WEBVTT

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(Bret Mosley): My name is Bret Mosley.

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I am a fifth-grade teacher at Eliza Hart Spalding School of Math and Technology in Boise,

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Idaho, in Meridian School District.

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The lesson today started off with a contextual problem of asking the kids to divide 20

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and one-half by one and three-quarters of an inch.

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The importance of a context problem to me is huge.

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Numbers are numbers to kids, but when you put them

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in the meaning they see them a little bit different.

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And being able to understand what you are asking is huge for kids.

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Putting them in context for kids makes them vested in what they are looking at.

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(Student): Shane and I were playing in the garage,

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and he wanted to be just like Spiderman, big shock.

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He asked if we can make him a web shooter out of the rope that he found.

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To make each web shot, it takes one and three-quarters of an inch of rope and if he found 20

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and a half inches of rope, how many web shots can we make for my Spiderman?

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What is the mathematical sentence?

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Then solve.

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(Mosley): B says once you figure your answer for A, how much rope is left over?

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C says how much more rope is needed to make another web shot?

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And D, which I think might be the most challenging, is what would your mathematical model look

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like for the way you solve the problem.

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(Mosley): We had measuring tapes, yards sticks, or meter sticks.

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We had yarn that was precut at 20 and a half inches.

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They also had Cuisenaire rods, and whatever manipulatives they wanted to use.

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I would recommend that you work out our problem before you give it

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to the students because the numbers are huge.

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I wanted to make numbers that were easy to work with but were also problematic,

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so they had to find the equivalent fractions of halves

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and fourths to be able to solve this problem.

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So making it problematic, but doable, as well as working out the problem to see what kind

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of answers you could get from students, so you are prepared as an educator to be able

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to answer the questions and know where to go.

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(Student): I drew up big long number line from zero to 20 and a half.

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First, I went up to the first one and three-fourths and that would be one.

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Then second, two.

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I just kept doing that continually until I got to 20.

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Right there I could do another one, so that leaves me with a half.

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So my answer was 11 remainder one, remainder one-half,

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but since a half wouldn't count as a shot, it was 11 shots.

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(Mosley): So that top row here represents the total length of string.

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What does the bottom represent in his case?

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What does your bottom numbers represent, the one, the two, the three,

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the four, the five, all the way to 11?

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What does it represent?

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(Student): The shots.

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(Mosley): The number of shots.

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(Student): I got one and three-fourths equals one of the ...

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and if you times that by two, it will equal three and a half.

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And I did the same thing with my three.

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I did 3 x 2 = 6 and then 1/2 x 2 = 1, 6 plus 1 = 7.

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And then I did 7 x 2 = 14, and I kind of tie in to14 again, so that would equal 16,

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and that would equal 28, so I couldn't do 16, so I did 19.

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So I did, so I added 1 3/4 to 14 to equal 15 and 3/4, and I added 1 3/4 to 15 to get 17 1/4,

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and then did the same thing with that and got 19.

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(Mosley): What does that represent?

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(Student): Rope shots.
(Mosley): Okay, web shots.

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So one web shot gives you that.
So what does this represent?

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(Student): How much the length of the rope.
(Mosley): Thank you.

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(Student): I multiplied 1 3/4 x 6 and that got me 10 1/2, so 10 1/2 - 20 1/2 would equal 10.

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So I was thinking that I could do six one more time, but I couldn't because it's a half over,

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so I went down to five, and I multiplied 1 3/4 x 5 and that got me 8 3/4.

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And then 10 - 8 3/4 would be 1 1/4.

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So 6 plus 5 = 11, and 1 1/4 is the remainder.

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(Mosley): I want you to show me your six on your partial quotient is ten and a half.

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Where is that represented in Kyle's?

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(Student): Yeah two-fourths is the same as one-half, two-fourths.

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(Mosley): So what are they?
(Student): Fourths.

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(Mosley): Okay. So they are dealing with fourths.

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(Student): Yeah, but I just put a half because it's the same thing.

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(Mosley): We go up to the board often with usually several different strategies up there,

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so the kids gets comfortable with seeing different strategies and solving it different ways.

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A lot of times I will ask for multiple ways of solving it,

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so it gets them different ways of thinking.

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So they can check their answer.

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They are always asked a couple of questions like "Will it work all the time?"

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because some tricks work every once in a while, but they won't work all the time.

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And that's where multiple strategies come in because a kid could get a wrong answer one place

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and get another answer, but the ability to see different strategies

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and talk through those strategies with their peers is huge because I think kids,

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when they talk about their strategies with other classmates,

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defines their own understanding as well as helps others.

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So those multiple strategies are huge in math.