Grade 10 Math MCAS Review – A Prezi! April 27, 2013

You can get to the Grade 10 Math MCAS review Prezi here or by clicking the above screenshot.

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It’s about that time again. No wait, it is that time again: Grade 10 Math MCAS. Forget about grades 11 and 12 as these grades are meaningless. The new Grade 12 is Grade 10. The new SAT is MCAS.

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I write this with both a migraine and with my tongue in cheek. As a Special Education 10th grade Geometry teacher, I have very mixed feelings about this dreaded test. As a teacher who never had to take MCAS, I think that my students will come out perfectly fine without proving their 10th grade knowledge on some expensive test. I did. All [most] of my friends did. As a person who has taken a boat load of tests and who has become very aware of the unique sense of accomplishment that comes from passing the seemingly-impossible, I want to give my students every tool to show this test who is boss. There is no better feeling than whipping a test’s ass. I want my students to experience this feeling.

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I learned an important lesson from an unlikely source at UMass: Kids in Mr. Chandler’s inorganic Chemistry class who had internet and could access Chandler’s old exams would do better than me. Why? Because his tests were partially-recycled. Above is a screenshot of a Prezi I made from 2012′s Grade 10 Math MCAS multiple choice questions.  Every kid gets 4 colored index cards with either “A”, “B”, “C”, “D” written on it. My “A” is red, but that part doesn’t matter so much. As we click through the slides, kids do their work on scrap paper then hold up the colored card that corresponds to their answer choice. This does two things: makes the kids feel that they’re playing a game and lets me see the class-wide weaknesses to focus on during explicit cramming. In addition to practicing the concepts exemplified in these multiple-choice questions, we’ve been doing the open response questions in class, being sure to review Statistics. MCAS creators love mean, median, mode, range, box-and-whiskers, stem-and-leaf, line plots. “When will I ever use a box-and-whiskers thing in real Life?” Never kids, just possibly on May 13th.

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The best of luck to your students!

Solving Equations Flowchart: free download poster September 30, 2012

On a Friday, my Geometry students couldn’t remember how to solve simple equations.  The next Monday, after giving them a hand-drawn flowchart, they were solving equations with variables on both sides.  Below is an improved flowchart, complete with “combining like terms” for those pesky equations with all the terms on one side.  By clicking the picture, you can download the PDF version that doubles as a handout and as a poster.  It has helped my students tremendously.

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New (free) ZeroSum ruler – for teaching addition with negative numbers

Below is a new version of the ZeroSum ruler.  This one needs no hardware to construct, just scissors and glue.  You can download, print and use this proven tool right now by clicking on the picture, which will bring you to the PDF file that contains 2 ZeroSum rulers. 

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Wanna be a Math Hero? Answer these questions! September 17, 2012

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These Math students need YOUR help.

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If you’ve checked all recent posts on Facebook, refreshed your Twitter page until it can be refreshed no more, all of your Pinterest friends seem to be on vacation and your email is all read, why not answer some Math questions?

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http://www.algebra.com/Answer/

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I’ve been addicted to this site since last night, which in 2012 terms is an eternity.  All I can imagine are kids all over the US toiling away at their Math homework, one hand on head, one wrapped around a pencil, foregoing food, sleep, showering, just to get tomorrow’s math work complete in time for their teachers to put a small check in the corner.   Hey, maybe a few teachers are stickerers, I don’t know.  Personally, I’m a grape-flavored stamper.  So here I come to the rescue!  The THANK YOU! emails are cool to get; I do feel a bit like a hero today.

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Questions range from “Plz help me graph y = 45x + 40” to “What is the square root of 1 – i?“  So try it out!  It’s a great way to put that advanced degree to good use!

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The Distributive Property (“FOIL”) Through Pictures December 15, 2011

The transitive property was always my favorite as it could be applied to so many situations.  I like chocolate, there is chocolate in those cookies, so I like those cookies.  Totally useful.

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But a close runner up to this cookie property has got to be the Distributive Property.  With strange rules of “first, outer, inner, last”, I liked its mystery.  I could multiply two things together with no mention of a multiplication sign and somehow it meant something.  Something big.  I was doing real Algebra now.

It wasn’t until I became a teacher that I really had to think about what was being done.  My students would make mistakes when “F.O.I.L.ing” (I do not like this acronym.  What if one piece is a trinomial?) and I would attempt to explain what was happening.  It’s difficult to explain something that has been taken for granted for 15 years.  But as I made my way through my graduate program where being able to explain math was seen as the most important, I began to rethink this important property.

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The Example:

I always like to start with a concrete example.  Let’s take the problem “14 x 7”

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“14 x 7” is no easy problem for most of us as neither of these numbers is easy to work with.  To begin, let’s look at “14 x 7” as a geometric area in a picture:We can easily count up the small rectangles to find how many there are, though that would take time and leaves a lot of room for error.  Or, we could break the picture down into smaller pictures to make it easier to work with:

Here, we’ve broken “14 x 7” down into (10 + 4) x (5 + 2), or simply (10+4)(5+2).  Is this form familiar?

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Now we can see that “14 x 7” = (10 + 4)(5 + 2).  And now we can simply use multiplication to find the areas of the different colored pieces and add them up:

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10 x 5 = 50

10 x 2 = 20

4 x 5 = 20

4 x 2 = 8

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50 + 20 + 20 + 8 = 98!  And in fact, 14 x 7 = 98.

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The Generalization:

Now let’s make a generalization that we can apply to other similar problems:

Here, we’ve replaced all of the numbers with letters and we can rewrite the problem as:

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(a + b)(c + d)

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Using the method we used before, we multiply each colored piece to find its area and then add up all the areas to find the total:

 

(a)  x (c) = ac

(a)  x (d) = ad

(b)  x (c) = bc

(b)   x (d) = bd

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The area is: ac + ad + bc + bd  !

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Not the prettiest of answers, but done correctly.  Using this model, can you multiply (3x + 4)(5x + 2)?

We’ll use the same picture because “x” can stand for any number at all.

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We have:

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(3x + 4)(5x + 2)

(3x)(5x) = 15x²

(3x)(2) = 6x

(4)(5x) = 20x

(4)(2) = 8

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Putting the pieces together, we have the trinomial:

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15x² + 26x + 8 !

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The Error:

The biggest error I have seen with the Distribute Property is forgetting to multiply a piece or two.  Students sometimes will answer:

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(3x + 4)(5x + 2) = 15x² + 20x + 8

Can you see what they forgot?  Can you imagine what other mistakes could be made?

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If you always remember the area of each piece, you will be The Best Distributor and Master of the Distributive Property!

 

 

 

 

 

The Language of Math Poster August 19, 2011

Below is a poster I hang in my classroom every fall.  Each year it grows longer as more and more terms come up for the different operations of math.  When I was a kid, no one told me to look out for these words, or that math was even a language at all, which made word problems pretty tough.  By clicking on the poster you will be sent to the original Excel file on Google Docs.  Do you have any words to add?

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Link to Google doc:

https://spreadsheets.google.com/spreadsheet/ccc?key=0Asra4GjkRBNidGhoZlZYcjk4dmhISDlSNHJDbjBPTXc&hl=en_US

Geometric Transformations (video) July 18, 2011