Variables Stand for Unknown Quantities

Hey there! I'm Lumi, and I love finding patterns in the world around us. Imagine you're at the farmers market. You grab a bag of apples, but you haven't counted them yet. You could write a question mark on the bag — or, like mathematicians do, you could write a letter. That letter is called a **variable**. A **variable** is a symbol, usually a letter like x, n, or b, that stands in for a number we don't know yet — or a number that can change depending on the situation. It is a placeholder, like a reserved seat at a table: the seat is real, but we don't know who will sit there yet. Here's why variables are powerful: the expression **n + 3** can describe ANY situation where you start with an unknown amount and add 3. If n is 5, then n + 3 = 8. If n is 100, then n + 3 = 103. One expression, infinite situations! When you replace the variable with a specific number to find the result, that is called **substitution**. Example: if n = 4, then n + 3 = 4 + 3 = 7. **If you get stuck during the activity:** pick the tile that shows the letter standing for the unknown — that tile is always your variable. Start there, then decide what number to add or subtract. Variables let us write one rule that works for many numbers at once. That's the magic of algebra!