Last time the mystery number hid in a box. Now we'll give it a name — a letter — and learn to write expressions, read them, and find their value.
Drawing a box every time gets tiring. So instead, we use a letter to stand for the mystery number. That letter is called a variable — letters like n, x, or b are common choices.
This reads as "five more than a number." A variable doesn't have one fixed value — n could be 1, or 10, or 100. It's a placeholder, just like the box was.
An expression is a math phrase that combines numbers, variables, and operations — like n + 5 or 3 × x. It's not a question and it has no equals sign. Think of it as a recipe waiting for an ingredient.
One shortcut to know: when we multiply a number by a variable, we usually drop the times sign. So 3 × n is written as 3n, and 2 × x becomes 2x. The number in front is called the coefficient.
The trickiest part of algebra is often just translating English into math. Read the phrase, then build the matching expression by tapping the tokens. Order doesn't have to be perfect — anything that means the same thing counts.
An expression doesn't have one answer until you know what the variable equals. Evaluating means swapping the variable for a value and working it out. Slide to change n, predict the answer, then reveal it.
When a number sits right next to a variable or a parenthesis, it means multiply. So 2n means 2 × n — and once you swap in a value, 2(4) means 2 × 4. Writing the number snug against the parentheses is just a tidy way to show multiplication, with no times sign needed.
Notice how the answer changes every time you move the slider. That's the whole point of a variable — one expression describes a whole family of answers, one for each value you plug in.
Here's a difference that matters a lot going forward. An expression is just a phrase. An equation adds an equals sign, claiming that two things are the same — and that's something you can solve.
A phrase. It has a value once you know n. You evaluate it.
A full sentence with =. It can be true or false. You solve it to find n.
Quick test: if you can spot an = sign, it's an equation. No equals sign means it's an expression. We'll start solving equations in the next lesson — for now, make sure you can tell them apart.
Eight problems: translate phrases, evaluate expressions, and tell expressions from equations. You earn a point for each one you get on the first try.