Turbo Texting

The original idea for this lesson came from Al Overwijk. Thanks again Al!
The possible Ontario overall curriculum expectations covered in the activity:
  • Grade 10 applied:
    • graph a line and write the equation of a line from given information
  • Grade 9 applied & academic:
    • solve problems involving proportional reasoning;
    • apply data-management techniques to investigate relationships between two variables;
    • demonstrate an understanding of constant rate of change and its connection to linear relation
  • Grade 8:
    • solve problems by using proportional reasoning in a variety of meaningful contexts.
  • Grade 7:
    • demonstrate an understanding of proportional relationships using percent, ratio, and rate.
  • Grade 6:
    • demonstrate an understanding of relationships involving percent, ratio, and unit rate.

Act 1: Turbo Texting:

I started with “I was with my brother one afternoon and I needed to text my wife. After texting her, my brother informed me that I was a ‘terrible texter’. He said I was soooooo slow. I on the other hand disagreed. Then we decided to settle this once and for all—- race!!!”

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What do you notice? What do you wonder? Allow students a few minutes on their own to jot down their ideas. Then share with partners, then the class.
Here are a few questions/tasks I asked them next. I wanted to slowly build into deciding if this relationship was proportional.
  • What relationships can you see? — Number of characters in a text vs. the time to text it.
  • Create a scatter plot sketch of how the number of characters in a text affects the time to text that message.
  • How does this graph look with both texters on the same grid?
  • Who is the faster texter? Predict. How does your sketch show who is faster?
  • Kevin finishes first does that mean he is the faster texter?
  • How will we determine who is the faster texter? What will we need to see?
We took our time with these questions so we could develop and understand the relationship between characters in a text and the time to text it.

Act 2

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ME: “Use any method you choose to determine: Who is the faster texter?” I allowed them time here to work on a strategy. I watched carefully what strategies they used or didn’t use.

Seeing the different strategies gave us a nice discussion the importance understanding what rate we are determining and how to interpret it to answer the problem.

I showed this picture next:

and this piece of info…

Students completed this problem and we discussed the assumptions we needed to make.

Texting Time

How do your students compare to Jon and Kevin? Have them time each other while texting the 165 character message. Have them determine their texting speed to see who the fastest texter is in the class.

Linear Modelling

ME: “Now you may have texted that message in 18 seconds, but would you do this all of the time? Would you keep that same rate for a shorter message? Longer message? We better keep this experiment going.
I set them off to text various messages of different lengths using this handout (I modelled the handout format after Mary Bourassa’s Spegettini and Pennies handout – thanks Mary).

Click to download a copy

Students used Desmos and the regression tool to create a linear model. They used that model to predict how long it would take to text 140 characters, 200 characters, and this message: “Dear Mom and Dad I promise to never text and drive.” They finally timed themselves to compare the calculated time and the actual time.
Extension: Compare the relationship between the number of words in a message and the time to text the message. How would the equation change? Is it still proportional?

Fav & Fix – Dec 1

For the Favourite & Fix series I’m posting one idea from my lessons that week that was my favourite and one topic that I need help on. Something I hope to fix. I’m hoping that in the comments or on Twitter (#Fav&Fix) you amazing readers can help me out with some hints, tips, and suggestions.

Favourite: The Cheating Quiz

This week I gave a quiz to my grade 9 applied students. It consisted of 4 questions – Two on linear relations and two on reading distance-time graphs. After the quiz was over I said “It’s time to do a little cheating.” Each student is to find another student they were comfortable sharing their work with. I said, “For question 2 only, share your work with each other. Discuss what you notice about each other’s solution. Do you have the same? If you have different solutions who is more right? After you discussion go back and adjust your solution if you need to. Hand in after.

I really enjoyed listening to them share. It was interesting to see how they defended (or didn’t defend) their answers. After reviewing their new work on that question it not only gave me insight into that one students thinking, it gave me some insight into what their partner was thinking too. For the student below I can see some really good thinking about how the linear relation changes. But now I know for both of these students we need to have a discussion how the increase of 100 every 5 people affects the equation. Looking at each students paper in the room now tells me a lot more about my class’ understanding compared to not having a “cheating quiz”

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Fix (just a comment)

My MEL3E class is coming off a two week themed activity where we designed, built and launched rockets. Today we were completing the Sugar sugar Desmos Activity and a student says to me: “When are we going to do something fun?” I relply, “Fun?”….he says, “yeah, like watch a movie.”

I’m not one to show movies in class. 

Why do students always equate fun in class with movie watching? How does the student who just smiled through two weeks of math class, built and launched rockets, helped me fix the launcher numerous times, and today, yes today, defended his choice on which sugary cereal was the best choice not know he was having fun?

I guess enjoying class does not equal “having fun”.

Math class doesn’t have to be fun…just worth it. 

Flippity Flip, Bottle Flip!

How are all these middle schoolers/grade 9s landing these bottle flips?


Before today I hadn’t seen any of our students doing this bottle flipping thing! But I had a feeling they had all done it before. Today we started an activity with watching trick shots of bottle flips and will end with us creating and solving linear equations.

I showed this video:

My students wanted to argue that some of the tricks were fake…. but they were glued to watching. They all had tried flipping bottles before and some said they were amazing at it.

I had a full water bottle with me and asked if I could flip this. They all shouted that it was too full. I tried flipping and it was a no go. So I cracked it open and drank a few gulps. “Nope….you still won’t be able to flip that Mr. Orr — too much water still.” Again, I tried flipping it and nope. Still not even close. “Mr. Orr you probably won’t be able to flip it even if it had the perfect amount of water.”  So I took a few more swigs. “Still no good sir.” As I was chugging….someone yelled out for me to STOP! I did…..then flipped that bottle…. and…..Boom! The class was blown away!

I had them log into a simple Desmos activity that asked them to choose which bottle would be ideal for flipping.

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Almost everyone had chosen yellow.

The next slide had them moving a line to show the water level and then having them estimate how many ml would be ideal.

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Students were estimating between 100 and 200 ml.

“I think it’s 125 because that would be a quarter of the bottle. I think a quarter is the perfect amount of water.”

“I think it’s not 250ml because it has to be less than half…..but I think it’s not exactly half of that….so half of 250 is 125….but I’ll say 150ml.”

I shared all of their guesses:

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They kept asking if they were going to get to flip any bottles?? I said, “This is math class….do you think we flip bottles in math class?”

Then I broke out the bottles.

Here is the plan. We are going to have a bottle flipping contest. Rules:

  • Draw a line on your bottle where you think the ideal amount of water should be. Determine how much water to put into it in ml.
  • When you know how much water you need record it on our chart….put exactly that much water in there.
  • You must use your bottle for the contest.

Here are some pics of them working on this first part.

img_2250 img_2248 img_2247 img_2243 We had just enough time in this class to determine our volume, fill the bottle to verify it met the line, and practice flipping for about 10 minutes.

Part 2: The Contest

Students complete in five one minute trials. Recording how many “lands” they get each trial. screen-shot-2016-10-07-at-1-37-07-pm

We average those five trials to develop your “Landing” equation! Who was the winner? What does their graph look like?

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We use that equation to solve some problems. How many after ____minutes? How long will it take to make 100 lands? What does the equation look like if you have a head start of 5 lands?

I’ve modelled this lesson structure after this Paper Tossing activity and ultimately after Alex’s Card Tossing activity.

Featured Comment:

Mason:

 Well I am a middle school student and I go to chesnee middle school and I think that I just might show this to MY math teacher even though I don’t like math but you just made me want to like math. I’m in the sixth grade.

MEL3E Day 24 – Shortest Routes with Desmos

Warm Up: Estimation 180

Since last week we did the 1/4 cup of candy corn today we looked at estimating how many would be in the big bag.

We remembered that there was 19 candies in the 1/4 cup. For their too high and too low today I also had them find how many scoops of candy that would be. For example, Joey said too high might be 1000. So I had them determine how many scoops of 19 that would be. I then asked if this now still seems too high?

After all students had voiced their best guess and how many scoops it would be I showed the answer:

I asked them how Mr. Stadel determined the answer of 893 if he didn’t count. I let them study the info shown. Shanice piped up, “there was 47 scoops….so 19 x 47 = 893.”

Today we switched strands from Saving & Borrowing to Travel and Transportation. They all got out an iPad and went to this Desmos Activity.

The first problem has students drawing a route from our school to a Tim Horton’s. I asked them to try to draw the shortest route possible.

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This had them hooked. Each wanted their route to be the shortest. screen-shot-2016-10-11-at-11-28-30-am

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I took time here to show different routes students had drawn.

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As a class we moved to the next screen where we estimated the actual distance.  A student pointed out that the map image had a scale in the bottom right corner. A small section was labeled to be 200m. They used that to help estimate the distance for their routes. But we needed a better way to determine who would have drawn the shortest route! Moving to screen 3 we used the points to determine the “map distance” for each section of our route.

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Students filled in a description of each leg of their route and the distance in map units.

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Click to download a copy.

We measured the scale at the bottom to create a scale factor for this map.

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I demonstrated how to use the scale factor to determine the actual distances in metres and kilometres. We went around the room voicing how far our routes were to see who had the shortest!! Moving to the 4th screen showed what Google would say.
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That was problem 1 out of 5 in this Desmos activity. We started problem 2 but did not finish it. Tomorrow’s work!!

Having the students guess the shortest route first allows them to try something informal before we try to formalize it with actual distances. Desmos’ sketch tool allows them to draw, erase, undo, and re-draw those routes. The ability to wipe away their trials is so valuable. It allows them to take risks. It allows them to get deeper into their understanding.

Give it a try. I feel I’m missing some extension questions, or questions that dig a little deeper. Can you help me out and leave me some feedback in the comments? Thanks.