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. 

Really Big Lights – A math problem

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/

Fav & Fix – Nov 25

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.

The Fav

WouldYouRatherMath.com has been a huge part of the MEL3E course that I’ve written about here, here, and here. Having my students pair up and work on the chalkboards and vertical whiteboards toward a choice opened up great discussion, and improved our classroom atmosphere! For a while our classroom atmosphere was a little shakey….but the warm ups and paired work has brought us closer together. Download the MS Word docuement that has all the warm ups week by week for this class. The idea and format of the document I took from Mary Bourassa’s Warm up file.

This week we completed this one:

I asked the class to make a gut check on which option pulled them immediately….and most said drive yourself. Ok….let’s verify that gut check. “Is there anything we would need to know more about?” A few students had some ideas and we worked as a class to narrow down some open items.

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From here they were off to the walls to justify their choice. And I love that there were still more questions from every group

  • How many people are going?
  • Does each have to pay $40 each way?
  • Do you have to drive to the shuttle?
  • Do you have to pay for parking in option 2?
  • Are we taking into account getting a speeding ticket? insurance on the car? wear and tear?

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I let the groups come up with answers to their own questions…..I added in, “if you drive yourself, is it likely that you only need to park for one day?”

The conversation that comes out of this warm up was great for us. So many questions and lots of answers. Most groups changed their minds after great debate to take the shuttle (if they were going on a trip for a week)…..less hassle.

The Fix

This is not really a fix yet…but I wanted to grab some thoughts from you. On the weekend Jules and I worked on some puzzles. After we dumped the puzzles out I would ask her how big would the puzzle be? She would look up and with that wonder look and say pretty big or pretty small, but nothing exact….she’s only 6. So I would narrow the question down. How many pieces would be along the bottom? Along the side? And she would make a guess. We would do the puzzle and then find out.

This got me thinking.

Read more here

Favourite & Fix: Nov. 11

For the Favourite & Fix series each week I’m posting one idea from my lessons that was my favourite and one topic that I need help on. A topic 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:

This week I introduced the unit circle to my MHF4U class. I wasn’t happy with the way I introduced the circle in years past so I made a change. I want students to see that our special triangles are just reflected around the circle. Instead of drawing them, or imagining that they are reflected….I wanted them to physically pick them up and flip them and move them. I wanted them to see that the lengths are the same. So I cut out 30-60-90 triangles and 45-45-90 triangle each having a hypotenuse of 10 cm. I created a circle with radius 10. Now each time you place the triangle on the circle we can easily see the principal angle it creates and the coordinates of the point on the circle….It’s the lengths of the triangle….and since the hypotenuse is one the lengths correspond to the Cosine and sine value of that angle. The physicality of this I believe helped allow the students to grasp what the circle shows.

Fix

This week in our MEL3E class used Fry’s Bank from Dan Meyer.

This problem, like many 3-Act Math problems, allowed my class to discuss, question assumptions, and uncover math. The problem helped restore some of our great classroom atmosphere that we’ve been missing lately. I want more! This coming week we’ll keep working through compound interest problems. I’m planning on doing Robert’s Not Cashing the Cheque problem.  After that my resources for compound interest problems are pretty thin. I want to continue posing interesting problems to my students. Can you suggest some? Do you have great compound interest problem that keep students curious and questioning? I’m looking for some!! Share those great problems here or on #fave&Fix on Twitter. I’m looking forward to what you come up with.

[Update]

Thank to all of you who commented through Twitter on great compound interest problems. Here is one from Diana,

Here’s where our class went on Monday:
We started off with Robert Kaplinksy’s How Much Did Patrick Peterson Lose By Not Cashing His Check problem. Go ahead and read his lesson plan.

What made this problem great for our class was the discussion that occurred before any math happened. An amazing argument bubbled up with one side saying “Who cares….what’s the big deal” and the other side saying “That’s just super insensitive…..I could use the interest off that account”. My class from the beginning of the year was back! They had put away the drama that had happened between them and focused on the problem. We guessed at the interest he was losing daily. And then using the info from Robert’s site calculated the interest in the first couple of days. Then broke out the Finance Solver to determine how much was lost for the 27 days.

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The class wanted to know more! They wanted to know what he would lose if he didn’t cash it for the year, 2 years, 5 years!! So we did that too.

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Next, we investigated Robert’s How Much Should Dr. Evil Demand?


Read Robert’s post to see the plan.

Again, with this group, we didn’t use exponential functions…but the Finance Solver to determine what $1000000 would be worth 3o years later with average inflation of 5.33% per year. We also extended to find how long we would have to wait for $1 million to be worth $100 billion.

Thanks for the help!