# Fraction Circles

Canonical: https://manipulatives.org/manipulatives/fraction-circles/

Equal-sized circles divided into equal parts for comparing fractions of the same whole.

![A circle assembled from colored equal fractional sectors](https://manipulatives.org/_astro/fraction-circles.i8iNXNn_.svg)

Published: 2026-10-09
Reviewed: 2026-10-09

Topics: fractions, operations

## What they teach

### 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

1. **Set out the whole.** Use one full circle as the reference. Compare every fraction piece with that same whole.

2. **Cover and compare.** Place two quarter pieces over a half-circle region. Check the boundaries match.

3. **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](https://manipulatives.org/manipulatives/number-lines/) to connect the pieces to distances from zero and to numbers greater than one.

## Choose your toolkit

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.

- [Stochastic Box Magnetic Fraction Circles (51 pieces)](https://www.amazon.com/dp/B0BB366X8Z) — Fifty-one magnetic circle pieces model a whole, halves, thirds, fourths, fifths, sixths, eighths, tenths, and twelfths for comparing and composing fractions.

- [D-FantiX Wooden Fraction Circles & Tiles Set](https://www.amazon.com/dp/B0F2FRW6H9) — 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.

### 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 app](https://apps.apple.com/us/app/manipulatives-hands-on-math/id6780701668)

## Related tools

- [Fraction Tiles](https://manipulatives.org/manipulatives/fraction-tiles/)
- [Pattern Blocks](https://manipulatives.org/manipulatives/pattern-blocks/)
- [Number Lines](https://manipulatives.org/manipulatives/number-lines/)