You might say this blog post is the third in a series on fractions and number sense. It’s not surprising that the majority of our upper elementary kiddos lack number sense when it comes to fractions. Don’t believe me? Conduct a survey and ask students which fraction is larger, 1/8 or 1/4. Many (most?) will say 1/8, because in the world of whole numbers, 8 is bigger than 4. If you change the question slightly and ask if they’d rather have 1/8 of a pizza or 1/4, they might fare better because they can now create a visual of what the fraction means. If you’d like to know about building general fraction number sense, I suggest you read this post about candy bars and halfness.
About a year ago, I wrote another blog post about using multiple strategies to compare fractions. The answer is NOT cross multiplying or the ‘butterfly’ method! I’d suggest you hop over and read the post and grab a free poster showing the different strategies.
So, earlier this week I was planning with my 5th grade team, and they wanted something they could use to have the kiddos practice the different strategies. We brainstormed and came up with what you see below. When I created the sheet, I carefully chose the fractions I used so each pair lends itself to a particular strategy. There’s a back side, too, so there are ten problems in all.
The order of the strategies I listed on the right side is also intentional. This is really the mental list, in order, that our kiddos should go through when they are comparing fractions–kind of like a flowchart.
Are the denominators the same? No. (move down the list)
Are the numerators the same? No. (move down the list)
What is their relationship to 1/2? Hmmm, one is greater than 1/2 and the other is less than 1/2. Bingo!
I mean, really, why find common denominators if there’s a more efficient, number sense based, option?