Download - Turtle Travels
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TURTLE TRAVELSBeginning to divide fractions with
6th graders
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What do you think of when you hear “dividing fractions”?
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Some Related ideas Contexts: Partitive (sharing) vs.
Quotative (measurement) What to do with the remainders Scaling up and down Division as fractions
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A turtle travels 2/3 mile in one hour. How long will it take him to travel 6 miles?
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Student Work This student modeled discrete thirds and grouped every 2 together to represent each hour.
The difficult part was keeping track of not only the hours, but also the total miles.
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Keeping trackThese students found a way to keep track of both the hours and the miles.
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Explaining 3/22 /3 mile per hour or 3/2 hours per mile ??
2/3 MILE : 1 HOUR1/3 MILE : 30 MINS3/3 MILE : 1 ½ HRS
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What we learnedWe were interested in what informal knowledge
students would rely on. We were surprised that more students didn’t draw a
linear model given the context. We were surprised that a boy who was typically not a
strong student saw 3/2 in the problem. We noticed some students who are accustomed to
working only with symbolic forms struggled more that others who were willing to draw a model.
This lesson reinforced the need to choose carefully who will share their work and to be thoughtful about questions we ask to support student thinking and connections.
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Other questions How will they handle “leftovers”? What if
he traveled 9 hours and still had a little distance left to go?
What about the partitive context? Can we share with 2/3 of a person??
Which student methods are generalizeable and which have specific purposes?
What knowledge is necessary before beginning this work and what is gained as we go along?