# Series: Engaging Students with "Productive Struggle"

Math.A.CED.2

Common core State Standards

• Math:  Math
• A:  Algebra
• CED:  Creating Equations
• 2:
Create equations in two or more variables to represent relationships
between quantities; graph equations on coordinate axes with labels
and scales.

Download Common Core State Standards (PDF 1.2 MB)

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Math.A.REI.1

Common core State Standards

• Math:  Math
• A:  Algebra
• REI:  Reasoning with Equations and Inequalities
• 1:
Explain each step in solving a simple equation as following from the
equality of numbers asserted at the previous step, starting from the
assumption that the original equation has a solution. Construct a
viable argument to justify a solution method.

Download Common Core State Standards (PDF 1.2 MB)

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Math.Practice.MP2

Common core State Standards

• Math:  Math
• Practice:  Mathematical Practice Standards
• MP2:  Reason abstractly and quantitatively.

Mathematically proficient students make sense of quantities and their relationships in problem situations. They bring two complementary abilities to bear on problems involving quantitative relationships: the ability to decontextualize--to abstract a given situation and represent it symbolically and manipulate the representing symbols as if they have a life of their own, without necessarily attending to their referents—and the ability to contextualize, to pause as needed during the manipulation process in order to probe into the referents for the symbols involved. Quantitative reasoning entails habits of creating a coherent representation of the problem at hand; considering the units involved; attending to the meaning of quantities, not just how to compute them; and knowing and flexibly using different properties of operations and objects.

Download Common Core State Standards (PDF 1.2 MB)

Reviewing Linear Equations in Two Variables
Lesson Objective: Review understanding of linear equations
Grades 8-12 / Math / Assessment
Math.A.CED.2 | Math.A.REI.1 | Math.Practice.MP2

#### Thought starters

1. How does Ms. Morehead use the pre-assessment to inform her pairing of students for collaborative work?
2. What do the math teachers learn from sharing their students' misconceptions?
3. What kinds of feedback questions do the teachers use to respond to the students?
I like how all teachers collaborate. I like the student's behavior, they all want to learn. Desks are perfect for group work and independent discovery time.
Recommended (1)
this is great! I like the ability to gauge student work in a non formal assessment in a timely manner.
Recommended (0)
I like how the students have to explain what the slope means with words, and not just numbers.
Recommended (0)
I am also impressed with student behavior and participation in the classroom. I appreciate that teachers are teaching the same topics in the same manner and collaborating on student performance and how to clear up misconceptions. How are these students grouped together?
Recommended (0)

#### Transcripts

• Reviewing Linear Equations in Two Variables Transcript

Susie: Okay, here we go, first question. This should be quick. On your whiteboard,

Reviewing Linear Equations in Two Variables Transcript

Susie: Okay, here we go, first question. This should be quick. On your whiteboard, please answer: Name a line that has a negative slope. Hold your board up when you're ready.

My name is Susie Moorehead. I teach at Turkey Foot Middle School in Edgewood, Kentucky, and I teach eighth grade pre-algebra and algebra.

Second equation: Name a line that has a slope of zero. Show me your board.

Today's lesson was a wrap-up of linear equations. Some of the systems of equations, but kind of more the meaning behind it, what do these things mean?

Wow! We've got an alphabet soup here, we've got them all. Put your boards down. Somebody who said D. This one. Can a negative slope also be zero?

Speaker 2: No.

Susie: Is a zero negative?

Class: No.

Susie: Is zero positive?

Class: No.

Susie: So then we'd have a tough time if we said the negative slope was D. I don't think we can call D slope of zero.

Speaker 3: I just want to explain myself. Why I said D is because I didn't know we were using the graph, so I was kind of confused until I was like, "Oh, there's a graph." So that's why I said D.

Susie: So, the light bulb just clicked on?

Speaker 3: Yeah.

Susie: Okay.

I have just pulled some application problems that I wanted to see if they really knew their stuff. Not the manipulation of the math, but what things really mean.

All right, clear your boards, let's go to a story. The following ordered pairs represent the number of hours worked, and the pay received. So calculate the slope of the line that connects these points, and then I need you to write down what the slope represents for the story. I need your explanation. What does the slope represent in this case? What does that number mean?

My students have practiced the different formats that a linear equation might appear, and what the different parts represent. What the inner section point might mean, why we even find it. Different ways of solving it.

Okay guys, I've got some boards here that I want you to take a look at. Some of these have different numbers on them. This one says 22.95 divided by 3; that says 22.95 divided by 3; and then it says this 7.65 business. And then, may I borrow yours? Because I just saw some new numbers here. 15.3 divided by 2. How does that happen that we have different numbers? Macy, what do you think?

Macy: They may have just chose two different points to find the slope between.

Susie: Does it matter which ones I pick?

Class: No.

Susie: A.J., why doesn't it matter?

A.J.: Because they're linear. They're all going in a straight line.

Susie: The slope is the same no matter which two points you pick.

We're trying to approach math in a way that is different than how many of us learned it, that is much more logical. We're trying to think about the learning that is going on with the students, and how can we enhance their understanding of the mathematics so that they can move between content within mathematics at the same grade level, but then also through grade levels, so that we're always trying to connect what they already know and build that towards where they need to head.

We're going to be working on an activity over the next two days and I'm going to give you a little pre-assessment about that activity. I want to see how much you learn over the course of the activity. This is kind of important stuff because we're going to need these things that we've been learning for the future. So if there's anybody that's still making some slight mistakes that we need to fix, we can work on fixing those. So, I need you to read this carefully, show all your work so I can see what you were thinking, and you have about 10 minutes or so to do your best.

We did the pre-assessment for the formative assessment lesson. I will, along with my colleagues, analyze the math misconceptions that they might have. We put them in a type of spreadsheet that I can check off if a particular student made that error. I can pair them up either with somebody that is strong in that area, or someone who has common misconceptions for the activity. And then, when they take the post assessment, we compare them to the pre-assessments to see their growth.

Okay, guys, have a fantastic day. I shall see you tomorrow.

They misinterpreted the variables in the first equation. They assumed N is notebooks, not number of notebooks. And when they did that, they pretty much said Dan was correct, and Dan is not correct. It appears that not everybody read everything in the beginning to figure out that the 39 was the total amount of money, so they didn't know what the 39 meant.

Speaker 4: One of the things that we've really tried to do is make sure that teachers have a lot of opportunities to collaborate with one another, so that they can have that support, they can share ideas, and just to kind of have that sense of community, that we're not going through this alone.

Speaker 5: I've just figured out where the 52 came from is some other issues. They were trying to do elimination, and when they multiplied both equations to get those opposites, they didn't set it up correctly. So they have the N's in the same column, but then the P's are not in the same column. They're not on the right side of the equal sign, so it threw it off. That's where the 52 is coming from.

#### School Details

Turkey Foot Middle School
3230 Turkeyfoot Rd
Edgewood KY 41017
Population: 1075

Data Provided By:

Jenny Barrett

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