Comparing fractions, when you look at just the numbers, can be deceiving. For example, which fraction do you think is bigger: 1/2 or 1/16. Most of the third graders informed me that 1/16 is bigger than 1/2. “Explain your thinking,” I prompted. “Because the number is so much bigger!”
Thus, I began our lesson on ordering fractions with a challenge to list their fractions from biggest to smallest. “Do you see a pattern?” I asked. With a little guidance, the third graders learned to see that the smaller the bottom number (aka the denominator), the bigger the fraction.
The Magical Minds explored this concept further by comparing two fractions using < , > , or = signs. I asked them to complete this activity sheet, from the NCTM Illuminations lesson that informed this learning experience.
Having compared two fractions, the Magical Minds were ready to look at a set of three fractions. I asked them to order their fractions on the activity sheet from least to greatest. The relationships between fractions is much easier to see when you are using fraction strips.