WEBVTT

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[Music] Welcome to Teaching Symbols

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and expressions.

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I am Terri Porto.

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I teach seventh grade Honors Algebra

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and eighth grade Algebra

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at Twin Groves Middle School

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in Buffalo Grove, Illinois.

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In the sequence of instruction,

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we start really back

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in the basic math classes where,

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in addition of integers,

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we will have multiple numbers being

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added together,

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and we stress to add the positives

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together and add the negatives together.

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And we say let's add the like numbers,

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so that the vocabulary is

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established early.

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In pre-algebra,

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we advance to combining single variable

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problems like 2x+x, 3y-2y,

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so that in algebra,

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we can advance to problems

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that have multiple variables and powers.

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There's many necessary math concepts

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that are involved in teaching symbols

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and expressions.

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Some of them are adding

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and subtracting integers,

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the distributive property,

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and actually understanding what a

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variable is and how there are many

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different variables.

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The objective for my lesson was

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that students would be able

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to simplify expressions

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by combining like terms.

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I start my class off by doing a review

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of the distributive property,

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making sure that they remember how

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to distribute not only a positive number

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but also a negative number

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and including the subtraction.

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After that, we go into a discussion

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about what is an expression

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and when would we write them.

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A very important part is

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that they understand the different parts

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to an expression like the coefficient,

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terms, like terms, and constants.

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The way that I approached the lesson was

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to model for them how they would go

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about combining the like terms.

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I would put the problem on the board,

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and I personally would circle like terms

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so that they could see

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which terms should be combined together.

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We talked about how you should add only

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the coefficients together,

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and we also demonstrated

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to them how the final answer should be

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in the alphabetical order.

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I start with problems that only have one

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like variable to kind of warm them up

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and make them feel comfortable.

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Then, I will throw in a second variable.

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Then, I will put in a problem

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with different variables and constants,

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making sure that I include the

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coefficient of 1 and -1

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in both the problems and in answers.

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Then, we put in the distributive

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property, only one distributive,

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and simplify.

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Then, I throw at them two distributive

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properties in simplifying.

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And then, if things are going well,

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we'll throw in the problems

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that have the same base

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but different exponents.

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And to conclude,

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we will do an application problem

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with perimeter so that they can see

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that this was all done with a purpose.

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The questions that I asked off the

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students as we were going

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through them was I would ask them,

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"Which of these terms are alike?"

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After they found some, then I would say,

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"Are there any other terms

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that are alike?"

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so that they could show me

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that they're understanding what

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like terms were.

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There are times

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when I will put an answer

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in an incorrect order,

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and then I will ask the students

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if this is a correct answer to see

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if they have picked up on the rules

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for the correct way

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to write their answer.

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The type of practice that I provide

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for the students during the lesson is I

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will put a problem on the board,

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and I will have them show me

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on their whiteboards what they are

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doing, and then they hold their

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whiteboards up so

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that I can get a quick feeling

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as to how things are going.

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Also, I will have students go

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to the board and explain

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to the class what steps they went

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through to get the answer.

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And then, I also have students work

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on a worksheet in pairs

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so that it gives me an opportunity

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to listen to how the students are

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communicating between themselves

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and also answering any questions

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that they may have.

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And then, at the end of the lesson,

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I provide them with additional practice

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in a worksheet that they can take home.

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In the lesson,

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most of the students were able

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to do the beginning problems,

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and they were moving along quite easily

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and pretty happy with themselves.

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But I noticed as it got a little more

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complicated, they were slowing down

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and having to discuss.

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But once they saw that they were able

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to get the correct answer,

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you could see that they were very

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pleased with themselves again.

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When they got to the problems

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where they had the same base

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but with the different exponents,

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that's where I could sense

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that there were some frustration coming

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from the students

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because they didn't have necessarily a

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clear understanding about the difference

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between those variables.

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So, I would go back in the future

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and make sure that they're understanding

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that x is x, x

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to the second power is x-squared

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and that means something totally

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different, so that they can have a

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better understanding

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that you can't have the x's

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and the x-squared's together.

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Some of the skills

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that students are weak

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in that can cause errors

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or misunderstanding are their basic

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adding and subtracting integer rules

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and also the distributive property.

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Obviously, if they can't add

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and subtract accurately,

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then they are not going to be able

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to combine their like terms.

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What I found helps them to understand is

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by modeling with different color ink

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or by using shapes

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to circle the like terms.

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They, many times, don't understand

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that the x and the y can't be

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put together.

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So, what I will do is I will take let's

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say a red pen and I will circle all my x

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terms, a blue pen

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to circle all my y terms to show the

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like terms, and then I can,

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in my answer, show how they end

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up coming together.

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For the visual learners,

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I will bring in pretzels and I show them

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on an overhead that a problem like two

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of the rod pretzels plus three

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of the twist pretzels,

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we have to keep them as different types.

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It shows them that we are only putting

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like things together.

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So, when we are looking

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at our variables,

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we only combine the terms

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that have the x's, the y's and so on.

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For the next lesson,

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what I would do is I am going to plan

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on working on more problems

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with the exponents,

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and then to challenge them,

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I am going to add in terms

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that have several variables in them like

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"2ab plus 3ac,"

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and see if they can figure

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out what they would do with problems

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that have different types of variables

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than what they are used to seeing.

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To learn more about teaching symbols

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and expressions,

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please explore the additional resources

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on the Doing What Works website.

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[Music]