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A formula is a rule about a quantity, written with letters so it can be used rather than just read. Learn how to build one, and match formulas to the shapes they describe in an interactive playground.

An expression only becomes a number once you choose what the letter stands for. Learn how to substitute a value safely, and work out an expression for several numbers in an interactive playground.

An expression is made of terms, and each term is a number multiplied by some letters. Learn the names for those pieces and read them off real terms in an interactive playground.

Only terms with exactly the same letter part can be added together. Learn the test for like terms and simplify three sums in an interactive playground.

Expressions are named after how many terms they contain, and that is the whole rule. Learn the names and sort real expressions in an interactive playground.

Adding two expressions means collecting the terms that are alike. Subtracting means the same, with one trap. Work three of them in an interactive playground.

Multiplying out a bracket means the term in front reaches every term inside. See why on a rectangle's area, and match three brackets to their pieces in a playground.

Multiplying two brackets means every term in the first meets every term in the second. See the four pieces as areas and match three products in a playground.

Most of a word problem is done before any solving starts. Learn how to name the unknown and translate a sentence into an equation in an interactive playground.

Transposing looks like a separate rule with its own sign-flipping magic. It is the two-sides move with the middle line left out. See what it hides in a playground.

When the letter appears on both sides, one extra move comes first: collect the letters onto one side. Walk the whole solution on a balance scale in a playground.

A bracket in an equation can be multiplied out, or it can be divided away. Learn both routes and follow the solution on a balance scale in an interactive playground.

A fraction in an equation is a division waiting to be undone by a multiplication. Learn how to clear it and follow the whole solution on a balance scale.

A solution is the value that makes both sides agree, so checking is simply putting it back in. Learn what a check proves and test three values in a playground.

An equation is true for particular values; an identity is true for all of them. Learn to tell them apart and sort real statements in an interactive playground.

Squaring a bracket is not squaring each piece. Four pieces come out, and the two middle ones are the part people lose. See where they sit in an interactive playground.

Factorising is expanding run backwards. Learn how to find what all the terms share and pull it outside, then match expressions to their factorised forms in a playground.

Four terms with nothing shared by all of them can still factorise, if you pair them first. Learn the method and match expressions to their brackets in a playground.

Some expressions factorise the moment you recognise them. Learn the difference of two squares and the perfect square, and match three to their brackets in a playground.

A pair of coordinates is an address on a grid, and the order is the whole of it. Learn how to read and plot a point in an interactive playground.