Sneaking in Factoring

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!

Speedy Squares

Last week I attended the annual OAME (Ontario Association of Mathematics Educators) in Toronto. It was so great to finally meet some of the people I’ve been tweeting with.

I was pumped to attend Mary Bourassa’s double session on great classroom activities. One of the activities that I’ve seen on her blog, but not used in my own classroom was Speedy Squares. So when I had an opportunity to try it, I jumped on it!

There is something special about doing the lessons yourself while learning about a lesson at a conference.

Read about the lesson:

You can read about the lesson on her blog here part 1 and here part 2.

The big question: We want to determine how long it will take to build a 26 x 26 square out of link cubes.

More Curious

While actively building the squares I had a great idea to make the introduction to the activity a little more curious! So when I got back to my classroom I broke out the cubes and created this….

Maybe before the time trials of building the squares, we can dive into generating questions and wonderings first.

  • What is he making?
  • How many squares will he use?
  • How long will it take?

Now that we have generated questions….we can then move onto Mary’s awesome two day lesson.

Once students have got an answer to how long they would take to build the 26 x 26 square, you could show the video of me building it!

I’m really interested to see if elementary teachers can use this in their classes and what they come up with!

Function Matching – Down the Desmos Rabbit Hole!

Before our break I created a set of challenges for students to investigate translations of different functions. I had a few goals in mind:

  • Introduce a few basic functions that we will work with in this unit (square root, rational, cubic, quadratic).
  • See how certain points on the function are translated.
  • How does affecting the values in the equation affect the graph of a variety of functions?
  • Use function notation to represent translations.

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