Sorting fractions is a great way to help students apply and solidify their understandings of 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.)

(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).

Tell me what you think!

This lesson and materials are part of my Equivalent & Comparing Fractions math unit (4.NF.1-2).

Tell me what you think!

Click here to take a 2 minute survey and share your thoughts on teaching fractions.