Ninth Grade · Math · week 1

The language of algebra

Translate between words and algebraic expressions, and evaluate expressions by substitution.

Algebra is a language for patterns. Instead of saying "some number," we write a letter — x — and suddenly we can talk about EVERY number at once. "Five more than a number" becomes x + 5. "Double a number" becomes 2x. The letter is called a variable because its value can vary.

An expression is a phrase in this language (like 2x + 3); it has no equals sign, so it isn't claiming anything — it's just a recipe. To evaluate an expression, substitute a value for the variable and follow the order of operations. That's the whole game this week: translate carefully, substitute carefully.

📋 For the grown-up teacher
Teach it (10–15 min):
  • Say: "Algebra lets us talk about ALL numbers at once — x is a placeholder for any of them."
  • Translate three phrases together out loud before writing anything: "double a number," "six more than a number," "six less than double a number."
  • Flag the classic trap: "less than" flips the order. "5 less than x" is x − 5.
  • Have them evaluate one expression at two different x-values to feel the variable varying.
Talk about it:
  • Why do we bother using letters instead of numbers?
  • What's the difference between an expression and an equation?
  • Why is "7 less than x" written x − 7 and not 7 − x?

Mastery looks like: They can translate a two-step phrase into an expression and evaluate it correctly with order of operations, unprompted.

Common stumbles: Writing "7 − x" for "7 less than x," and skipping order of operations when substituting (compute 3(4) − 7 as 3 · (4−7)).

Homework for this lessonType it, write it with a stylus, or print it for pencil & paper.open →
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