Common core State Standards

  • Math:  Math
  • 3:  Grade 3
  • OA:  Operations & Algebraic Thinking
  • B:  Understand properties of multiplication and the relationship between multiplication and division
  • 5: 
    Apply properties of operations as strategies to multiply and divide. (Students need not use formal terms for these properties.) Examples: If 6 × 4 = 24 is known, then 4 × 6 = 24 is also known. (Commutative property of multiplication.) 3 × 5 × 2 can be found by 3 × 5 = 15, then 15 × 2 = 30, or by 5 × 2 = 10, then 3 × 10 = 30. (Associative property of multiplication.) Knowing that 8 × 5 = 40 and 8 × 2 = 16, one can find 8 × 7 as 8 × (5 + 2) = (8 × 5) + (8 × 2) = 40 + 16 = 56. (Distributive property.)

Download Common Core State Standards (PDF 1.2 MB)

Reasoning About Multiplication & Division
Lesson Objective: Build understanding of multiplication and division
Grades 3-5 / Math / Strategies

Thought starters

  1. How do Mr. Crandall's students learn from each other?
  2. Mr. Crandall says it's important to give students time to make sense of their ideas. How does he do that?
  3. How does Mr. Crandall give students opportunities to revise their thinking?
Teaching children to count on their fingers is outrageous. Children way back when were discouraged to count on their fingers. Each problem takes longer and robs the children from other learning time. If the old math is not good then we all must be a bunch of idiots!
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Hi Drew, Thank you for this Number Talk! I will use it tomorrow in my Math Seminar class for pre-service teacher at San Jose State. So excited!
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Become Master Of Multiplication Table !! :-)
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Our son had some success learning multiplication through board/card games. His favorite was a card game his teachers friend created called Math Grab it's worth checking out. There are other free games you can also make at home that were fun, he really liked this one I think because of the speed of the game and that we could all play as a family.
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I love the ownership you are giving the kids for their thoughts, but you are also putting them in a leadership role to help teach through those turn and talks, even though they may not know! As the students were proving their knowledge in the standards you were focusing on, you allowed them to take the time to share their strategy in order to prove their answer.
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  • Reasoning About Multiplication & Division transcript

    Reasoning About Multiplication & Division

    Drew Crandall VO/OC All right, mathematicians, can I

    Reasoning About Multiplication & Division transcript

    Reasoning About Multiplication & Division

    Drew Crandall VO/OC All right, mathematicians, can I get your eyes up here, please? Today we're going to do a couple of math activities that are going to be around the idea of some multiples of four.

    Drew Crandall VO/OC My name is Drew Crandall and I teach...

    Drew Crandall 3rd Grade Lakeridge Elementary School, Renton, WA

    ...third grade at Lakeridge Elementary School which is in Seattle, Washington in a part of the Renton School District.

    Drew Crandall OC We're going to count until I say stop. Ready, begin.

    Group OC Four, eight, 12.

    Drew Crandall VO/OC Today's math talk, I have two objectives I want my mathematicians get to, to both understand the properties of multiplication and how multiplication and division work together, what their relationship is. As well as notice the structure of how the numbers work, and kind of make sense of the structure of their core count.

    Drew Crandall OC/VO Can you look at our count of multiples of four and see if you find any patterns in there.

    Drew Crandall VO/OC In the common core standard, they need to understand, really understand what multiplication and division are. Not just say back mathematics facts.

    Drew Crandall OC Will you guys turn and talk with your partner and share the patterns that you see?

    Drew Crandall VO It's important that they have time to kind of make sense of their own ideas and to be able to defend those ideas.

    Male Child In Red Sweater OC .

    Drew Crandall VO/OC So Reliance, do you notice a pattern that's happening in the tens place?

    Reliance VO/OC One, one, two, two, two .

    Drew Crandall OC Oh, okay.

    Reliance VO Two, three.

    Drew Crandall VO/OC It gives them a sense of ownership in their math. And then when they're sharing them, it helps them both learn from each other. But it also helps them revise or defend their own thinking.

    Drew Crandall VO/OC Does anyone have a pattern that they notice that they would like to share? Abib, what did you and your partner talk about?

    Abib OC Me and Franklin talked about it jumps 40 every time, from four to 44. Because we're counting by fours and four tens equals 40.

    Drew Crandall OC I saw a couple of connections signs. If you and your partner talked about that, could you say that to me?

    Group OC That's me.

    Drew Crandall VO That's me.

    Drew Crandall VO/OC They really honestly feel like mathematicians. And they take ownership over their ideas. And it's not, they're not repeating back to me something that I have taught them. They're coming up with these on their own.

    Layla OC It's going, it's, the, the circle, it's going one, two, three, four, five, six, seven, eight, nine, ten. And then over again.

    Female Child In Black & White Top VO/OC I agree with Layla but I have something to add. She got the four because we were counting by four. And she got the ten because the row it has ten in it.

    Drew Crandall OC/VO So she got the four because we're counting by fours. And she got the ten because there's ten numbers in each column.

    Drew Crandall VO/OC I think that we're going to be ready for the move to Common Core Standards because the mathematical practices are something that we have been doing for several years. I mean our talk moves and our mathematical discussions are consistent with the practices in the Common Core.

    Drew Crandall OC You guys were talking about the tens count. What happens in the tens count?

    Reliance OC/VO There's a . So like it would go two tens and three tens. And sometimes go like one one, then two, two, two. Two would be three times and one would be two times.

    Drew Crandall VO Right. Our tens changes as we move.

    Abib OC But even if it repeats itself, three times repeat itself two times.

    Drew Crandall OC Interesting.

    Drew Crandall VO After the count, I want them to start thinking about the relationship between division and multiplication. And I'm going to give them a division equation that takes one of the multiples of four and divides it by four. And I want them to be able to see that they can use what they just had previously done in counting forward to solve it.

    Drew Crandall VO I would like you to give me a thumb at your chest. Do you have a strategy to solve this equation? Moses, what did you get for that?

    Moses VO Six.

    Drew Crandall OC Six. Muno?

    Muno VO I got six.

    Drew Crandall OC/VO You got six. Sweda?

    Sweda VO Six.

    Drew Crandall OC Six. Jovan, I'm sorry. Did you have a number?

    Jovan OC Four.

    Drew Crandall VO/OC You got four for that? Could you guys turn and talk with your partner about how you solved that problem?

    Drew Crandall VO I want them to learn to think mathematically. And you can't do that if you're just thinking in terms of right and wrong.

    Emma OC We took four fingers and kept on counting until we got to 24.

    Drew Crandall VO Can I see how you, can I see how you did that? What does that look like?

    Emma OC/VO One, two, three, four, five, six, seven, eight, nine, ten, 11, 12, 13, 14, 15, 16.

    Drew Crandall VO It's a really smart strategy. Do you think you could share that with the class? Okay.

    Drew Crandall OC I'm really looking for why they believe they got the right or wrong answer.

    Drew Crandall OC I'm just going to write down some different people's strategies on how they solved it. Emma, could you tell me how you solved that?

    Emma VO So I put up four fingers.

    Drew Crandall OC Okay.

    Emma OC/VO And then I counted until I got to 24 and I got six fingers.

    Drew Crandall VO So I see your count. I just did it like that, like a core count. I'm wondering exactly in this answer, I see the six which you, was your answer. How did you, where's the four show up?

    Reliance OC Oh, because there's six fours.

    Drew Crandall VO Oh, because there's six fours. Okay, so one.

    Reliance VO I mean four sixes.

    Drew Crandall VO Four sixes.

    Drew Crandall VO/OC I think there's a lot of good things about moving to the Common Core Standards. As a teacher of math, I think the inclusion of the practices is something that I have seen a widespread positive effect in my classroom, in my school. I think that as that happens all over, I think math teachers are going to see really positive results.

    Drew Crandall OC Jovan.

    Jovan VO/OC I revised my thinking. I did the same way Emma did.

    Drew Crandall VO Okay.

    Jovan OC And I got six as the answer.

    Drew Crandall VO/OC So do you want me to cross out the four? Okay. Is there any other way to do this? Muno.

    Muno OC Four times six equals 24. So that means if just one of the numbers are missing it would have been the answer.

    Drew Crandall OC I'm going to go ahead and put that in the box.

    Drew Crandall VO/OC I think my students are going to walk away from how they've been learning math with confidence in their academic ability. A lot of our skills that we do in math talks translates throughout our entire day. That would be a big hope of mine that that kind of carries with them through their lives.

    Drew Crandall OC Can you guys give yourselves a big old yeah?

    Group OC Oh, yeah.

    Drew Crandall VO Okay.

    Tch Teaching Channel

    Special Thanks To Drew Crandall And All The Students And Staff At Lakeridge Elementary School, Renton, Washington

School Details

Lakeridge Elementary School
7400 South 115th St
Seattle WA 98178
Population: 420

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Drew Crandall


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