We've been working on fractions quite a bit, and have been working on division this week.

During the summer, I read the book

__Minds on Mathematics: Using Math Workshop to Develop Deep Understanding in Grades 4-8__by Wendy Ward Hoffer, and planned to spend more time this year having students "struggle" with problems that required them to think and explore.

However, I haven't done as much of this as I had planned. As we were ready to start fraction division, though, I decided to present students with a problem to solve, to see if they could make sense of the situation without knowing the mathematical process for dividing fractions. Based on their pre-tests, most of my students did not know this process when we started the fraction operations unit, so I knew this problem would be a struggle for many.

I presented my students with this question and allowed them to work with a partner or two to find a solution:

*Sharon has 34 ½ inches of string that she’s planning to use to make bracelets. Each bracelet needs 5 ¾ inches for each bracelet. How many bracelets will she be able to make?*

During my first math class, there was quite a bit of whining! They really did not want to think about this themselves and just wanted me to tell them how to do fraction division (I was glad that they knew they needed to divide, because I did not tell them that). I refused and told them they could draw pictures, use a ruler, use whatever materials they wanted, but they could not use their note sheet, book, or calculator.

When they realized that I really wasn't going to help them, they started thinking. A few students did a really great job drawing pictures to help them figure out the answer, while a few other students grabbed a yard stick and started marking every 5 3/4 inches (in this picture, the students used calculators as markers....not quite sure why....but it worked for them.)

If students figured out the answer to that problem (some did not find the answer by the end of class....it was a shortened class that day, which gave us about 30 minutes to think and then discuss), they tackled a second one.

*Sharon is designing a cover for the yearbook, and she wants to draw stripes as part of her design. She wants to make the stripes ¾ inches wide. If the yearbook cover is 12 inches wide, how many stripes will she be able to fit? If she alternates the colors green and yellow, will she be able to start with green and end with green?*

It was interesting to see which classes and which students found the answers more quickly. In some classes, most students got to the second question and to the extension of that question, but it took some students much longer to tap into their thinking abilities. I was happy with the results of the class periods, and definitely need to spend more class periods allowing them to grapple with problems.

What have you been working on?

Sounds like a fabulous activity! We have been asked to do more of this type of thing, but I need to remember to spend the time. Well done!

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