WEBVTT

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[Music] Welcome

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to Problem Solving in Algebra.

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Hello, my name is John Lawless.

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I'm the Math Content Lead here

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at Castle View High School

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in Castle Rock, Colorado,

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and we are part

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of the Douglas County School District.

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I think a lot of the difficulties

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that I see students having

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in solving problems

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with Algebra are looking

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at the initial problem and being able

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to put it into a math sentence

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or be able to put into math variables.

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Many times the problem is difficult

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because they don't have a picture.

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They can't visualize what's going on,

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so I'll have them either draw a diagram

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or put it on a graph.

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The class we are going to see today is

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on linear equations--

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the graphing and all.

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We have already spent time reviewing

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linear equations.

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We've defined a polynomial

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in general terms.

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The kids have an idea

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of what a polynomial is,

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and we've touched on monomial, binomial,

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and trinomial and those terms.

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That's not really the goal right now.

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We are really focusing just right now

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on the linear equations.

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And so we are going

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to start simple today and we are going

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to do a birdhouse, and this is leading

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into the letter or the word WAX

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with linear equations,

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and then we are going to do WAX again,

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but we are going to use polynomials

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where they have

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to make a W using a fourth degree

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polynomial, and the letter A is a

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quadratic that has been reflected

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or flipped so the negative A value,

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and then the X is two cubics.

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So that's our goal

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that we are leading up to.

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Can they represent things

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on a graphing calculator?

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Today is a very introduction to that,

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and they are starting to see how

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to limit their domain on the calculator,

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how to make a segment on the calculators

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to input endpoints on your polynomial,

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and there is specific technology

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or specific algorithms you have to do

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on your graphing calculators to do that.

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So they'll also learn the beginnings

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of that today too.

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Students are given a birdhouse,

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it's made by linear equations

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and they are going to have to put

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that on their graphing calculator

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and where do they start.

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And we lead up to

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that by previously addressing equations

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of lines, reviewing that,

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reviewing the two forms,

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and this is leading

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into the transformations of equations.

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How do you get kids

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to practice transforming equations

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in different forms

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so that they are useful?

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We are going to look

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at slope intercept form,

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and they see that's nice and useful

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for the Y intercept,

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but if you don't have real nice Y

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intercept sometimes it's more useful

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to be in factored form,

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or what we will call X intercept form.

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And if they can see the difference

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between the two forms,

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sometimes one form is more helpful

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than the others.

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And in doing this birdhouse problem

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today some kids just

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like slope intercept,

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and some kids will just do the

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factored form.

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And my goal is

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that they can connect the two and see

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that if you are given this problem--

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you got to make a birdhouse

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on the calculator-- how do you do that?

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Let them explore

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with their partners first,

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and let them try stuff,

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and then as a class we will come back

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together and share ideas.

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The way that we try

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to approach students developing

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proficiency in areas of, say,

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translation, where they are going

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to take a problem from the verbal

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and put it into the equation,

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make meaning of it.

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One of the best ways that I found,

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one of my philosophies that I truly try

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and take and encourage others to take,

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is students don't just learn math

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by doing, they learn

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by discussing what they have done.

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And when students are talking

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about the mathematics they may get an

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idea from a partner on how

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to translate it from the verbal

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into the equation part.

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And so if they can see it presented

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by another student,

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if they can really get a picture,

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they can get an understanding--

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a visual representation

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of what's going on,

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it helps them make meaning

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for the translation part.

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The modeling of problem solving

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that I do after the students have

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struggled with it a little bit

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or after they have tried it,

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I will put up on the board, and say,

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"Here is one method that works,

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and here is a technique.

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Now we will show you a skill.

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Some of you were asking,

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'How do we do this?'

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or 'How can I do this step

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in this problem solving?'"

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So what I will do in front

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of the class is

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on the board I will show them and model

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for them, "Here are the steps

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that I would take,

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and here is the most efficient

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that we have seen

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in mathematics that works.

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If you do these steps..."

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And I will do a model to write in

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and go step by step by step.

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If they have already explored it a

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little bit, I will try

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and honor the techniques they have used

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and then show them another technique

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by actually modeling it.

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When I am modeling, think-alouds come

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up quite a bit.

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As I am writing on the board,

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I am saying, "Boy, what can I do here?

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Here is what I am thinking

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in my head."--

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kind of the metacognition piece

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that I use as a teacher going,

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"Here is what I am thinking here.

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I am not sure..."

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For example, say the degree is two,

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"I know I need two solutions

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or two zeroes,

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but I am not seeing them on my graph.

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Why is that happening?"

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And then I can go back and walk them

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through how I would check

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and see why my graph is not agreeing

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with what I know should happen

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from the equation, per se.

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I think that metacognition piece is

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really big for them

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to see what I am thinking,

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and when I make a mistake usually it

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turns into a really good thing

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because I can say, "Boy,

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that shouldn't happen.

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Why is that happening?"

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If I say it, I have to remember to say

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that out loud so the students can hear

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that and go, "Wow,

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he has those same struggles,"

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or "I had that same issue,

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and now I see what the process is he

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would use to solve that problem."

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When students can take a big problem

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that is not like stuff they specifically

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have seen, but it addresses similar

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skills that we have covered

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through the whole book

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or whatever we are at in the year,

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"Can you take all the skills we have

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done, and can you solve this problem?"

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When they can do that individually,

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in pairs, or in a team, then I can start

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to see, "Wow."

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And when I can give them any problem,

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and they can do problem solving,

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that's the ultimate goal.

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And that's a hard step to get to,

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but that's when I know

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that they really have it.

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To learn more about Problem Solving

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in Algebra, please explore the

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additional resources

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on the Doing What Works website.

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[Music]