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Unit 3 - Multiplying and Dividing with Fractions
Lesson 1- Multiplying by a Unit Fraction.
There are 3 ways we have looked at multiplying a whole number by a fraction:
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- finding a fraction OF a group
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-repeated addition
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-multiplication as comparison
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See videos below.
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Repeated Addition
Multiplication as Comparison
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In the video, they are showing how to use a comparison bar. In class, we are also using the comparison bar to show that Carl has 1/3 as many markers as Jesse.
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Multiplying Mixed Number x Mixed Number
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One of these videos shows a model of what it means to multiply mixed numbers. The other shows a strategy for getting the product easily. We do want students to get an answer quickly and easily, but we also want to continue developing the concept of multiplication. The area model relates to the ideas we explored with multiplying whole numbers in 4th grade.
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The videos below show two students solving a problem about finding the area of a garden that is 3 1/2 yards long by 2 3/4 yard wide.
DIVISION WITH FRACTIONS
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For this work, it will be important to remember that division can be modeled in 2 ways. 6 divided by 2 can mean "Make 2 groups" or "How many 2's are in 6?"
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Our work with fractions asks us to think about both models.
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Dividing by a fraction (Note: 5th grade will only be asked to divide by a unit fraction. Moms and Dads, please don't teach a "trick"! Use the pictures to show what happens when we divide by unit fractions.
Use the "Simplify First" strategy when multiplying fractions.
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This is not a strategy that all students are expected to master, but many have found it useful. Can you figure out why this strategy works? Spend some time exploring it!
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Many thanks to the 5th graders who worked on this video for us!
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Dividing by a fraction
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