Leo and I were discussing the problem 5 ÷ 1 1/2. As we worked together, we came up with 2 solutions, both of which were correct! Read the new section I added and make sure you show this to your students: it will enhance both their understanding of division AND fractions!
AS OF FEBRUARY 10TH, 2014, THIS PRODUCT NOW HAS 58% MORE CONTENT!
If you're developing products for TpT or teaching dividing fractions, I can guarantee you're most likely doing it wrong. Yes, I'm talking to you. You think you aren't? Take my word for it: I've worked on fractions for a long, long time and this is the sum of 30 years of work in this field.
I was once like you: I modeled a few problems, maybe with a pie and then I galloped off to the "invert and multiply" method, but all along I knew I was fooling myself and communicating all the wrong things to children. I spent a lot of time thinking about what division meant, then I spent a lot of time thinking about what fractions meant, then I thought about the two together, and then I finally came up with answers. 6 to be exact.
If you are teaching fractions, or you are going to be developing activities for other TpT teachers involving dividing fractions, you must, MUST read this first. It will set you straight when it comes to using models, creating excellent word problems and understanding the "secrets" of dividing fractions. Believe me, you'll think about dividing fractions completely differently after consulting this guide.
This document is 12 pages long (actually, it's now 19 pages long!). Here's what you'll learn from reading it and following my recommendations:
1) How to build a "good" model that explains dividing fractions.
2) How a small change in notation can increase comprehension dramatically.
3) How to write a "realistic" word problem
4) What does it mean to "invert and multiply"
5) Why denominators are so important when dividing fractions (and what you can do about them)
6) How and why you should connect division of fractions to something that your students are much more familiar with.
I seriously guarantee that you will be a much better teacher of this topic after reading these recommendations carefully and following them. I have curriculum materials that will be issued soon, but in the meantime, read this and follow it before you make another attempt to teach or write curriculum materials about dividing fractions.
I am not putting up a preview or thumbnails because the thumbnails will not be detailed enough for you to preview, and a preview will not make sense. After reading this guide, you will probably know more about dividing fractions than most math specialists and even mathematicians.
• A "conversation starter" to use in your class to distinguish between "small into big" and "big into small" when dividing fractions.
• The "Chicken and Egg" problem, which, when solved using the most efficient method, requires your students to solve 1 ÷ 1 1/2, and some ways to explain it to them.
• A "Search and Solve" activity sheet where your students look for "shortcut" solutions to fraction division problems; it also includes an answer sheet, as well as "word problem" extension.
MORE TO COME, BUT GET IT NOW!
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