Your First Steps in Algebra

Algebra starts by answering a question nobody usually asks out loud: what is a letter for? This series builds the answer in book order — why a rule needs a letter at all, what that letter stands for, how to write a rule as a formula and work out what it comes to, and finally what an equals sign claims and how to solve for the letter on a balance scale.

1 hr 14 min to complete
Beginner level
7 Parts

CodePLU Goal

Upgrading Human Mental Models

Learn how to think in Workflows

One rule that works for a number you cannot draw
Beginner 10 min Part 1

Why Does Maths Use Letters Instead of Numbers?

Letters are not there to make maths harder. They are there because some rules have to cover every number at once, and you cannot write them all down. Build the rule for a growing pattern in an interactive playground.

One letter, three jobs — and what tells them apart
Beginner 10 min Part 2

What Is a Variable, and Why Use Letters?

A letter in maths is not a mystery or a code — it is a number you have not pinned down yet. Learn the three jobs letters do, and build a letter down into each in an interactive playground.

From a sentence anyone could say to a line you can use
Beginner 10 min Part 3

How Do You Turn a Rule Into a Formula?

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.

One stem, three symbols, three different things you are allowed to do
Beginner 10 min Part 4

What's the Difference Between an Expression and an Equation?

One can be simplified, one can be solved, and one gives you a range rather than an answer. Learn to tell them apart by building one stem into all three in an interactive playground.

Put the number in, then do the operations in the right order
Beginner 10 min Part 5

How Do You Find the Value of an Expression?

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.

See what each move does to an equation's balance
Beginner 12 min Part 6

Why Must You Do the Same Thing to Both Sides?

An equation is a claim that two sides are equal, so any change to one side alone makes it false. Learn which moves keep the balance and which ones actually help.

Take 2x + 3 = 11 apart until x stands alone
Beginner 12 min Part 7

How Do You Solve for x, Step by Step?

Solving is undoing, in reverse order. Learn why the last thing done to x is the first thing you remove, and build the whole solution yourself.