TURTLE TRAVELSBeginning to divide fractions with

6th graders

What do you think of when you hear “dividing fractions”?

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 trackThese students found a way to keep track of both the hours and the miles.

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

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.

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?