This is a post I made on my teaching blog last year. I am putting it here, because I am beginning to show the class this simple and easy way to find equivalent fractions. It is a good way to check and work with fractions as student learn to understand this tricky topic. Not many people know or use this easy way to work with fractions. This is how I wrote it for teachers.
This is one of my favorite math tricks that can really help your students as they try to understand how to work with equivalent fractions. I learned it at a workshop a couple years ago and have yet to meet a teacher who previously used or was aware of how simple this chart is to help students.
Many simple equivalent fractions (most of the ones used in upper elementary years) are easy to find on a regular multiplication chart. I feel it is very helpful to point this out to your students. Many students struggle as they try to learn the many steps that it takes to find equivalent fractions. When you look left to right on the chart you are viewing the multiples of a number. When you view two different rows of multiplies you are viewing equivalent fractions.
For example using the 1's and 2's. Look at the two rows as if they were fractions.
1/2 = 2/4 = 3/6 = 4/8 and so on. You can split rows apart. Look at the rows for 1's and 3's. 1/3 = 2/6 = 3/9 = 4/12 and so on. To show how the chart works with my class I use an overhead projector and circle the numbers to make them easy to locate. To find 1/5 = ? / 30 I circle the 1 and the 5 underneath it on the ones column on the chart. Then I move my finger from the 5 until I get to the number 30 and circle that. I can block out or just cross out other numbers to make it clearer. Then I follow the 1 across and the 30 up until they meet at the number 6. and circle that. If you do it correctly the circles will form a square or rectangle.
Of course, as the students understand how to work the chart, teach them the other ways of finding equivalent fractions. It makes it much easier for them, however, to "see" the equivalent fractions for a number and the students even start memorizing the most common equivalent fractions.
Now for the most important part. When students take a test they usually cannot use a printed multiplication chart. So what! Train them on how to make a multiplication chart from their facts and have them practice often. Then at test time, they can reproduce the chart onto their test before starting the work. It should take less than 5 minutes. Not only can they use the chart for checking fraction, but they can use it as they do multiplication and division problems too! No it is not cheating. It is about being smart, observant, and prepared!
Do play around with the chart on your own. I didn't believe it would work that simply until I practiced with it and used it with my class. There are some other tips and techniques that you can quickly figure out on your own that even make using the chart easier.