What do the three tile types represent?

A unit tile represents 1, a rectangular tile represents x and a square tile represents x². Every tile has a printed positive or negative sign as well as a color. The summary adds those signed integer coefficients. Three positive x tiles and two negative x tiles produce x. The pixel dimensions are illustrative; the model does not assume that x is a positive physical length.

How do zero pairs cancel?

A positive and negative tile of the same type add to zero. Cancel zero pairs removes matching pairs only on the active mat and within the same group name. Ungrouped tiles match other ungrouped tiles. Tiles with different powers, sides or group names are not paired. Cancellation preserves the exact polynomial counts.

Does this solve an equation for x?

No. The tool shows both polynomials and their difference. If the coefficient difference is zero, both sides are the same polynomial for every x. Otherwise the equation may hold for particular values, but this workspace does not solve for them. Adding or removing the same signed tiles on both sides preserves their difference. A symmetric removal is refused without changing either side when one side lacks enough matching tiles.

Can I arrange tiles without dragging?

Yes. Focus a tile and use arrow keys to move it one pixel, or Shift plus an arrow to move ten. Enter or Space toggles selection. The complete tile list provides checkboxes, and Selected x and Selected y move the first selected tile to an exact position. Same-side grouped tiles move together. Flip, rotation, grouping and side edits apply to the selected tiles only. Pan mat enables touch scrolling instead of dragging.

What can I enter as a target expression?

Use signed integer terms in 1, x and x², for example 2x² - 3x + 1. Each combined coefficient is bounded to magnitude 240. Parentheses, fractions, decimals, other powers and function calls are unsupported. Targets compare exact coefficients without changing the tile model. Apply title and targets before including those edits in an export.

What does saving or printing preserve?

Project JSON retains every tile identity, sign, type, side, position, rotation and group, along with the title and targets. Import validates the complete project before replacing the current model. SVG and print show all tiles in their actual positions, so deliberately overlapping tiles remain overlapping. The complete text report lists every tile. Browser storage remembers valid edited models on this device when available; Undo keeps 30 local revisions.

How large can a model be?

A project supports up to 240 tiles across two 1000 by 620 pixel mats and up to 100,000 JSON characters. Add 1 to 20 tiles at a time. New tiles reuse grid positions after 24 slots, so larger models may need arranging. Movement outside a mat is refused without clamping or losing tiles. The scrolling mats keep individual tiles at a usable touch size on smaller screens.

Algebra Tiles

Arrange positive and negative unit, x and x² tiles on a free expression mat or two equation sides. Read exact integer coefficients as you add tiles, cancel matching zero pairs, group pieces and change their positions. Apply the same addition or removal to both sides atomically, compare optional targets, and keep the complete model in a printable drawing or editable JSON project.

Build with + and − tiles. Color supports the printed sign. The tile lengths illustrate powers of x and do not assign x a measured value.

Tile typeSignActive matNumber of tiles (1 to 20)

Expression mat

Each mat scrolls and keeps tiles at usable touch size. Drag, use arrow keys (Shift for 10 pixels), or enter a position. Grouped tiles on the same side move together. New tiles reuse grid positions after 24 slots; overlap is allowed. Every tile remains listed below.

Selection and groups

No tiles yet.

Selected: 0. Position uses the first selected tile; the movement carries its group. Flip, rotate, side and group edits affect the selected tiles only.

Selected xSelected y

Group name (up to 32 characters)

Title and optional targets

Model titleLeft target expression

Use integer terms in 1, x and x². Targets are optional and compared by exact coefficients. Title/target drafts are applied explicitly; exports always contain the current applied model.

Add a tile to start a model. Positive and negative tiles are distinguished by their sign and color.

Expression: 0

Actual tiles: 0 / 240

Complete model report and project

Every tile and exact counts

Algebra tile model
0
Integer polynomial counts from the actual tiles.
Models bounded integer-coefficient quadratic expressions; not an unrestricted symbolic solver. Tile pixel lengths are illustrative and x need not be a positive measured length.

Complete applied project JSON

{
  "version": 1,
  "mode": "expression",
  "title": "Algebra tile model",
  "tiles": [],
  "nextId": 1,
  "targetLeft": "",
  "targetRight": ""
}

Import a project JSON

Project JSON to import

Projects stay on this device when browser storage is available. A project holds up to 240 tiles and 100,000 JSON characters; Undo retains 30 models. Zero pairs match type, side and group. A symmetric removal requires sufficient matching tiles on both sides and otherwise changes neither side.

Accuracy. Models bounded integer-coefficient quadratic expressions; not an unrestricted symbolic solver. Tile pixel lengths are illustrative and x need not be a positive measured length.

Algebra tile model

Left: 0

Models bounded integer-coefficient quadratic expressions; not an unrestricted symbolic solver. Tile pixel lengths are illustrative and x need not be a positive measured length.

Common questions

What do the three tile types represent?: A unit tile represents 1, a rectangular tile represents x and a square tile represents x². Every tile has a printed positive or negative sign as well as a color. The summary adds those signed integer coefficients. Three positive x tiles and two negative x tiles produce x. The pixel dimensions are illustrative; the model does not assume that x is a positive physical length.
How do zero pairs cancel?: A positive and negative tile of the same type add to zero. Cancel zero pairs removes matching pairs only on the active mat and within the same group name. Ungrouped tiles match other ungrouped tiles. Tiles with different powers, sides or group names are not paired. Cancellation preserves the exact polynomial counts.
Does this solve an equation for x?: No. The tool shows both polynomials and their difference. If the coefficient difference is zero, both sides are the same polynomial for every x. Otherwise the equation may hold for particular values, but this workspace does not solve for them. Adding or removing the same signed tiles on both sides preserves their difference. A symmetric removal is refused without changing either side when one side lacks enough matching tiles.
Can I arrange tiles without dragging?: Yes. Focus a tile and use arrow keys to move it one pixel, or Shift plus an arrow to move ten. Enter or Space toggles selection. The complete tile list provides checkboxes, and Selected x and Selected y move the first selected tile to an exact position. Same-side grouped tiles move together. Flip, rotation, grouping and side edits apply to the selected tiles only. Pan mat enables touch scrolling instead of dragging.
What can I enter as a target expression?: Use signed integer terms in 1, x and x², for example 2x² - 3x + 1. Each combined coefficient is bounded to magnitude 240. Parentheses, fractions, decimals, other powers and function calls are unsupported. Targets compare exact coefficients without changing the tile model. Apply title and targets before including those edits in an export.
What does saving or printing preserve?: Project JSON retains every tile identity, sign, type, side, position, rotation and group, along with the title and targets. Import validates the complete project before replacing the current model. SVG and print show all tiles in their actual positions, so deliberately overlapping tiles remain overlapping. The complete text report lists every tile. Browser storage remembers valid edited models on this device when available; Undo keeps 30 local revisions.
How large can a model be?: A project supports up to 240 tiles across two 1000 by 620 pixel mats and up to 100,000 JSON characters. Add 1 to 20 tiles at a time. New tiles reuse grid positions after 24 slots, so larger models may need arranging. Movement outside a mat is refused without clamping or losing tiles. The scrolling mats keep individual tiles at a usable touch size on smaller screens.

Models bounded integer-coefficient quadratic expressions; not an unrestricted symbolic solver. Tile pixel lengths are illustrative and x need not be a positive measured length.