📚 Unit Plans → 🌍 Y7/8 Introduction to Algebra — Te Tātai Tauira → 📄 Practice: Translating Words to Algebra
Years 7–8 Pāngarau / Mathematics

Practice: Translating Words to Algebra

Turn these everyday phrases into the language of algebra. Use 'x' for the unknown number.

Part 1: Expressions

  1. The sum of x and 12: _________________
  2. The difference between 20 and x: _________________
  3. The product of 7 and x: _________________
  4. A number x divided by 10: _________________
  5. 8 more than x: _________________
  6. 15 less than x: _________________

Part 2: Equations

  1. A number x increased by 5 is 18: _________________
  2. When a number x is doubled, the result is 24: _________________
  3. If you subtract 9 from x, you get 7: _________________
  4. A number x shared among 5 people is 6: _________________

Challenge: Two-Step Translations

  1. 3 more than twice a number x: _________________
  2. 5 less than a number x divided by 2: _________________
  3. When you multiply x by 4 and add 1, the answer is 21: _________________
🔑 Kaiako answer key

Part 1 — Expressions (these are expressions, so there is nothing to solve)

  1. x + 12
  2. 20 − x
  3. 7x
  4. x ÷ 10, usually written x/10
  5. x + 8
  6. x − 15

Part 2 — Equations (the equation is the answer; the solution is given in brackets if you want to push further)

  1. x + 5 = 18  (x = 13)
  2. 2x = 24  (x = 12)
  3. x − 9 = 7  (x = 16)
  4. x ÷ 5 = 6  (x = 30)

Challenge — Two-Step Translations

  1. 2x + 3
  2. x/2 − 5 — also accept (x − 5) ÷ 2. The wording “5 less than a number x divided by 2” admits both readings, so mark either as correct and ask the ākonga to say which phrase they attached the “divided by 2” to.
  3. 4x + 1 = 21  (x = 5)

Watch for: the first two challenge items are expressions and the third is an equation — only the third has an equals sign in the wording (“the answer is 21”). Also watch for “15 less than x” written as 15 − x; the order matters.

📋 Teacher Planning Snapshot

Ngā Whāinga Ako — Learning Intentions

Fluency practice for Lesson 2: turning worded statements into expressions.

Ngā Paearu Angitū — Success Criteria

  • ✅ I can turn a written phrase into an algebraic expression.
  • ✅ I can tell an expression from an equation, and say which the words are asking for.
  • ✅ I can get the order right in "15 less than x" and explain why it is not 15 − x reversed.

Differentiation & Inclusion

Give ākonga who need it a word bank on the board: sum → +, difference → −, product → ×, shared → ÷. Part 1 can be done orally in pairs before anything is written. For ELL ākonga the hard words here are "product", "difference" and "increased by" — pre-teach those three and most of the sheet opens up.