Series: AFT CCSS Math

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)

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Math.Practice.MP3

Common core State Standards

  • Math:  Math
  • Practice:  Mathematical Practice Standards
  • MP3:  Construct viable arguments and critique the reasoning of others.

    Mathematically proficient students understand and use stated assumptions, definitions, and previously established results in constructing arguments. They make conjectures and build a logical progression of statements to explore the truth of their conjectures. They are able to analyze situations by breaking them into cases, and can recognize and use counterexamples. They justify their conclusions, communicate them to others, and respond to the arguments of others. They reason inductively about data, making plausible arguments that take into account the context from which the data arose. Mathematically proficient students are also able to compare the effectiveness of two plausible arguments, distinguish correct logic or reasoning from that which is flawed, and--if there is a flaw in an argument--explain what it is. Elementary students can construct arguments using concrete referents such as objects, drawings, diagrams, and actions. Such arguments can make sense and be correct, even though they are not generalized or made formal until later grades. Later, students learn to determine domains to which an argument applies. Students at all grades can listen or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments.

Download Common Core State Standards (PDF 1.2 MB)

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Math.K.NBT.A.1

Common core State Standards

  • Math:  Math
  • K:  Kindergarten
  • NBT:  Number & Operations in Base Ten
  • A:  Work with numbers 11-19 to gain foundations for place value
  • 1: 
    Compose and decompose numbers from 11 to 19 into ten ones and some further ones, e.g., by using objects or drawings, and record each composition or decomposition by a drawing or equation (such as 18 = 10 + 8); understand that these numbers are composed of ten ones and one, two, three, four, five, six, seven, eight, or nine ones.


    Drawings need not show details, but should show the mathematics in the problem. (This applies wherever drawings are mentioned in the Standards.)

Download Common Core State Standards (PDF 1.2 MB)

Beyond Fingers: Place Value & the Numbers 11-19
Lesson Objective: Understand the numbers 11-19 as 10 ones and some further ones
Grades K-2 / Math / Reasoning
Math.Practice.MP2 | Math.Practice.MP3 | Math.K.NBT.A.1

Thought starters

  1. What does mathematical reasoning look like in kindergarten?
  2. How are students encouraged to share and learn from each other?
  3. What supports does Ms. Lassiter use to further her students' thinking?
96 Comments
Awesome Lesson. Can you provide worksheet?
Recommended (0)
Loved how she modeled, had them writing and doing journaling to do an assessment!Having a good understanding of numbers 11-20 and placevalue builds every year so it is so important that kids are proficient so they can move on easily and feel confident.
Recommended (0)
Place value connection is so extremely important! Thinking about the numbers 11-19 as "ten and some ones" and focusing on how to write numbers correctly will help students better understand this connection.
Recommended (0)
Awesome math strategies, questioning, and modeling!
Recommended (0)
Thank you for such great insight into Common Core Math for our younger group. I love how Common Core allows for so much hands on learning. I also love how the video demonstrates different strategies to teach, and how it shows the student's accountability.
Recommended (0)

Transcripts

  • Beyond Fingers: Place Value & the Numbers 11-19 Transcript
    Luna Productions
    Program: Beyond Fingers
    Teacher: Karen Lassiter

    Voice identification: Teacher in

    Beyond Fingers: Place Value & the Numbers 11-19 Transcript
    Luna Productions
    Program: Beyond Fingers
    Teacher: Karen Lassiter

    Voice identification: Teacher in Classroom/Teacher in Interview:
    Student (for any/all student who speaks)

    Teacher: Hi, I’m Karen Lassiter and I invite you to join my kindergarten class as we explore this lesson Beyond Fingers

    Teacher in Classroom: Very good. When we were working at our desks and our journals yesterday I noticed that you guys could get this part, you understand that the numbers from 11 to 19 on our number line right there …

    Teacher in Interview: The heart of this lesson is working with the numbers from 11 to 19 and in the common core it has a different approach to that. [gap] ____ thought of as 10 and some more 1s.

    Teacher in Classroom: And it means that we have just 1, so that would mean that we have just one. This number right here means that we have 10.

    Teacher in Interview: They’re working with the 10 frame and that’s pretty familiar to them. And I’m stretching it to the numbers that are 10 and some more ones

    Student: Because 2 plus 8 equals 10

    Teacher in Classroom: Oh, very good. OK, I’m going to ask Alexia to come up and prove that.

    Teacher in Interview: One of the ways that you can get a proof out of a kindergarten child is to give them the manipulatives and just ask them to prove whatever it is that they’ve said.

    Teacher in Classroom: Tell me what you’re thinking while you’re doing it

    Student: I’m going to put the 2 and then I’m ___

    Teacher in Classroom: Excellent, OK

    Teacher in Interview: Kindergarten mathematics is very conceptual. You’re trying to build that conceptual base that you can then lead into the abstract and so their reasoning is very much tied to the concrete items that they’re using. So when you say prove it, then they can prove it with manipulatives. That is their proof, that is their type of proof for kindergarten.

    Teacher in Classroom: If you can just look up there and tell me if that’s 10. Olivia? How do you know?

    Student: Because [can’t understand …..]

    Teacher in Classroom: Ok, the 10 frame is full so you know that it has to be 10 in there because it’s full. OK, but what if I did this …..

    Teacher in Interview: Moving the magnets around on the white board is a good way for students to begin to make those connections between what they know and how it doesn’t change.

    Teacher in Classroom: OK, so now how many do I have? Arman?

    Student: Ten, because you just moved them around. You didn’t take any away or add any

    Teacher in Classroom: So when I moved them around it’s still the same, is that correct?

    Student: Yeah

    Teacher in Classroom: Well now what if I did this? Justin?

    Student: Twelve.

    Teacher Classroom: How did you know that, that was very fast?

    Student: Because you put two in and that makes 12

    Teacher in Classroom: And how do you know that that makes 12? What did you do, what did you think, how did you think from 10 to 12?

    Student: I moved the 10 frame _______

    Teacher in Classroom: OK, so you started with the 10 frame and then you went 11, 12. Is that what you did? Great job. That’s good thinking. Now what if I do this one, are you ready? All right. Aiden?

    Student: Twelve

    Teacher in Interview: Students come with different knowledge levels.

    Student: [can’t understand ]

    Teacher in Classroom: OK, so you’re just counting. Did you start here?

    Student: Yeah

    Teacher in Interview: He was really not counting on from 10 but he was counting them all; so he started with the very first one and he counted all

    Student: Eight, 9, 10, 11

    Teacher in Classroom: Eleven. So how many are there?

    Student: Eleven

    Teacher in Interview: You don’t want to stop their learning because they aren’t where you want them to be for the next lesson so what you try and do is take where they are and build them continually with the knowledge that you’re learning now but also fill in that gap so that they can get there

    Teacher in Classroom: And you noticed that she put the 1 right here, who knows what that 1 means? Arman?

    Student: It means …um one 10

    Teacher in Classroom: One 10, one 10. This means one 10 and we put it here because if we did this, where we put the zero here and the one here, what number would that be? ____?

    Student: One

    Teacher in Classroom: One.

    Teacher in Interview: They worked really hard this year. So they have cardinality which means that they can take a set and like move it around and they understand if that none haves been added or taken away, it’s still the same number. They have worked with a 10 frame. They understand that a 10 frame is designed to help them with the number 10. They have done counting on from a number, any number, and so all of those little pieces fit together to build a foundation on which to build this lesson.

    Teacher in Classroom: But the numbers from 11 to 19 are tricky numbers because it doesn’t sound like what they are. So it says 13, hummm, and yesterday I saw somebody look at 13 and say this is 13 …..

    Student: That’s 31

    Teacher in Classroom: That’s 31, how can you tell that’s 31?

    Student: Because the 3 is in the first spot and the 1 is in the second spot

    Teacher in Classroom: Right, and that’s why it’s so important to know how the numbers work together.

    Teacher in Interview: We started this yesterday. They knew the numbers right away, so they knew that 10 and 3 more was 13. But what I noticed was that they did not write the numbers correctly. The connection that they were missing is the place value connection where you write the number of 10s first and then the number of 1s. And so based on that I altered the lesson to include more of how to write the numbers and less of identifying the numbers.

    Teacher in Classroom: OK, this is what I want you to do. We’re going to do a little work in our journal

    Teacher in Classroom: The math journal today covers the numbers 11 to 19.

    Teacher in Classroom: So what I want you to do now is draw a circle around 10 sailboats and then count how many more and come up with a number, and I’m just going to walk around and look

    Teacher in Interview: In today’s journal I put all kinds of different graphics and I tried them in different formats. I tried them set up as if they were in a 10 frame; I tried scattered. Because I wanted to see if children could make sense of numbers in a scattered format.

    Teacher in Classroom: So if you started counting at 10 can you count on?

    Student: Yes

    Teacher in Classroom: OK, do it for me

    Student: Ten, 11, 12, 13

    Teacher in Classroom: OK, so what number should be the total for that page?

    Student: Thirteen

    Teacher in Classroom: Good, can you write that

    Teacher in Classroom: I think that we have a little difficulty with the boats today. Who can tell me why it was harder for the boats today? ____?

    Student: Because they’re not set like a 10 frame

    Teacher in Classroom: OK, they’re not set up like a 10 frame

    Teacher in Interview: I think when you’re doing a lesson you have to watch for how is the lesson developing. The lesson first developed with the modeling and student interaction; from there it went to them writing it down and kind of formative assessment. From there it went into the individual journals which is their accountability piece

    Teacher in Classroom: Ok, this 10 frame is absolutely full so how many kids do I have sitting here?

    Students: Ten!

    Teacher in Classroom: Ten. And how many do I have back there?

    Teacher in Interview: This lesson is really important for kids. We as adults tend to think that learning to count is an easy kind of thing but it is not, it’s really hard work. Numbers up to 20 are crucial understanding for all kindergarten children.

    ² end of transcript

School Details

Manatee Cove Elementary School
734 West Ohio Avenue
Orange City FL 32763
Population: 766

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