Virtual algebra tiles

What algebra tiles show

Algebra tiles stand for parts of an expression. The big square is x² (it is x long and x wide), the long rectangle is x (x long and 1 wide) and the small square is 1. Blue, green and yellow tiles are positive; red tiles are negative. Add tiles with the buttons, drag them around the mat, and drop a tile on its opposite to make a zero pair, which disappears because +x and −x make 0.

Group like terms sorts the tiles into rows by type, with positives on the left and negatives on the right. Take away a zero pair does the same as dragging, one pair at a time. The readout shows the mat as it stands (such as x² + 2x − x + 3 − 1) and in simplified form (x² + x + 2), and works out the mat's value for any x from −5 to 5.

Why use tiles

Like terms are the same shape, so you can only combine tiles that match: an x tile and an x² tile clearly aren't the same thing. Zero pairs make the rules for negatives concrete. 3x − 5x is three green tiles and five red ones; after three zero pairs, two red tiles are left, so the answer is −2x. The value feature shows that an expression is a recipe for a number once x is known, which is practice with substitution, exponents and the order of operations.

Common mix-ups

• Combining unlike terms. 2x + 3 is not 5x, because an x tile and a 1 tile are different shapes.
• Thinking x² and 2x are the same. With x = 3, x² is 9 but 2x is 6.
• Getting the sign wrong. 3x − 5x is −2x, not 2x: count which tiles are left after the zero pairs.
• Thinking a zero pair is worth something. A positive and a negative tile of the same type always add to 0.

A 10-minute algebra tiles lesson

• Clear the mat. Add 2 positive x tiles and 3 positive unit tiles and ask students to write the expression.
• Add 1 negative x tile and 5 negative unit tiles. Ask for a prediction of the simplified expression.
• Drag the zero pairs together, then compare with the readout.
• Press Simplify it for a fresh example to do alone.
• Set x to 2 and ask students to find the value of the mat by hand before reading it.

Where it fits by grade

• Grade 6: evaluate expressions at given values, including exponents and the order of operations (6.EE.A.2c), and write equivalent expressions (6.EE.A.3, 6.EE.A.4).
• Grade 7: a number and its opposite make 0 (7.NS.A.1a), and add, subtract and simplify linear expressions (7.EE.A.1).
• Grades 8 and 9: model quadratic expressions with x² tiles as a step toward factoring.
• England: Key Stage 3 simplifies expressions by collecting like terms and substitutes values into expressions.

Learning more

Negative numbers, exponents and solving equations are skills on Eurekami's skill map, and Daily Practice brings them back when they start to fade. Our algebra balance page continues the story with equations, and the AI tutor asks guiding questions when an expression is tricky.