Welcome back for part 2 of comparing fraction strategies and activities. Click here if you missed part 1!
In part 1, we talked about using food as a fun introduction to comparing fractions. From here, let’s move into using fraction tiles (or other concrete fraction manipulatives) to compare fractions. I choose comparisons that guide us gradually through these 6 strategies, starting with the least complex to the most complex. Click the link to grab the strategies for Comparing Fractions Poster.
Usually at this point students can quickly compare fractions with similar numerators or denominators. In Texas, students learn this in third, so by the time they get to fourth this should be review. And with yesterday’s food lesson, they very well remember that a bigger denominator actually means smaller pieces, and vice versa!
Comparing Fractions Strategy – Connecting Concrete to Representational
While using fraction tiles, we have to be intentional about connecting this to representation or pictorial models of fractions. The two representations (concrete and pictorial) have to overlap! Brittany’s mats make this super doable! We build the fractions using tiles, then we represent the fraction as an area model or on a number line before completing our comparison. These mats are part of the resources available through Mix and Math 360.
After working with tiles and models for a bit, I will start having students make predictions and justify their thinking before building or drawing the fractions. This is where we really get into our strategies for comparing fractions and start moving into abstract thinking. So, for instance when comparing 3/4 and 2/6, I might expect students to say something along the lines of “3/4 is greater than a half and 2/6 is less than a half, so I think 3/4 is the greater fraction.” Then we will build and/or draw the fraction to prove our thinking.
In my experience, comparing fractions is a skill that takes students the longest to master abstractly. It is important as we help students along in this that we provide them with various tools and strategies, as well as opportunities to practice. I will constantly refer back to our food activity, grab a set of fraction tiles, or quick sketch a number line in order to help students truly understand fraction sizes.
When in doubt, common denominator…it out?
As fraction comparisons start to become more challenging and trickier (i.e. comparing 4/5 and 5/6 or 11/20 and 6/10), we want to continue pushing students in their thinking about fraction sizes. We also want to equip them with a variety of strategies. I always have students start by deciding what benchmark fraction (0,1/2,1) each fraction is close to. In the examples above, 4/5 and 5/6 are both close to a 1. Both 11/20 and 6/10 are both close to a half. This makes them tricky to compare. When starting out I will often talk to students and demonstrate on a number line how we can look at how close to a whole or a half each fraction is. This can be a tricky concept and really requires some high-level thinking.
I also teach students to find a common denominator when two fractions are close in size. This works out super nicely when one denominator can be changed to match the other. But in some cases, both fractions will need to be changed. We practice this A LOT! Once we learn this skill, we will continue to use our knowledge of fraction sizes and benchmark fractions to compare fractions. Then will use common denominators as a way of checking our answer, especially when we know two fractions are very close in size.
My go to activity for students to practice any skill is with a math maze. I love that they are self-correcting and can be easily differentiated for different levels of students. For comparing fractions, I like to provide students with three different levels to choose from. The first has models on the page with more simple comparisons that have a common numerator or common denominator. This can be paired with fraction tiles as well. The second “level” would be the 4th grade maze but accompanied by fraction tiles, printed fraction tiles/number lines, or some other type of support. The most challenging would be the 4th grade maze but without any of the previously listed supports.
Comparing fractions is something we have to circle back to and review as the year goes on. I use these additional would you rather questions to review this concept later on in the year. This resource uses fun…and sometimes gross scenarios to engage students in comparing fractions.