Day 141: Grudge

Algebra reviewed factoring trinomials today. A colleague shared with me a review game he used late last week, which he found over at Nathan Kraft’s Blog.

This is hands down one of my favorite.

Nathan has a great write up with detailed directions, so I am just going to highlight a few fun things I observed (I did add a few rounds where students could add an X instead of remove one).

  • Politics; Students would make treaties with others or try to bribe them (with their own homework passes or negotiate a two-turn treaty)
  • In one period, a group of students would answer each question correctly and then form a huddle to decide on which student to turn into a zombie each round… This eventually led to members of the group betraying one-another.
  • One particular student convinced 8 others to give him lives during a health round… This set the cross-hairs on him and he was quickly eliminated the following round.
  •  “Next time we play this I’m not gonna trust you”… “Can we play this again next week?” THEY WANTED MORE.
  • Lots and lots of great math happened throughout the period.
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Day 140: Transformation Project

Last week I gave geometry a project where they had to apply multiple transformations to an image. *Credit goes out to Perfect Squares.*

Here is what I put up on the board:

-Start by drawing an image
-You must: 1. Reflect
2. Translate
3. Rotate
Your image, order doesn’t matter, it has to fit on the graph paper provided though.
-Document and label vertices/transformations.

(I probably also told ’em somewhere along the way that they needed to have some color in there…)

Students worked hard and the results were awesome.

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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 132: The Locker Problem

Spring break is next week for us. Algebra finished up multiplying polynomials and after the break we will start factoring. Today, students worked through one of my favorite problems The Locker Problem, which is out of Fostering Algebraic Thinking by Mark Driscoll.

The Locker Problem

There are 20 lockers in one hallway of the King School. At the start of the school year, the janitor closed all the lockers and put a fresh coat of paint on the doors, which are numbered from 1 to 20.

When the 20 students from Mrs. Mahoney’s class returned from summer vacation, they decided to burn off some energy. They came up with a plan: The first student ran down the row of lockers and opened every door. The second student started with locker #2 and closed every second door. The third student started with locker #3 and changed the state of every third locker door. The fourth student started with locker #4 and changed the state of every fourth locker, and so on, until all 20 students had passed by the lockers.

Which lockers are open after the twentieth student is finished? Which locker or lockers changed the most?

I like this problem so much because it has a very low point of entry and investment for students. I had each group work on the problem by themselves for about 10 minutes then they broke into groups.

The problem also has various exit points depending on the direction each group decided to take. I had some students looking at differences of squares while others were using pictures, and another group was looking at factors. Either way, all students were able to engaged in the problem.

Day 117: Estimates

Algebra is working on classifying polynomials. Today students dove into a note taking guide. This is the only one I will give all year. I am not quite sure how to approach this topic other than direct instruction. So… instead of lecturing at them I wanted to try having them read the book. It went okay.

I am excited about a sort of gallery walk activity that should go down tomorrow with classifying.

Today I opened all my algebra classes with this

Estimate

I love all the estimates over at Estimation180, however, these are at the top of my list.

Anytime I have high and low students engaged in a mathematical discussion is a win. I all students were into it for about 15 minutes at the start of the period today.

If you haven’t tried this set of estimates with your class…. You should.

Day 66: Racecar Math

I didn’t have good feelings about only spending two days on the slope equation in algebra. I had originally planned to print off a few Pizzazz worksheets and spend another day practicing. I didn’t feel good about that either.

Instead I looked over at my bookshelf and saw the remote control monster truck I bought last year. It ended up being a good move…

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Old picture… my desk is not this organized.

Both Dan and Andrew have posted about this sort of review. I tweaked it a bit and used it as a way of getting students to practice a concept more without the monotony of back to back days of book work and worksheets.

I picked this up from Target for $14.99 last year.

IMG_0444After our opener I threw this up on the board

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I explained there were two types of problems; individual and group, each slide would indicate the type of problem. For group problems they would work on the large whiteboards on their desks.

I gave students about a minute for each problem, once they had an answer they stood up. Only one person from each group could be standing at a time.

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I paced around, looking at students work. After the timer I read out all the answers I saw and called up the standing students with the correct answers to drive the car. Those who were incorrect worked with their groups to correct the mistake.

Students drove the car in a 25 foot L shape the ended with this:

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Each box was worth points equal to its number. If they back the car into the box it was worth double points.

All my students were on board today. The only downside to this is we spent about equal time driving the car as we did doing math. I will fine tune the process in the future.

Best part of the day… Geometry came in begging to drive the car today. They had been hearing about it all day I guess.

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.