Ordering Fractions

I know. How dull! If I find it boring students must find it even more boring. As I mentioned before I’m kind of a number theory nut. After learning about the Farey sequence during my summer in PROMYS I knew it would be a great addition to my fraction bag of tricks. I tried it and students did it, but they weren’t getting where I wanted them. I don’t think I was asking the right questions.

I recently found this activity and tried the Farey sequence again. Students loved it. They wanted to try to get the next sequence. I shared it with a colleague and she couldn’t believe one of her students asked if it would be all right to do F9.

Here is F4:

Fourth Farey Sequence

from nrich.maths.org

I love lessons like this one. There is so much mathematics packed into it. We have mixed ability classes so students that are struggling with multiplication are sitting next to students that can solve equations in there heads. This problem allows students to move through at their own pace. I want students to practice comparing fractions. The fact that they are discovering patterns and symmetry along the way is a bonus.

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