Does anyone have any hands-on activities to teach finding common denominators for adding fractions? Also for teaching reducing fractions?
Although it's really very simple, I have found color coding to help some students. You have them use one color for the numerator and one for the denominator. This helps to remind them what they are adding. They know they can add one color, but not the other, for example.
There is a commercial variety of what timbrady talks about called "Pizza Math" which is worth the investment. It has cardboard, realistic looking pizzas divided into pieces from 2 to 16.
I really like the plastic fraction towers. It is very visual and hand-on, and if you get the accompanying percent and decimal sets, they are all color-coded the same way (ie, green for 1/5, 20%, and .20 sized pieces) I have also just figured out that if I write on the back of the percent and decimal pieces w/dry erase markers, I can use them as "extra" fraction pieces, which has REALLY helped w/ improper fractions and mixed numbers. The sets only have enough pieces to add up to one whole, each.
You can cut two pie shapped pieces of wood into different size pieces (4 eights, 2 quarters and 2 halves) and then use them to show that you can only add pieces if they fit totally on top of each other (eg. you can't directly add 8ths and quarters). Then you can show that 2 8ths cover a quarter, and that, if you mentally break up the quarters into its 2 8ths components, you can then all them up because they all "fit" on top of each other. You can do the same thing with the quarter and the halves. Students catch on pretty quickly that you have to have all the pieces in the smallest unit's "size" to add them --- and they have arrived at the concept of the least common denominator. Since they also learn that there are 2 8ths in a quarter, they're well on their way to understanding reducing fractions.
I hope this make sense ... as I read through it, the numbers/words thing can get confusing ... but it works great :)
Reducing Fractions: Ex1: Reduce 4/6 means 4 group of 1 out of 6 groups of 1 model with tiles(let a=1 tile) Here's the model
(a)(a)(a)(a) / (a)(a)(a)(a)(a)(a) --> 4*1/6*1. What are the largest groups that you can make with more than one square with 4 and 6?
(aa)(aa) / (aa)(aa)(aa) --> 2 groups of 2 out of 3 groups of 2
Explanation: 4 groups of 1 out of 6 groups of 1 is the same as 2 groups of 2 out of 3 groups of 2. That is,
4 out of 6 is = to 2 out 3. The largest group possible was of two elements. Therefore, 2 is the gcf of 4 and 6. I hope this helps.
say 1/2 + 1/3 use square tiles. Let a=square. Then, 1/2 is a/aa and 1/3 is a/aaa. Repeat the fracions until the denominator are the same as shown:
1/2: a/aa a/aa a/aa this becomes-->aaa/aaaaaa-> 3/6
1/3: a/aaa a/aaa this becomes aa/aaaaaa --> 2/6. Now,
put them together to get aaaaa/aaaaaa----->5/6!
so 1/2 + 1/3 = 5/6. I hope this helps.
Can be introduced the concept of eating fractions:
- first of all, establish the concept of the denominator as being the total number of equal parts and the concept of numerator which is the part of the whole group.
- spill out some different colours candies onto a desk (20 of them should be enough).
- call a student to count the total number of the candies and write down this number on the board. Explain that this number will be the denominator because it is the "whole".
- create a chart on the board listing the various colors. These will become the numerator values because they are the parts of the "whole."
- call another student to count the total number of each color candies out of the total. Write that number on the chart next to that color.
-do this job until all the colors have been counted and the chart is completley filled in.
- show to students the manner of creating fractions from this chart.
- add all numerators together to show that all the parts are adding up to the whole.
A more economical way might be to use paper plates--each student gets two so that one can be cut, the other to be used as the comparison.
I found that cooking projects work well, but that is hard to manage with larger groups and/or lack of kitchen space.
Middle school students find Danika (her last name escapes me at the moment--she was the actress on the tv show the Wonder Years and has a degree in Mathematics) called "Math Doesn't Suck" is an especially useful resource.