Quandaries
and Queries 

My name is C.J. and I am a graduate student at Indiana University working on a Math Education project. I have some questions about the lesson, "Understanding Fractions" by Diane Hanson, Regina Catholic Schools. How successful was the lesson? Are there any changes you would recommend? If someone could email back to me the answers, I would appreciate it. Thanks, CJ 

Hi CJ, I still use the lessons on Understanding Fractions. At this time in my career I am math/science consultant for K8 in the Regina Catholic Schools. A big part of my work is modeling the problem solving process and the use of manipulatives in classrooms. I would say that about half of the modeling lessons I do are about fractions, from grades 4 to 8. So I usually use these lessons as the basis for my lessons and it is part of the handout I give teachers. I also hand out a unit I developed subsequently for a combined grade 6/7 classroom and this unit can be found at http://www.sasklearning.gov.sk.ca/docs/midlmath/model6.html Over the years I have learned to adapt the lessons as I go along. I now incorporate more work on finding patterns. For example, when we find fractions equivalent to ½ using the blocks, we then use the fractions generated and look for patterns. Students will usually tell me that the denominators are even numbers but the numerators are a mixture of odd and even. They will tell me that if you multiply the numerator by 2 you get the denominator and that when you divide the denominator by 2 you get the numerator (obvious things to us but amazing how they never connected these things or voiced them or even thought about them!). They also tell me other things such as 2x6 = 12 or that all the denominators are factors of 12. But anyway, having done this as a group, we then proceed to use this to create other fractions equivalent to ½. If the numerator is 10, what is the denominator; if the denominator is 100, what is the numerator (we can then relate these to decimals). When I model these lessons (and I usually do 23 consecutive lessons in a classroom), I usually have teachers working along with their students. I can actually pinpoint to the minute when the teacher realizes the wonder of this manipulative, by the fact that their jaw usually drops to the floor. And I can count in the hundreds the number of students who have that aha! moment. I now also introduce my lessons on fractions by talking about the different ways that students learn: some are auditory, some are visual, some are kinesthetic, some like to discuss what they know, etc. All I can say is that it works. Students get to understand the why of fractions and not just memorize the how of fractions. Hope this helps, 

