Puzzles

Fav & Fix – Nov 25

by Jon Orr

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

Puzzling Dimensions

by Jon Orr

I wanted to grab some thoughts from you on a possible lesson idea.

On the weekend Jules and I worked on some puzzles. After we dumped the puzzles out I would ask her how big will the puzzle be? She would look up, and with that wondering look say …”pretty big” or “not too big,” but nothing exact….she’s only 6. I narrowed 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.

I was thinking about factors of numbers and how that relates to the dimensions. I also thought about optimal dimensions of rectangles given a set area.

If a puzzle had 60 pieces what could the dimensions be? 100 pieces? 1000 pieces? 

Take Elsa for example. With 48 pieces do you know what the dimensions will be? Think of some possible combinations. Got them? 


And….. bam! Did you think of 8 pieces by 6 pieces? 


The puzzle we worked on had 100 pieces and it was a 10 piece by 10 piece puzzle.
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I feel like there is a lesson here but I’m not 100% sure where it fits. It may fit in many places.

If Act 1 is a short clip of us putting a puzzle together like below, then how does the rest of the lesson go? How do you see the rest of the lesson play out if you teach Kindergarten? Primary grades? Middle school? High school?

I would love to hear your ideas on the lesson goals as well as the lesson format! Together we can do it!

Sneaking in Factoring

by Jon Orr

I started a series of new warm ups for my MPM2D class today. My goal is to sneak in factoring as warmups throughout the semester. By the time we need to learn it (like when we need to factor to solve equations) we will have mastered it already. I also previously snuck in multiplying binomials when we tackled quadratic patterns as Mary Bourassa did in her 2D class.

So today I gave them this slide and said I want you to solve a puzzle!

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They broke out their iPads and used the Algebra Tile app to put together the rectangle. The kids worked away and you could see them trying to put tiles in a way to make the rectangle

….and they soon found out that they had to fit a certain way!! 
On take up we made sure everyone had either my rectangle or a rotated version.

Then we did this one…..

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After we were done I asked the class: “If the combination of squares and rectangles makes up the area, what are the dimensions of the rectangle?” They had a little bit of a hard time here, but finally could see the x + 4 and the x + 2 as the length and the width. I then wrote …

 And then I heard some “aaah”s. We had previously seen both versions of the quadratic expressions and discussed why the factored form helped us out quite a bit if we wanted to find the x-intercepts.

We stopped there….It only took us 15 minutes. Tomorrow we will do a few more…..always writing the factored form after. I will also try to get students to notice efficient strategies to make the rectangles.

  • Why did you put 4 x terms along the width and 2 x terms along the length?
  • How does that relate to the number of singles?

Where I hope to go with these warm ups is to factor all types of trinomials:

  • Perfect Squares

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    This time…..make a square

… and get this…

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  • Trinomials of the Type ax^2 +bx + c


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  • Completing the square too!!!!
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This time…make a square




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We’ll be definitely working our way out of the app and onto paper with area diagrams…

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Factoring

 

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Completing the square

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Completing the square

I think working with these puzzles for the next few weeks first will give us a strong base when it’s time to factor to help solve equations and then complete the square. I think I’ll track all the warm ups we do like this and I’ll post them all!