Algebra Studio

Beginner → Advanced

Every symbol is a thing you can move. A letter is a cup with a number inside, an equation is a balance, a product is a rectangle. Move the things, and watch the algebra move with them.

Already fluent in school algebra? Try Olympiad Algebra →

1
The unknown
A letter is a number in a cup. Build expressions, fill the cups, and gather what belongs together.
Picture: cups and counters · Case: The mind reader
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2
Balance
An equation is a level balance. Keep it level and the unknown walks out on its own.
Picture: a balance · Case: Diophantus' age
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3
Expand and factor
A product is a rectangle. Build it from tiles, then take it apart again.
Picture: area tiles · Case: 47 × 53 in your head
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4
Functions
A machine turns inputs into outputs, and the outputs draw a graph.
Picture: a machine and a graph · Case: Which taxi?
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5
Systems
Two balances at once, or two lines that cross.
Picture: two balances · Case: Chickens and rabbits
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6
Parabolas
Squares make curves; slide one until it fits.
Picture: a curve on sliders · Case: The biggest field
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7
Completing the square
Fold the strips around the square and find the missing corner.
Picture: area tiles · Case: Al-Khwarizmi's square
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8
Inequalities
A tipped balance, and a number line that flips.
Picture: the number line · Case: Where to meet
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9
Exponents
Repeated doubling, and why the pattern keeps going below one.
Picture: folded paper · Case: Paper to the Moon
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10
Logarithms
Counting the doublings, and a ruler that multiplies.
Picture: a slide rule · Case: The rule of 72
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11
Sequences and series
Staircases, and the square you can halve forever.
Picture: staircases · Case: The bouncing ball
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12
Numbers that turn
A number whose square is −1 is a quarter turn.
Picture: the plane · Case: The pirate's treasure
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Final round

Ten problems from the whole studio. Nothing tells you which idea to use.