Series: Meeting Students' Needs in Number Talks

Math.Practice.MP4

Common core State Standards

  • Math:  Math
  • Practice:  Mathematical Practice Standards
  • MP4:  Model with mathematics.

    Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. In early grades, this might be as simple as writing an addition equation to describe a situation. In middle grades, a student might apply proportional reasoning to plan a school event or analyze a problem in the community. By high school, a student might use geometry to solve a design problem or use a function to describe how one quantity of interest depends on another. Mathematically proficient students who can apply what they know are comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later. They are able to identify important quantities in a practical situation and map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts and formulas. They can analyze those relationships mathematically to draw conclusions. They routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose.

Download Common Core State Standards (PDF 1.2 MB)

|
Math.5.NF.B.4

Common core State Standards

  • Math:  Math
  • 5:  Grade 5
  • NF:  Numbers & Operations--Fractions
  • B:  Apply and extend previous understandings of multiplication and division
  • 4: 
    Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.


    a. Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = ac/bd.)
    <br />
    b. Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas.

Download Common Core State Standards (PDF 1.2 MB)

Meeting Students' Needs in Number Talks
Lesson Objective: Use number talk check-ins to formatively assess students and provide tailored instruction
Grades 5-8 / Math / Assessment
Math.Practice.MP4 | Math.5.NF.B.4

Thought starters

  1. How does Ms. Morey structure her class in order to provide tailored, small group instruction?
  2. Why does Ms. Morey decide to use manipulatives with her small group?
  3. How does Ms. Morey use this lesson as an opportunity to build her own skills?
16 Comments

Thank you! I needed this idea!

Recommended (0)
Hi, i can’t see videos!
Recommended (0)
That is great to hear, Jai! You may also want to check out these number routine videos: https://www.teachingchannel.org/blog/2017/07/14/number-routines-second-wrap/ Good luck, and let us know how it goes!
Recommended (0)
Thank you, Gretchen. I am a middle school principal who is attempting to bring number talk practice to the math department.
Recommended (0)
Hi Jai, Check out the video https://www.teachingchannel.org/videos/independence-in-learning to see the math menu activity the other students were working on while Ms. Morey met with her small group.
Recommended (1)

Transcripts

  • Meeting Students' Needs in Number Talks Transcript

    Crystal Murray: My name is Crystal Murray. I teach six grade Math at Enumclaw

    Meeting Students' Needs in Number Talks Transcript

    Crystal Murray: My name is Crystal Murray. I teach six grade Math at Enumclaw Middle School in Enumclaw, Washington. My Getting Better Together project is in Making Number Talks Matter a book study. Early on in the project, I asked one of the authors, Ruth Parker if she would give me a feedback if I did one of my own number talks. Out of that conversation came this idea of how was I getting at each child's needs within a number talk.

    We've been working a lot on division and we've also been looking at this connection between multiplication over the last couple of weeks. We have such a safe climate within the number talk that I only hear from perhaps five or six students a day. Today's lesson is a response to this need that I was sensing. That need that I was sensing was that I didn't know where each child stood.

    I wanted to be able to bring a small group of students together in hopes of understanding their misconception and then the second, in responding to that misconception.

    We've done enough number talks now that I needed to just do a number talk check in with all of you.

    Ruth suggested that I might do number talk check ins and frequently, about once every two months.

    I need to know if I haven't heard from you in the number talk, I needed to take a second to see what you know by having you put it on a card. After, you're going to walk into menu. You'll notice that our menu task are on the very back counter. If I tap you on the back, then I'm going to have you come and work in a small group with me.

    Now, we're going to do our number talk check in.

    This morning, I picked a number talk four and two thirds times three for the number talk check in. I was looking to see evidence that students had an initial strategy and a backup strategy.

    These are either too low or too high. These are accurate. This is the misconception that I expected to see.

    Ahead of time, I'd plan for this misconception of twelve and two thirds.

    Out of this misconception that I'm trying to now go through quickly and see who I worked with in a small group and who needs more support. Now, I'm picking out four kids that I'll work with. I'm going to work with you Carter. can I work with you, please?

    I'm hoping when I bring this small group together that A, they're willing to open up, also that I can figure out what's this misconception, like why is this happening and using that to guide not just this one small group discussion, but to guide me and my future practice as well.

    Could you try to find and highlight three tenths on that picture? Who can tell me how they knew that that was three tenths?

    Male Speaker: Because three out of ten.

    Crystal Murray: Where do I see the three out of ten?

    Male Speaker: One, two, three, and then out of ten.

    Crystal Murray: Out of ten? OK. Did everybody else see that same way?

    Class: Yeah.

    Crystal Murray: In one of the chapters early on in the book, they talk about this conversations to have with your students. One of those important conversations is that a student can double a number or have a number.

    What if now I want you to highlight two groups of three tenths?

    Male Speaker: Six tenths.

    Crystal Murray: Where do I see that on your picture?

    Since [inaudible 03:28] give up multiplication, I thought that doubling would be this nice linkage into multiplication. In that, if they can double something, they could think about other multiples that were bigger.

    What's three groups of three tenths?

    Class: Nine tenth.

    Crystal Murray: The focus was to really think about if my students could double a number, how they double that number, and what I could learn if they could or couldn't.

    I'd like you to build this number with blocks. Could you make a model for a one and two thirds?

    One reason I chosen our small group to really focus on them using blocks is so that they could understand that there's both a visual model for division, but also really see what is their visual model that they have for multiplication. It's hard to voice that out, but I find that manipulatives and building really give me a better idea of where the students misconception is.

    What do you have Elena?

    Female Speaker: This is my one and then this is my two thirds.

    Crystal Murray: OK. What do you have Mercer.

    Male Speaker: Since I said the last time, I was [inaudible 04:31] together. I did one and two thirds.

    Crystal Murray: OK. What do you have, Carter?

    Male Speaker: That's why I was trying to do it.

    Crystal Murray: OK. How would I make one and one fourth? Where do I see your one and one fourth?

    Female Speaker: All this, all big ones, they make fourths.

    Crystal Murray: Can you see five fours in Elena's work?

    Class: Uh-huh.

    Crystal Murray: What do we know about five fours and one and one fourth?

    Female Speaker: You can convert it to one and one fourth.

    Crystal Murray: They're the same. Where do I see your one and one fourth, Carter?

    Male Speaker: This would be the one and then the four from one and one fourths.

    Crystal Murray: Once I understood the misconception that was happening across this group, this told me we needed to step back. Two of the students weren't seeing that relationship within the next number itself. I was prepared for something today, that wasn't what I actually got. That threw me for a second.

    Which number is bigger, the one or the one fourth?

    Class: The one.

    Crystal Murray: Which number should have more blocks? The one or the one fourth?

    Class: The one.

    Crystal Murray: One area that I'm really trying to work hard on is to ask questions that really helps students understand their own misconceptions.

    In this model, the one looks a lot smaller. Isn't it?

    Class: Uh-huh.

    Crystal Murray: How could we make a model where the one looked bigger than the one fourth?

    Male Speaker: We can maybe put together.

    Crystal Murray: OK. Let's put out blocks back in here and let's do another.

    You notice that sometimes today, I quickly switched to a new topic when I asked a question and it felt like the student got stuck. They didn't understand their misconception and I almost felt like they were going to shot down on me.

    Now I want you guys to do this. Let's see what happens. OK? Can you guys make again one and two thirds?

    When that happen, I wiped the slate clean and I asked them a new topic, right then and there. I'm also doing that for myself. Sometimes, I need to let myself off the hook. In which case, I don't have another question. I just seem to start again. What do I need to know now?

    Will you please break yours apart to just show me the one? Let's look at Marissa's everybody. Where is the one in Marissa's model?

    Female Speaker: This three and this three.

    Crystal Murray: Those are the wholes? OK. Who else has a model that's kind of like Marissa's? What do we notice about Marissa's model? What happens with both of the wholes? What do we notice about Marissa's model?

    Male Speaker: When you put them together it makes like a two.

    Crystal Murray: Why do you think Marissa chose to have three as the whole in both groups?

    Male Speaker: Because it's two thirds.

    Crystal Murray: Because it's two thirds so you looked at the ... Did you connected that with the denominator?

    Male Speaker: Yeah.

    Crystal Murray: OK. Can I ask you to double? One and two thirds.

    Two of the four students were able to double a mix number.

    What did you get?

    Female Speaker: Three and one third.

    Crystal Murray: Those particular students now need to see what would happen if I tripled or quadrupled? How could they use this to make models? Is this relative size? Is she going to come up again?

    What I'm going to have you guys do is to dry out your model and explain your model on a card right now.

    The other two students, their answers were more reasonable. They're answers showed more in depth thinking than they had in the initial number talk check in.

    I'm going to take this and you guys can go back.

    After this experience with this class, I also got the opportunity to then work this out with three more classes. First off in the next class, I asked them the question, how are these two models different? This one, they could see instantly as five fours or one and one fourth. With this model, they had a really hard time seeing this as one and one fourth.

    Using that and having a conversation about which model might make up the most sense, they could see the relationship and thus could double and they could extend that into higher numbers as well.

    Then right next period, knowing that relative size was going to be a misconception that I was going to see, I was able to adjust that and ask slightly different questions that help students see that misconception earlier and be more successful in the end. For that, I felt there's a little bit of success criteria that's in me. Do my questions make an impact on student learning? I think in the second class period, it did.

    I want you to double it.

    When I do a number talk the next time around, I'm hoping that the tangible objects that they created today help them be a risk taker in the whole group.

    When you have a connection, can you show me with a thumb.

    If I don't hear from them in a whole group, I'll do it probably an individual check in with these four students. I will see if they'd have a real opportunity to really confront their misconceptions in the weak side of [inaudible 09:33].

    Through this book study, I feel like I can really meet my students, where they're at and support their growth overtime.

School Details

Enumclaw Middle School
550 Semanski St
Enumclaw WA 98022
Population: 448

Data Provided By:

greatschools

Teachers

Crystal Morey
Math / Kindergarten 1 2 3 4 6 / Coach

Newest

TCH Special

Grades 6-12, All Subjects, Civic Engagement

TCH Special

Grades 6-12, All Subjects, Civic Engagement

TCH Special

Grades 6-12, All Subjects, Civic Engagement

Teaching Practice

All Grades / All Subjects / Collaboration

TCHERS' VOICE

Differentiation

TCHERS' VOICE

New Teachers