Equivalent Fractions

Almost a half century ago, my teacher taught a math lesson that I still remember today. We were learning how to add and subtract fractions, and she explained how to make equivalent fractions in order to have a common denominator. She started by asking us to multiply 1/2 by 1, 3/4 by 1, 5/6 by 1, etc. Then she wrote several names for 1 on the board - 2/2, 6/6, 10/10, etc. She explained that we could multiply the numerator and denominator by the same number without changing the value of the fraction because we were really multiplying by 1. I realize now that she was teaching us both the how and why in math, and I think that is why I still remember the lesson and have been able to manipulate fractions ever since.

Whenever I help students learn to make equivalent fractions, I always try to replicate my teacher's lesson. This week, I came across a great visual in a Wikiversity article and decided to make a laminated version on 4 x 6 cards, so students could use them with dry erase markers. I think this will help them understand what they are doing and why they are doing it.

February 2011 - Last week I started making the cards reversible by changing from multiplication to division, so they can also be used to reduce fractions to lowest terms by dividing by a form of one. Students have had very positive responses to these cards.