WEBVTT

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[Music]

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Jennie Logan: My name is Jennie Logan, and I teach sixth grade at Patriot Elementary

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in the Papillion-La Vista School District.

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The lesson for today, I had two main goals, and those goals were for students

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to really develop an understanding of what it means to find part of a part.

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And then I also wanted to have a problem that they could work

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through where they could use multiple strategies to solve a problem

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that involved finding part of a part.

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Logan (to class): My scenario is that Mrs. Logan went

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to the Pride Council Bake Sale to buy some brownies.

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All of the pans of brownies are square.

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A pan of brownies costs $12.

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Customers can buy any fractional part of a pan and pay that fraction of $12.

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For example, half a pan costs half of $12.

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Mrs. Logan bought 3/4 of a pan that was 2/5 full.

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How much did she pay?

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Logan: There are several things that I considered.

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The first thing is I wanted it to be a real-life problem and something

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that the students could relate to.

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So we had just had a bake sale-our student council had sponsored a bake sale.

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So I used that context of purchasing something from the bake sale.

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And then I had the goal, I wanted a problem that would lend itself to multiple strategies

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for the students to work through and to see.

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Student 1: Well, I am thinking is if you find the power of 10,

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you multiply this you get 40/100.

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Student 2: Yeah.

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Student 1: And then what's 3/4 of 40/100?

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Student 2: 3/4 would be 30.

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30 percent.

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Student 3: There are 20 pieces, and each one, each piece .

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. . and $12.

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Student 4: And 12 divided by 20.

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So, this is how we got that it was 60 cents each.

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Logan: When I was planning out the lesson,

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I listed the strategies that I thought would emerge.

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And we had done a lot of work with area maps,

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so I knew that that would be a strategy that would emerge.

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The students that used their benchmark fractions and converted it to fractions

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over 100 was a strategy that I had not thought of.

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I did think that a number line strategy would emerge; it didn't, and so my next step will be

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to come up with a similar problem and kind of facilitate that number line,

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and how could we have used a number line to solve a similar problem.

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I think it's really important to expose students to multiple problem-solving strategies,

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and that is why every day in our workshops, students are working with a partner

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or with a small group, and they're discussing the strategies that they use.

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And then a majority of my math time is spent summarizing those strategies and calling

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up the different students and having them explain to the class what they did,

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and then asking the other students, "Can you repeat what they did?"

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or "Can you explain to me what your classmate did?"

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so that they can see that there are so many different ways to solve one problem.

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Student 5: First we made an area map, and we cut into fifths vertically

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since that was the denominator of the second fraction, and then we colored

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in two of those since it was 2/5.

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Then we divided it into fourths horizontally and we colored in three of those

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because that was a fraction, 3/4.

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And then we counted how many pieces we double-shaded in,

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and then we counted how many total squares there were, and then we figured

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out that how many total squares there were was the denominator

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and how many squares were double-shaded was the numerator.

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So we figured out that it was 6/20, and then we simplified it to 3/10, and then we divided $12

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by tenths and got $1.20 and then multiplied it by 3 because it was 3/10,

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and then we got our answer $3.60.

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Student 2: What we did was made 2/5 the denominator of 100, which is 40/100.

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And 3/4 of 40/100 is 30 because 1/4 is 10, and if you multiply it by 3, you get 30.

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Then we knew we had to make it out of the whole, not just 3/4, so we made it 30/100,

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and then we simplified it to 3/10.

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We knew $1.20 was 1/10 of $12, and we multiplied it by 3 to get $3.60.

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Logan: I choose strategies to highlight during my summary.

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I usually look for a strategy that most of the students have used

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because I know that's a very familiar one and obviously a very important one.

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I try to choose strategies where students have maybe used something

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that we've learned in the past and applied it.

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So with this brownie pan problem, we had spent a lot of time talking about benchmark fractions.

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When I had a group that used that strategy that had taken that knowledge and transferred it

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over to this problem, I definitely wanted to highlight that strategy.

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I try to choose a strategy that sometimes I'm a little confused with

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and maybe I don't quite understand.

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The last group of boys that used the common denominator of 20 and 12,

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that strategy threw me for a little bit.

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I wasn't quite sure what they had done, so I wanted them to explain that strategy

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so it could be clear to me and then to their classmates.

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So I just try to use a variety

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of different...make sure I highlight a variety of different strategies.

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[Music]