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Maths

Forming and Solving Linear Equations

Overview

Students move from solving given equations to forming their own from written problems — a critical algebraic thinking skill that underpins all further algebra.

Learning Objective
Students translate word problems into linear equations and solve them systematically, checking solutions by substitution.

Resources needed

  • Mini whiteboards
  • Worked example cards (optional)

Lesson stages

0 / 7 done
  1. 1 Quick practice: solve 3x + 5 = 20. Students show working on mini whiteboards. Establish the inverse operations method (subtract 5, divide by 3). Check: does 3(5) + 5 = 20? ✓
  2. 2 Read: 'I think of a number, multiply it by 4, and subtract 3. The answer is 17. What is the number?' Model the translation: let the unknown = n. 4n − 3 = 17. Solve: 4n = 20, n = 5. Check: 4(5) − 3 = 17. ✓
  3. 3 A rectangle has length 2x + 1 and width x. The perimeter is 32cm. Form an equation and solve. Perimeter: 2(2x+1) + 2x = 32. Expand: 4x+2+2x = 32. 6x+2 = 32. 6x = 30. x = 5. Check dimensions make sense.
  4. 4 Three consecutive numbers sum to 54. Let the smallest be n. Form: n + (n+1) + (n+2) = 54. Simplify: 3n+3 = 54. n = 17. Numbers: 17, 18, 19. Check: 54 ✓. Students try with consecutive even numbers.
  5. 5 Partners write their own word problem and swap. Each solves the other's and returns it. Discuss: was the problem well-formed? Did the equation match?
  6. 6 Show three worked examples — each with a different error (wrong equation formed, arithmetic error, forgot to check). Students identify and correct each.
  7. 7 A bag contains red and blue counters. There are 5 more red than blue. There are 23 counters in total. How many of each colour? Students form and solve the equation independently.

Tap a step to mark it as done.

Variations

  • Extend to equations with unknowns on both sides once forming is secure
  • Use angle problems (angles in a triangle sum to 180)
  • Include ratio-based word problems
More information

Display keywords: let, form, substitute, verify. Practise the sentence: 'Let the unknown be n. The equation is ___.The solution is n = ___. Check: ___ ✓'

Provide a translation guide: 'think of a number' = n, 'multiply by' = ×, 'subtract' = −. Scaffold equation-forming with partially completed equations.

Does the equation correctly model the problem? Do students maintain balance when solving? Do they substitute back to verify? Can they identify when their answer is unreasonable?

All problems can be presented orally or on the board. Mini whiteboards replace printed worksheets.

Students may write the equation incorrectly (e.g. writing the wrong quantity as the unknown). Stress defining the variable clearly before forming the equation.

Activity details
Secondary Medium 40 minutes 5 minutes prep Solo, Pairs Indoor
Topics
Algebra Linear Equations Forming Equations Problem Solving