Students learn to translate between verbal descriptions and mathematical expressions. "Add 8 and 7, then multiply by 2" becomes 2 x (8 + 7) or (8 + 7) x 2. "Multiply 8 by 7, then add 2" becomes 8 x 7 + 2. Students also interpret expressions without evaluating them: they can compare "3 x (12 + 8)" and "3 x 12 + 3 x 8" and explain why they are equal (distributive property) without computing. This skill bridges arithmetic and algebra -- the ability to read and write expressions is the foundation for all equation-solving and algebraic reasoning.
Start with verbal-to-symbolic translation: give word descriptions and have students write the expression, paying careful attention to where parentheses are needed. Then reverse: show an expression and have students describe it in words. Include comparison problems where students determine whether two expressions are equivalent without evaluating. Use real-world contexts ("double the sum of your scores").
You already know the order of operations — the rules that say multiplication happens before addition unless parentheses say otherwise. Writing numerical expressions is the flip side of evaluating them: instead of computing an expression someone handed you, you're constructing the expression yourself to capture an intended calculation. The challenge is that English word order and mathematical operator order don't always match.
Consider "add 8 and 7, then multiply by 2." The word "add" appears first, which might tempt you to write 8 + 7 × 2 — but that expression, following order of operations, multiplies 7 × 2 first, giving 8 + 14 = 22. The intended computation adds first: (8 + 7) × 2 = 30. The parentheses are doing essential work: they override the default order and preserve the sequence of operations the words described. Any time a verbal description says "first do X, then do Y" and X is addition while Y is multiplication, you need parentheses around the addition.
The reverse skill — reading an expression and putting it into words — builds the same understanding from the other direction. When you see 3 × (12 + 8), you can say "3 times the sum of 12 and 8." You're parsing the expression as a recipe: what happens first (add 12 and 8 inside the parentheses) and what happens to the result (multiply by 3). Importantly, you can observe that 3 × (12 + 8) must equal 3 × 12 + 3 × 8 — the distributive property — without computing either side. The structure of the expressions reveals the equivalence; calculation isn't required to see it.
This topic is where arithmetic becomes algebra readiness. A numerical expression is just an algebraic expression where every value is a known number. The skills you're building now — recognizing what is nested inside what, translating between words and symbols, comparing expressions without evaluating them — transfer directly when variables appear. "The sum of a number and 7, doubled" becomes 2 × (n + 7). The expression-writing logic is identical; only the notation changes. Every student who struggles with early algebra can trace the difficulty back to not having fully internalized what a written expression *means*.