Series: Algebra Team

Math.Practice.MP1

Common core State Standards

  • Math:  Math
  • Practice:  Mathematical Practice Standards
  • MP1:  Make sense of problems and persevere in solving them.

    Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. They consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress and change course if necessary. Older students might, depending on the context of the problem, transform algebraic expressions or change the viewing window on their graphing calculator to get the information they need. Mathematically proficient students can explain correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for regularity or trends. Younger students might rely on using concrete objects or pictures to help conceptualize and solve a problem. Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, \"Does this make sense?\" They can understand the approaches of others to solving complex problems and identify correspondences between different approaches.

Download Common Core State Standards (PDF 1.2 MB)

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Math.A-SSE.3a

Common core State Standards

  • Math:  Math
  • A-SSE:  Algebra - Seeing Structure in Expressions
  • 3a:  Choose and produce an equivalent form of an expression to reveal and
    explain properties of the quantity represented by the expression.

    a. Factor a quadratic expression to reveal the zeros of the function it
    defines.


    b. Complete the square in a quadratic expression to reveal the
    maximum or minimum value of the function it defines.

    c. Use the properties of exponents to transform expressions for
    exponential functions. For example the expression 1.15t can be
    rewritten as (1.151/12)12t â\x89\x88 1.01212t to reveal the approximate equivalent
    monthly interest rate if the annual rate is 15%.

Download Common Core State Standards (PDF 1.2 MB)

Algebra Team: Overview of Teaching Styles
Lesson Objective: See a co-planned lesson unfold in two different classes (1 of 4)
Grades 6-8 / Math / Factoring
Math.Practice.MP1 | Math.A-SSE.3a

Thought starters

  1. How has the two teachers collaboration impacted their algebra program?
  2. How does the warm-up prepare students for the lesson?
  3. How do students "tiger up" and learn that struggle is a good thing?
18 Comments
Living in Berkeley, CA, it was thrilling and also fascinating to see two such talented and inspiring teachers. They are so different---yet the kids seem to show the same level of engagement and math perseverance! It's interesting to see "perseverance" raised as a core value....since I know so many students have difficulty muscling through some of the tougher math concepts.
Recommended (1)
I love the idea of using a school-wide phrase to encourage students to persevere through challenges! Did your staff come up with the phrase? Or the students? The hardest part about teaching Algebra (IMHO) is helping students become comfortable with struggle. Tiger up!
Recommended (1)
I like that 2 different energy/style/personality types are collaborating! They came up with a plan to present the challenges and new strategy as backwards thinking and it worked for them both. Collaborative teaching is incredibly powerful! Wish more teachers would buy in.
Recommended (1)
I love this and will share it with the middle schools and the high school in my district here in Austin!
Recommended (1)
can I use this in a powerpoint on a mac
Recommended (0)

Transcripts

  • Algebra Team – Overview of Teaching Styles with Marlo Warburton & Julianna Jones

    [01:00:07;11]
    Julianna: I'm Julianna Jones, and I

    Algebra Team – Overview of Teaching Styles with Marlo Warburton & Julianna Jones

    [01:00:07;11]
    Julianna: I'm Julianna Jones, and I teach Algebra.

    Marlo: I'm Marlo Warburton, and I teach Algebra 1.

    Both: We are the eighth grade Algebra Team.

    Marlo: "The bell's going to ring, but don't move."

    No student gets through the school without coming through the two of us, and we teach the same things on the same days. We give the same tests, and often, the same homework. And, as a result, our program is really consistent.

    Julianna: When you plan a lesson together, you teach the same lesson, you come back together and say 'Gosh, this happened and I didn't like that,' that's where the power is of a collaboration.

    "That's the key right there."

    Marlo: As a result, all the students who leave our school have had a solid math experience in Algebra 1.

    "I'm gonna give you the area."

    Narrator: Our classroom close-up cameras joined Marlo and Julianna as they each taught the same lesson on the same day in their respective classrooms.

    Julianna: "That's exactly right."

    Narrator: We begin with an overview of that days' lesson. Later on, we zoom in, taking a closer look at each teacher's style, philosophy, and classroom culture.

    Julianna: "Alright. Let's do this!"

    Marlo: "Good morning, Pam.

    Julianna: "Hi Chances."

    Marlo: "Good morning, Nandi. Please sit and get to work, your warm-up is posted today."

    I like students to come in to the classroom and get to work independently.

    Julianna: "Let's get started, like normal. I'm stamping. I want you to talk about this with the people at your table."

    We always start with a warm-up and partly that's to send the message that, like, the minute you walk in, you start doing mathematics. I want them to be talking about their ideas. I want them to be asking questions, and I want them to be interacting with each other.

    Student: "I agree with her answer because...well..comb...when you combine like terms, 15x and 4x becomes 19x."

    Student: "2x times 3x is 6x to the second power."

    Marlo: The warm-up included some multiplication of binomials by creating a rectangle, using the two binomials as length and width, and figuring out the area. That got their brains ready for what we were going to do, which is factoring, just doing the opposite.

    "I need you to open your notes to the table of contents"

    Julianna: "Get that table of contents going. That looks good. So, we're talking now, how do you factor a trinomial?"

    Today, we were introducing factoring trinomials. The trinomial is the product, or the trinomial is the area of a rectangle, and we have to think about what is the length and the width of that rectangle, or what are the factors that make that product?

    "We give you what's in the rectangle. What do you have to find?"

    Student: "The stuff that goes.."

    Julianna: "The stuff that go..."

    Student: "On the outside."

    Julianna: "OK. So that's, that's exactly right. Now help it. Bring out, bring out that language. So, what is that stuff on the sides called?"

    This piece of just going backwards, actually taking the rectangle, the area of the rectangle, and then going backwards and finding the length and the width, helps students' conceptual understanding.

    "What goes here? What goes here, to make the area?

    Marlo: "In our warm-up, you were given the length and width of a rectangle, and you were asked to find the area. Now, I'm not going to give you the length and the width. What do you think I'm going to give you?"

    Students: "The area!"

    Marlo: "The area, and what are you going to have to find out?"

    Students: "The length and the width."

    Marlo: "That's exactly what we're doing today."

    Julianna: "Alright. Let's do this! So, let me give you the inside."

    Both: "X squared, 12x, minus 3x, minus 36"

    Marlo: "I am giving you the area, and I would like you to figure out the length and the width. What did you write here in order to multiply and get X squared?"

    Student: "X and X."

    Marlo: "Audience, did you think about it like this? X times X equals X squared?"

    Students: "Yes."

    Marlo: "Alright, now keep going."

    The first problem that I gave them had a first term of just a plain X squared, so students could pretty easily say, 'Well, the binomials are both probably going to start with x."

    Julianna: "Corey, talk to me about, how are you gonna figure out what goes here, what goes...what...where do you want to go with this, Corey?"

    Student: "I think that's negative 3."

    Julianna: "Here?"

    Student: "Yeah."

    Julianna: "Why?"

    Student: "'Cuz negative 3 times X equals negative 3x."

    Julianna: "Multiplier. That's how you do this. You check yourself by multiplying. That's all you gotta do. Now, we gotta finish this. Somebody's saying 12. Caleb, why?"

    Student: "I put 12, because 12 times negative 3, is negative 36."

    Julianna: "Oh, he went for this one. He can do that. Twelve times negative 3 equals negative 36. Does this work?"

    Student: "Yeah, then X times...times 12 is 12x 'cuz it's a one in front of the x."

    Julianna: "What do you think about that? You see how he just went backwards. You started with what's in there, now you've got these."

    Marlo: "Length times width equals area. Factor times factor equals product. This is geometric, this is algebraic. Are we OK so far?"

    Julianna: "I'm gonna take a step forward on this. It's not gonna be an X squared here. It's gonna be this."

    Both: "5x squared, minus 4x, minus 10x, plus 8."

    Marlo: "I give you the area, you give me the length and the width."

    The next one, I gave them a polynomial that started with 5x squared, but 5, being prime, meant that it was gonna be either 1x times 5x or 5x times 1x."

    Julianna: "So, how 'bout 5x and x. Rosa?"

    Student: "That wouldn't work because if you have 5x times X, it can make 5x squared...

    Julianna: "Sh...sh...let her finish."

    Student: "Then if you..."

    Julianna: "You got something...It does make this, but..."

    Student: "It won't actually make negative 4."

    Student: "Yeah."

    Julianna: "You see how her brain's working? If you do 5x..."

    Student: "You can't do that."

    Student: "Five doesn't go into negative 4."

    Julianna: "So, this becomes a little game, where you might know that it's 5x and X, but you might put it down, and it don't work. So, you erase it, and you Tiger Up!, and you don't give up. You don't go "Ugh. I'm done. It didn't work." Right? You erase it, and you fix it."

    Marlo: "The area of the final rectangle is..."

    Both: "12x squared, minus 2x, negative 6x, plus 1"

    Marlo: "Twelve has many factors. So, I hope you play around a bit."

    The last problem Ms. Jones and I deliberately picked 12 as the coefficient because we wanted students to deal with 'Could be 12 and 1, could be 2 and 6, could be 3 and 4'. We wanted them to experience that it doesn't always happen on the first try, but we just Tiger Up! and we keep on going.

    "Good. Some of you are building good math endurance. You can struggle and struggle and struggle, and figure things out."

    The more students can get used to being presented with difficult challenges, the more they get used to that, the, the more willing they will be to push past it, and persevere, and the more they'll end up learning.

    Julianna: Teaching is as unique as all our students.

    "Does it matter?"

    There's no one way.

    "You bet it does! You bet it matters which way you put it!"

    You have to find your own style.

    Marlo: I like my classroom to be very predictable. It's very structured, very tidy.

    Julianna: Marlo's style is no less exuberant than mine, but it's more reserved.

    Marlo: Julianna's very high energy.

    Julianna: "I love you though! Like at least..."

    I mean, I'm louder, I think. Um....I'm pretty sure.

    Marlo: I can hear her from way down the hall sometimes.

    Julianna: Our personalities are a little different.

    Marlo: But, it's always really positive things that I'm hearing. I'm hearing her cheer for her class, as if she were at a football game or something.

    Julianna: "You do know! You do know" Sh!! Sh!!"

    Marlo: "Yeah, 5 times 12..."

    Julianna: Students are learning in our classroom, and it doesn't matter that we're a little different.

    Student: "X times X equals X squared."

    Julianna: "Now, there you go. Do this one."

    Students know that we care very much about their learning, and that gets communicated, and then students learn.

    Marlo: "Go ahead!"

    Students: "1,2,3"

School Details

Longfellow Arts And Technology Middle School
1500 Derby Street
Berkeley CA 94703
Population: 510

Data Provided By:

greatschools

Teachers

Marlo Warburton
Math / 8 / Teacher
Juliana Jones
Math / 8 / Teacher

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