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Activities & Lesson Ideas
Dividing Fractions Lesson
Webmaster note: Love the hands-on approach to teaching division of fractions! Thanks for sharing, Matt!
Teaching Division of Fractions
Submitted by Matt from Cincinatti, Ohio and Taiwan
Fraction Skittles (Not Skittles like you eat. Skittles are a manipulative teaching tool. See a picture here.) This material has 4 "skittles." The first one is a whole one and cannot be separated. The 2nd one is cut in half. The 3rd in thirds and the 4th in fourths.
Fraction insets (See a picture here.) These are 10 circles. The first one is not cut at all (it is a whole circle). The 2nd one is cut in halves, the 3rd in thirds, and so on all the way up to ten.
There are many things that can be done with these from just general exploration to high concepts of math. I am going to explain the division of fractions. It is not clear to many adults why we flip the 2nd fraction and multiply. With these two tools, it becomes obvious.
Let's assume the problem is 2/9 divided by 1/3. We take the 1/3 of the fraction skittle and set it down. We then have to give this 2/9, so we take 2 of the 9th pieces and set them down. The question in division always becomes "how much does each one get?" We know that 1/3 is not 1. So we investigate what we need to do to make it one. The obvious answer is to get the other two skittle pieces. The child can put them together to confirm that it makes one, then set them next to each other. "If he has 2/9 (pointing to the original one), what does he need? (pointing to one of the new ones)" The child will put down 2/9 under each one. "Now, let's put them together to see how much we have." When the child puts them together, thus creating one of the skittles, then puts the insets together, thus creating 6/9. By this time, the child has already worked with these materials enough to recognize that shape as 2/3. If they do not, it is ok at first, as there is plenty of time to work with that later. But it should be as simple at this point of just saying, "What can we change that for?" since they've already done an exchange work. They will put 3 of the 9 insets away and get 1 of the 3 insets. They will do this until they are left with its simplified version of 2/3