Bar Models (Whole)
A bar model represents numbers as lengths, making it easy to see how they compare, combine and break apart. This tool builds bar models on a number line, so every bar is anchored to a real value — a powerful way to reason about whole numbers, addition, multiplication, factors and multiples. 🧱
Build models freely by hand, or let one of the three automatic modes do the work: explore the LCM of two or three numbers, break a number into its factors, or split it into addition number bonds.
How to Use
Tab Navigation
Switch between manual building and the three automatic modes:
- Build: Create bars by hand or straight from a calculation.
- LCM: Find the LCM of two or three numbers.
- Factors: Break a number into rows of equal bars, one row per factor.
- Addition: Split a number into the pairs that add to make it.
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 the bar — its value snaps to whole numbers on the line.
- 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 in two at a whole-number mark.
- Stapler: Drop the stapler between two touching bars to join them into one.
- 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.
🧱 Build
The Build tab is an open canvas for composing and comparing bars.
To add a single bar, enter a Value and the Row it should sit in, then press Add bar.
To build straight from a calculation, enter two numbers and choose + or ×, then press Build Bar Model. Addition lays the two numbers side by side; multiplication makes the first number of equal bars of the second — a clear picture of repeated addition. Press Swap to reverse the numbers and compare, for example, 3 × 5 with 5 × 3.
🔗 LCM
The LCM tab shows why two or three numbers eventually “meet”.
Enter your numbers in the first, second and third boxes — each becomes a repeating bar in its own row. Press Find LCM and watch each row extend, copy by copy, until they line up at the same length. That meeting point, marked on the number line, is the LCM — the smallest number that every one of them divides into.
✖️ Factors
The Factors tab reveals how a number can be built from equal groups.
Enter a Number — or drag a bar into the bottom row — to set the value bar. Each press of Next factor drops in a new row of equal bars for the next factor; for 12 you’ll see rows of 1, 2, 3, 4 and 6, every one filling the same length. Use Order to reveal the factors increasing, decreasing, or as product pairs (each factor beside its partner).
Turn on Show count to float a running tally (1, 2, 3 …) above the bars as a row lands, so you can count how many of that factor make the number. Once every factor is shown, the Number Type reveal tells you whether the number is the unit, prime, a square, or composite.
➕ Addition
The Addition tab breaks a number into number bonds — the pairs that add to make it.
Enter a Number, then press Next bond to drop one part at a time: the first part, then the part that completes the row. Choose the Order the bonds appear in — increasing, decreasing, or from the middle. Turn on Commutative to also show each bond reversed (b + a) on its own row, a neat way to see that changing the order doesn’t change the total.