Bar Models (Fractions)
A bar model represents numbers as lengths, making it easy to see how they compare, combine and break apart. This tool builds bars that are fractions of a whole, anchored to a number line — so a fraction is never just a symbol, it is a length you can measure, cut and join. 🍰
Every bar knows its own numerator and denominator, so the labels are always exact and nothing is ever silently simplified. Build freely by hand, or use one of the three guided modes: count on in unit fractions, find the bonds that make a whole, or reveal equivalent fractions.
How to Use
Tab Navigation
- Build: Create fraction bars by hand.
- Counting: Count on, one unit fraction at a time.
- Bonds: Split a whole into two fraction parts.
- Equivalence: Show fractions that are different names for the same length.
The Base Fraction
The Denominator box sets the unit fraction new bars are made from — 2 gives halves, 5 gives fifths. It is available on every tab, and it controls two things: the size of any new bar you create, and how finely the number line is divided.
Crucially, changing it never alters bars already on screen. A 3/2 bar stays 3/2 when you switch to fifths; only what you make next changes. That means bars with different denominators can sit side by side — which is exactly what makes comparing and adding them interesting.
Turn on Mixed numbers to read every label as a whole and a part (5/3 becomes 1 2/3) instead of an improper fraction. This changes only how the numbers are written — the bars themselves do not move, and fractions are never reduced, so 2/4 stays 2/4 and does not become 1/2. A fraction worth exactly a whole number shows as one: 6/3 reads as 2.
Working with the Bars
These tools work on any tab, whichever mode you are in:
- Pull-out arrow: Drag the arrow at the top of the screen to the right to create a bar. The further you drag, the longer it grows — snapping one unit fraction at a time:
1/5,2/5,3/5… - Move & delete: Drag any bar to reposition it; a faint ghost shows where it will land. Drag a bar down into the number line to delete it, and the rest of its row closes the gap.
- Scissors ✂️: Drop the scissors on a bar to cut it at a fraction mark. The cut snaps to that bar’s own pieces, so a
3/2bar cuts at its halves into1/2and2/2— whatever the base fraction happens to be set to. - Stapler: Drop the stapler between two touching bars to add them together. The two bars do not need the same denominator: staple a
1/2to a1/3and you get5/6, worked out exactly. - Clone: Drop the clone tool on a bar to copy it alongside the original.
- Trash: Drop the trash tool into the bars to clear them all.
- Zoom & pan: Scroll the mouse wheel (or pinch with two fingers) over the number line to zoom in and out around the pointer. You can also drag up or down on the line to zoom, or left and right to pan. Every bar rescales to stay matched to the line, and you can zoom in far enough to work inside a single whole.
🧱 Build
The Build tab is an open canvas for composing and comparing fraction bars.
Enter a Value — how many unit fractions long the bar should be — and the Row it should sit in, then press Add bar. With the base fraction set to fifths, a value of 3 adds a 3/5 bar; each new bar is appended after whatever is already in that row.
Try building the same length two ways in two rows, or laying 1/2, 1/3 and 1/6 above each other to see how they stack up against the line.
🔢 Counting
The Counting tab counts forwards in unit fractions, one step at a time.
Each press of Count on adds a single unit-fraction bar to the row and steps the pointer along to the running total, shown above the bars. Read the total off the number line as you go: with quarters, three presses reads 3/4, and the fourth completes a whole.
The bars change colour at every whole, so a class can see the wholes forming as they count — the moment 4/4 becomes 1 and the count carries on past it into 5/4. This is the point where counting in fractions usually breaks down, and where the colour change and the number line together make it obvious.
Turn on Show count to float a tally (1, 2, 3 …) above each bar, so “three quarters” can be counted as three of something, not just read as a symbol. Switch on Mixed numbers to watch the total flip between 5/4 and 1 1/4.
Changing the base fraction starts the count again in the new unit.
➕ Bonds
The Bonds tab breaks a whole into fraction number bonds — the pairs of fractions that add to make it.
Enter how many Wholes to make; the target bar appears in the bottom row. Press Next bond to drop one part at a time: the first part on its own, then the part that completes the row. That pause is deliberate — it lets a class predict what is still needed before it falls into place.
With fifths and a target of 1, you’ll build 1/5 + 4/5, then 2/5 + 3/5. Choose the Order the bonds appear in — increasing, decreasing, or from the middle. Turn on Commutative to also show each bond reversed (4/5 + 1/5) on its own row, showing that the order doesn’t change the total.
Because the parts are counted in unit fractions, a target of 2 wholes in sevenths gives bonds like 3/7 + 11/7 — improper parts that still add to exactly 2.
🟰 Equivalence
The Equivalence tab shows why one length can have many names.
Enter a Numerator and Denominator to set the fraction you want to study. This is separate from the base fraction — you can explore equivalents of 2/3 while the rest of the field still snaps in fifths. Each press of Next equivalent adds the next one: 1/2, then 2/4, 3/6, 4/8 …
Every row ends on the same dashed guide line. The lengths are identical; only the number of pieces changes. That is the whole idea of equivalence in one picture — and it is why nothing here is ever simplified: 2/4 is shown as a real, distinct way of naming the same length, not as an error to be corrected.
Turn on Show pieces to mark each bar into its own unit-fraction pieces: one piece in the 1/2 row, two in 2/4, three in 3/6. The marks are exactly where the scissors will cut, so you can slice a row apart along them. Zoom out far enough and the finest marks step aside rather than crowd together.
Try a fraction bigger than one, such as 3/2, to see equivalence work above a whole as well.
Related Activities
- Bar Models (Whole) — the same number line and the same pull-out, cut, join and clone tools, but every bar is a whole number. Use it to explore LCM, factors and number bonds before moving on to fractions.