Sorting fractions is a great way to help students apply and solidify their understandings of fractions, especially comparing, ordering, and finding equivalent fractions. It’s a fairly straightforward, simple activity that allows for a lot of really good, higher order thinking and reasoning.

How to do a fraction sort:

1. Decide on the categories. Start with ‘between zero and one half,’ ‘equal to one half,’ and ‘between one half and one whole.’ Add in ‘equal to zero,’ ‘equal to one,’ and ‘greater than one’ as needed.(This is also a great opportunity for differentiation. Stronger students can have more refined categories- dividing by fourths or even eighths, and going above one and including improper fractions and mixed numbers.

2. Make cards for each category.

(To differentiate, make more or fewer cards, or make the cards more or less obvious- eg. 99/100 is more obviously close to 1 than is 77/99.)

3. Have the students sort the cards into the categories. This is a great center or partner activity, and is a wonderful opportunity for rich discussion.

4. Share and discuss the sorts.Misconceptions about fractions tend to be revealed here, and provide an opportunity for reteaching and discussion. It’s also a good chance for students to share their strategies and verbalize their thinking. (Hopefully, some minor ‘arguments’ will arise and allow students to ‘convince’ the other person!)

5. Have the students choose one card to write about and explain how and why they chose the category for that card. Have them use visual models and justify their responses. This works great as an assessment or portfolio piece- you can even assign the students a new (differentiated) fraction that hasn’t yet been sorted, to see how well they can individually apply what they have learned.

Why to do a fraction sort:

-helps with estimating and judging whether or not a response is reasonable

-helps solidify understandings about fraction benchmarks and how fractions are ordered from zero to one

-helps develop fraction on a number concepts, which are needed for measuring to the fraction of an inch

-provides practice and application with equivalent fractions, comparing fractions, and ordering fractions

-reveals misconceptions about basic understandings of fractions, their size, and how they are compared and ordered

-explaining and writing about their decisions helps students organize their thinking, and communicate using visual models and explanations

What to look for when students are sorting, sharing, and explaining:

-reasoning based on the relationship between the numerator and denominator

-reasoning based on not only how BIG the numerator is, but also based on the size of the missing piece needed to make a whole. (eg., 9/10 is close to one because there’s only 1/10 missing, and 1/10 is a small piece.)

-identifying equivalent fractions and using that information to help make decisions. (eg., 6/10 is equal to 3/5, so it’s between one half and one whole.)

-ability to clearly explain the thinking and strategy behind why they put a card in a certain category.

-reasoning based on using benchmarks. (eg., 5/10 is equal to half, so 6/10 is more than half)

-using critical thinking and asking good questions

-making sure they agree with their partner’s or group’s sorting decisions

-drawing visual models to clarify, verify, or explain their thinking

Happy (Fraction Sorting &) Teaching!!

Christine Cadalzo

This lesson and materials are part of my

Equivalent & Comparing Fractions math unit (4.NF.1-2).