the most part being doing pretty well on assessments. However, this year I noticed two inadequacies that I am trying to address.

  1. Most of my students didn’t actually know what an angle measurement of 65 degrees really means.
  2. They have a hard time determining what information is needed when solving multi-step angle problems. Lack of a good strategy.

Addressing #1

When having students determine angles in triangles almost all of them knew that all three angles should add to 180 degrees. The trouble came when I saw some answers like this (from more than one student). 

What bothered me was the location of the 40. I wondered why outside the triangle? I pressed this student for more info. I asked him to draw me any right triangle and label the three angles.

 

Hmmm…I asked him to point to one of the angles. He pointed to where he labeled the 85. What I found is that this student was mixing up length measurements with rotational measurements and he was not alone.

I found a great activity to hit this head on. Laser Challenge from Desmos worked wonders to get my students to understand and experience rotational measurements. Students have to enter values to rotate the laser and mirror to hit targets.

My students “felt” what 60 degrees is. Experiencing that rotation made all the difference to clear up what we were actually measuring. When second semester rolled around and my new crop of kids came in we started with this activity right away.

Addressing #2

Most of our students struggle with solving complex problems where they have to think of a strategy. Before I gave them something like this,

I wanted to them to experience what information would be useful to know first. I decided to turn the problem around and inside out.

I gave them this.

I wanted them to think backwards….just like we need to do sometimes when solving longer problems. On the “easy” side most filled in 3 angles in the quadrilateral. What was great was that prepared them to think what we could leave out for the harder one. This simpler diagram challenged my class to think, plan, and strategize!

It was great to do this before we introduced this puzzle Jim Roesch, Kristyn Wilson, and myself created:

[There is a video embedded here — Can’t see it? Click through to the post page]

Here is the puzzle

Click to download a PDF copy to print.

And to really challenge yourself or your students here is a blank one. Can you fill it in so it’s “hard” to determine that indicated angle? What is the least amount of info you can give to bring out the most amount of thinking? Share them out! 

 

Really Big Lights – A math problem

by Jon Orr

Here’s a really big problem you can work on with your students this holiday season.

Act 1:
Show them this video and ask: What do you notice? What do you wonder?

After allowing them to voice their noticing and wonderings guide them to wonder: How big is that new light? How many times bigger is the big light compared to the old light? How many Really Big Lights would you have to put up to cover the same length as last year?

Act 2: Here are some images to help make some conclusions:

Guess: How long is the big light? How many times longer is the big light than the small light?

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Reveal:

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Guess: How many small lights are in one string that stretches 15 feet?

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Reveal:

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Work together to determine how many Really Big Lights would replace the string of 50 lights? What assumptions will you make?

Act 3: Reveal

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Why might your calculated answer be different from the answer shown?

If you had 50 Really Big lights how long would could they reach? How many cars could you put in that garage?

Grab all files for this activity

You can see more info about the lights over at http://reallybiglights.com/

Pentomino Puzzles

by Jon Orr

A few years ago I was introduced to a series of activities (through my then districts math consultant) that builds a driving need for students to createscreen-shot-2016-09-30-at-8-14-39-am, simplify, and solve linear equations. I used the activity for a few years in a row while I taught grade 9 academic. Since then I had forgotten all about it (funny how that goes) UNTIL NOW!

The activity ran as a series of challenge puzzles around Pentominoes and a giant hundred grid chart.

Activity 1: Explore

Ask students in groups to choose this tile and place it on the hundreds chart so that it covers a sum of 135. The task seems so simple to start but unpacks some great math.

Allow them to determine this sum anyway they like.

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I circulate and listen to their strategies. I give them very little feedback at this point. After a few minutes I choose some of those groups I heard interesting strategies to share..then let any other group share out their strategy.

img_2198Activity 2: Keep Exploring

I have them use the same tile and try again. Place the tile so that it covers a sum of 420. Listen to those strategies! Most groups that didn’t have a strategy before will try to adopt a strategy they heard last round. At this point most students will catch the strategy “If I divide the sum by 5, being like the average then I should have the middle number in the shape.”

This is where I stop and have a formal discussion as to why dividing by 5 here works? Will this always work? Will this always work with other shapes? What other shapes will this work with then?

We formalize the strategy.

Our big problem to start is not knowing where to place the tile. Let’s say I label the middle square n. What will the square immediately to the right of n always be? The left? The top? The bottom? Have them check this out by placing the tile repeatedly back on the grid.

Now let’s add all of those expressions up

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The middle square must be a multiple of 5!!! I have them try this strategy out by throwing out another sum and have them place the tile.

Look at another tile!

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We go back and outline that we could have chosen a different square to label n. Which results in a new equation and solves for different value…..but results in the same placement of the tile!!

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We continue by me having them select different tiles, giving them sums, having them create equations and solving them. I love how hands-on this lesson is. Holding the tiles adds some “realness” which I feel drives the need to solve these equations.

However,

this year when I remembered this activity I wasn’t sure I still had the tiles kicking around (I found them later). I immediately made a digital version with Explain Everything.

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The digital version gives each student their own copy and while working in groups can chat about what strategy worked and what didn’t. Before on the paper version….only one student could hold the tile. Also, when students have to voice their strategy through Explain Everything they have to have careful thought. They think about the words they want to use. We this careful thought they get to make their thinking visible for me!

One new addition to the activity I get to make here is that they can create their own pentomino…..and then their own puzzle to share with their classmates.

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Since then I also created the activity with some help from the team over at Desmos

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Click to access and rune the teacher.desmos.com activity

I love their new conversation tools….I get to pause the class and discuss when needed!

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Students can even sketch their new tile and create an expression to match! screen-shot-2016-09-30-at-9-24-03-am

 

Desmos even added some nice extension questions. Love it! screen-shot-2016-09-30-at-9-24-23-am

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In the future the next time I explore this lesson I see a blend of hands on tiles with digital support. I think having the best of both worlds here can pack a powerful 1-2-3-4-5 punch!

Pick your favourite!

Download the Explain Everything Pentomino Puzzles .xpl file. 

Access the Desmos Activity