Donna has been a teacher, math instructional coach, interventionist, and curriculum coordinator. A frequent speaker at state and national conferences, she shares her love for math with a worldwide audience through her website, Math Coach’s Corner. Donna is also the co-author of Guided Math Workshop.

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 backside, 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?

Grab your freebie here, and here’s what I’d suggest you do. Try them yourself!! See how good your fraction number sense is. Just in case that makes you nervous, there is an answer key in the file.

TheElementary MathManiac
on December 6, 2013 at 12:58 pm

Love this! I had no idea how many ways you could compare fractions until I read a great book called A Focus on Fractions: Bringing Research into the Classroom. I guess I was taught how to compare fractions with a common denominator way to soon because I was an adult before I knew there was a different way. We do so much more service to kids if we let them develop some of these strategies on their own before jumping in and teaching algorithms.

Thank you, that was great! I never thought about having a “sequence” during the mental checklist. I never really thought about other strategies until I became a teacher either. As I was completing the worksheet, I found myself using a few other strategies. On #9, I compared using 1 as a benchmark. On #10, I simplified 2/8 to 1/4 then compared with a common numerator. I will definitely use this when we get to fractions though, last year I didn’t find a lot of resources with these ‘other’ strategies, so this will be great.

My partner and I did this last week and we LOOOVED it. Such a great visual and we are ALL ABOUT taking different routes/strategies. Keep up the older level math – it’s hard to find quality things like this! A BIG THANK YOU! 🙂

I have taught these strategies to my students, but was having trouble finding a resource that presented each strategy together. This is so clear and easy to use. Thank you!

Donna, I’ve used this for several years and absolutely love it! I was just wondering if you’ve done an updated version that includes some of the other strategies you’ve talked about in your blog, such as one unit fraction from a whole or finding a common numerator.
Thank you so much for all the wonderful ideas and freebies you share!

Hey, Tami! Glad you have found this activity helpful. No, I haven’t created and updated version, but that sure is a good idea. Maybe once back to school calms down I could do one.

Love this! I had no idea how many ways you could compare fractions until I read a great book called A Focus on Fractions: Bringing Research into the Classroom. I guess I was taught how to compare fractions with a common denominator way to soon because I was an adult before I knew there was a different way. We do so much more service to kids if we let them develop some of these strategies on their own before jumping in and teaching algorithms.

Thank you! This is just in time for my Intervention kids!

Thank you, that was great! I never thought about having a “sequence” during the mental checklist. I never really thought about other strategies until I became a teacher either. As I was completing the worksheet, I found myself using a few other strategies. On #9, I compared using 1 as a benchmark. On #10, I simplified 2/8 to 1/4 then compared with a common numerator. I will definitely use this when we get to fractions though, last year I didn’t find a lot of resources with these ‘other’ strategies, so this will be great.

My partner and I did this last week and we LOOOVED it. Such a great visual and we are ALL ABOUT taking different routes/strategies. Keep up the older level math – it’s hard to find quality things like this! A BIG THANK YOU! 🙂

I have taught these strategies to my students, but was having trouble finding a resource that presented each strategy together. This is so clear and easy to use. Thank you!

Donna, I’ve used this for several years and absolutely love it! I was just wondering if you’ve done an updated version that includes some of the other strategies you’ve talked about in your blog, such as one unit fraction from a whole or finding a common numerator.

Thank you so much for all the wonderful ideas and freebies you share!

Hey, Tami! Glad you have found this activity helpful. No, I haven’t created and updated version, but that sure is a good idea. Maybe once back to school calms down I could do one.