Fraction
Circles
Equal-sized circles divided into equal parts for comparing fractions of the same whole.
What
they teach.
Simple materials.
Powerful mathematical ideas.
Equal parts
Check that every piece in a named fraction family has the same area.
Equivalence
Cover the same region with different combinations of pieces.
Fraction addition
Join parts within a fixed whole and describe the combined amount.
How to use them.
Start with curiosity. Make room for discovery.
Set out the whole
Use one full circle as the reference. Compare every fraction piece with that same whole.
Cover and compare
Place two quarter pieces over a half-circle region. Check the boundaries match.
Name the amount
Say both the number of pieces and the size of each: two one-quarter pieces make one half.
Try an activity
Show one half three ways
Make one half of a circle using halves, quarters, and sixths. Sketch each arrangement and write an equality connecting the three representations.
Compare like wholes
One half of a large circle can be larger than one half of a small circle. To compare fractions as numbers with these pieces, hold the whole constant. Circle diameter is part of the setup, not a decorative detail.
A common mistake is to say that a sixth is larger than a third because six is greater than three. Place one of each piece within the same whole and ask what the denominator counts: the number of equal parts into which that whole was divided.
The circle model makes parts of a whole visible, but it is not the only fraction model worth using. Put the same values on a number line to connect the pieces to distances from zero and to numbers greater than one.
Choose your toolkit.
Find a format that fits your setting.
Choose a set whose circles share the same diameter and include repeated pieces of the denominators you need. Decide whether printed labels support the task or give away the comparison.
Physical options link to Amazon. Illustrations show the material, not the exact product.
Physical option · magnetic foam
Stochastic Box Magnetic Fraction Circles (51 pieces)
Fifty-one magnetic circle pieces model a whole, halves, thirds, fourths, fifths, sixths, eighths, tenths, and twelfths for comparing and composing fractions.
View on AmazonPhysical option · wood
D-FantiX Wooden Fraction Circles & Tiles Set
A wooden fraction kit with 60 fraction pieces, an operating board, three comparison-symbol blocks, and 36 double-sided activity cards. Includes a dry-erase marker and storage bag for building and comparing fractions.
View on Amazon
Digital alternative
Manipulatives app
The circle view gives equal parts a common whole. Ask which pieces cover the same amount, then connect the comparison to written fractions.
Explore the appSee our editorial and buying policy. Reviewed .
Related tools.
Explore the library →Fraction Tiles
Equal-length wholes partitioned into fraction strips for comparing, composing, and ordering fractions.
Explore Pattern Blocks
Geometric pieces for building shapes, exploring symmetry, and comparing parts of a whole.
Number Lines
Lines with equal unit spacing for locating numbers, comparing distance, and representing operations.
Explore