Turtle Travels Beginning to divide fractions with 6th graders
Some Related ideas • Contexts: Partitive (sharing) vs. Quotative (measurement) • What to do with the remainders • Scaling up and down • Division as fractions
A turtle travels 2/3 mile in one hour. How long will it take him to travel 6 miles?
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.
Keeping track These students found a way to keep track of both the hours and the miles.
Explaining 3/2 2 /3 mile per hour or 3/2 hours per mile ?? 2/3 mile : 1 hour 1/3 mile : 30 mins 3/3 mile : 1 ½ hrs
What we learned We 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.
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?