Day 139: Factor Dice

Today is Friday; one strike.

I also introduced factoring trinomials; two strikes.

It ended up being one of the best days of the year.

I was frantically digging around the MTBoS looking for activities to introduce factoring. I came across a whole lot of crazy techniques; X method, diamond method, bottoms up…. Honestly, none of them made sense.

Then I came across this gem over at Dan Meyer’s Blog.

I pulled out a whole lot of dice from the department closet and after our opener I rolled a couple in front of the class. I told ’em that my dice added to 9, paused for about 15 seconds, them told ’em that the two multiplied to 18.

No sweat.

We did a couple more, then I broke the class into groups of two. Each group had two dice; a red and green and a folder to shield their dice. One person rolled the dice, calculated their sum and product then the other guessed.

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They messed around with those for a while, this got old for some of the groups, so I gave ’em two more dice.

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They added the red dice to create a number and did the same with the green dice. Then one student calculated the sum and product while the other student guessed the value of the dice.

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For some groups, this wasn’t even enough. So… I kept increasing the number of dice.

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Somewhere in between one, two, and three pairs of dice I upped the difficulty even more:

Green = Positive

Red = Negative

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So now the sum is -2, and the product is -80.

This activity lasted about 15 minutes. I had 100% engagement across the board in 4 periods of algebra. No joke.

Students went back to their seats and I put this up on the board.

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Last year I had students expand out binomial products till they picked up on the pattern. This year they looked at why A and C wouldn’t work here. We talked about how FOIL works, which I have actually been referring to as F (O+I) L this year.

Then things clicked.

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Students understood where all that work with the dice came into play.

After a couple more multiple choice sort of problems, they were on their own.

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I am fully aware that the dice activity only serves as a stepping stone in developing factoring skills. However, I threw up a couple of trinomials with a = 2 and students took them down. They understand that factoring these things is a guess and check process, and with more practice things will get easier.

Monday will be the true test to see how well they absorbed everything after a weekend passes.

Day 121: Square Areas Cont.

Geometry continued with Square Areas today. It is always hard to continue a lesson into another day. I had a few absent students return and momentum is hard to rebuild. Most of the class seemed to have derived the Pythagorean Theorem, one student shared her work with the class.

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After, we looked at four proofs of the Pythagorean Theorem and a lot of students were lost. I messed up here in moving on instead of spending time letting students struggle. A lot of the class was off task, which seems to happen when they get backed into an uncomfortable place and I only reinforced that behavior by moving forward.

Next year I think I will trim down the assignment and get rid of some of the unnecessary fluff. It felt like the worksheet guided them a little too well and ended up going in a little different direction that I wanted to.

Day 120: Square Areas

In Geometry we skipped The Pythagorean Theorem and Special Right Triangles sections a couple months back so so 30-60-90 triangles would make more sense to students after equipped with trig. Today we came back around to those.

My students could regurgitate the Pythagorean Theorem for days. However, I don’t think any of them could explain where it comes from or write out a proof for it.

Today’s goal was to change that.

A few years back in college, we went through an activity using dot paper to find the area of certain squares. After much digging, I found a very similar activity.

I asked students to work through the square areas S-1 independently for 10 minutes or so. Then Instant Classroom broke ’em into groups where they discussed their progress.

Students who used the Pythagorean Theorem right off the bat were challenged to find another approach.

They struggled.

And struggled.

For a good 20 minutes.

Then the bell rang.

Darn. It was kind of an awkward place to end. On their way out I asked them to think about how they could find the area of a 3/y square and come back tomorrow with some progress.

The most interesting piece I observed today were students hesitant in trusting the math to work out. A majority of students had a correct expression set up which only needed to be simplified and were second guessing themselves. My money phrase today was “Trust the math”.

More on this tomorrow!

Day 92: Parallelograms

Algebra started parallel/perpendicular lines today while geometry dove into exploring parallelograms.

The Geometry Teacher has some great explorations for several concepts in geometry. I pull his exploration on parallelograms and used it in class today.

It was fun to see students struggle in creating a parallelogram without any knowledge of their properties. There were a lot of methods used; I had to restrict students from creating rectangles/squares because they ALL jumped to that solution first.

After they created a parallelogram, they measured the sides/angles and taped them up to a whiteboard (I messed up in not asking them to spread them out further).

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Students then gallery walked and filled out the table attached to the worksheet.

We talked about the properties and came up with a list hitting four big properties.

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Tomorrow we will prove a couple of these and practice using them.

Day 60: Slope

For the past two days algebra has been diving into the idea of slope. Fawn Nguyen has an awesome activity and post on using stairs to get students thinking about slope as steepness. This can be found right here.

All my classes pretty much reached the same point as her’s on the first day. I am not going to re-create an identical post to hers so go check her’s out… Seriously!

On the second day however I moved the class in a little different direction…

I lost quite a bit of student engagement when I pushed students to think about what we could do with the different bases/heights we measured. We went through all the operations and I asked students “What operation would be the best for COMPARING the base and the height?”

We settled on division. Some classes looked at the base/height some looked at the height/base. We talked about what a large base and small height would look like as a stair case and vise-versa. After that each group measured a the base and height of a particular case and we threw all those measurements into a spread sheet and ranked them.

There was some great conversation on what ranking the numbers from smallest to largest related to in terms of least/most steep.

I held on ever further in introducing the word slope.

After I had students measure the base and height of an individual step, we talked this and how measuring something in millimeters is a whole lot more precise than using inches. We also talked about how the measurements of each step are proportional to the measurements of the overall height and base.

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Then we dove into this:

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This activity came from James Cleveland over at The Roots of the Equation. I love this because it drives home the idea of slope as a ratio. I threw student’s rankings up on the board and then we quickly calculated the height/base of each.

Only at this point did I introduce the word slope, we talked a little more about what it measured and found the slope between a few points.

A great couple days of classroom action, students really seemed to enjoy the openness of these activities… even though they were complaining a little.

Day 54: Triangle Congruency

Here is what my classroom looked like after Geometry yesterday;

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We launched on a exploration about triangle congruency. I told students I would give them three different measurements and they had to create the rest of the triangle, labeling everything. What I provided looked like this:

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Before hand we talking about how side b needs to be opposite of angle B. Each construction was color coded.

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Today, we finished up the last two (SAA and HL) and then students had a gallery walk where they observed and discussed which groups of triangles appeared to be congruent.

We came together as a class and talked about it a little more then looked over a few examples of how SSA falls short and other combinations as well.

All in all I believe this was time well spent. We haven’t proved HL or AAS but this was a good way for students to enter into the concept of triangle congruency.