## Reflection: Flexibility Where Would It Be? - Section 2: Measuring to a Fraction

When I presented a yardstick with all the numbers carefully covered and the stick was then divided into 3 clear parts and I asked students how I might use it to measure, the students were convinced that I could still measure in inches even though the inches were no longer visible. I wanted them to see the thirds we had just talked about in the warm up, and to me it seemed so obvious, but to the students, it was not obvious.

They guessed that I could measure in inches, or feet, or centimeters, or even kilometers. Some wanted to draw the inches on the stick. Others said maybe I could just break my tower in half or just count the blocks in my block tower. They were not seeing the three pieces on the unmarked stick.

I listened to their suggestions and then went back to the stick. I said how many lines do you see on the stick now? (2) and how many parts. Many were blank on this. I asked them to show me with fingers how many parts of the stick they saw and about 1/3 (funny that is our fraction too!) did not see the 3 pieces. I had to go back again and we all counted the pieces together, 1,2,3. Ok I said, there are 3 pieces so if my stick is the whole thing, and it is divided into 3 equal pieces, what fraction is it divided into? Again I got blank stares and those who looked away so I wouldn't call on them.

I tried again. Ok, lets think about dividing this stick into fractions. The stick is 1 whole stick. I see 3 parts so I have divided it into 3 equal parts, 1,2,3. Can I label each one as a fraction? Finally hands went up and a student said it is thirds. (OK, I thought, now we are making progress). Ok, it is divided into thirds, so if I put it next to my block tower, how many thirds long is the tower? "TWO" students called out. Yes, it is 2 parts long and what fraction is that? (2/3).

I had to keep backing up and rephrasing my questions because students did not see what to me was so obvious, that the stick was in thirds. My thought is that while I understand what a fraction is, they do not, so the division into thirds was not obvious. I had to show them exactly what to look at to identify that the stick was indeed divided into thirds.

Once they jumped this hurdle, the rest of the lesson was easy for everyone.

You just never know what students will grasp or not grasp, so you have to check often for understanding by backing up and asking questions, breaking things into even smaller increments of understanding and by listening to what they are understanding and extending that learning with questions that will carry students even further, or you may be left with just a few survivors by the end of your lesson.

Beyond The Box
Flexibility: Beyond The Box

# Where Would It Be?

Unit 9: Fractions
Lesson 3 of 10

## Big Idea: Fractions are numbers and seeing them as a part of a whole and a length helps conceptual understanding of what a fraction is.

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Standards:
Subject(s):
Math, Measurement, Fractions, Number Sense and Operations, feet, inches, centimeters
60 minutes

### Beth McKenna

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