📚 Unit Plans → 🌍 Y7/8 Introduction to Algebra — Te Tātai Tauira → 📄 Practice: Two-Step Equation Marathon
Years 7–8 Pāngarau / Mathematics

Practice: Two-Step Equation Marathon

Remember to undo addition/subtraction first!

Part 1: Solve for x

1. 2x + 4 = 10

2. 3x + 5 = 14

3. 5x + 2 = 22

4. 4x - 3 = 13

5. 6x - 8 = 16

6. 10x - 15 = 35

Part 2: Division Involved

1. x/2 + 3 = 8

2. x/4 + 1 = 6

3. x/5 + 6 = 10

4. x/3 - 2 = 4

5. x/6 - 1 = 5

6. x/10 - 5 = 5

🔑 Kaiako answer key

Part 1 — Solve for x

  1. 2x + 4 = 10 → 2x = 6 → x = 3
  2. 3x + 5 = 14 → 3x = 9 → x = 3
  3. 5x + 2 = 22 → 5x = 20 → x = 4
  4. 4x − 3 = 13 → 4x = 16 → x = 4
  5. 6x − 8 = 16 → 6x = 24 → x = 4
  6. 10x − 15 = 35 → 10x = 50 → x = 5

Part 2 — Division Involved

  1. x/2 + 3 = 8 → x/2 = 5 → x = 10
  2. x/4 + 1 = 6 → x/4 = 5 → x = 20
  3. x/5 + 6 = 10 → x/5 = 4 → x = 20
  4. x/3 − 2 = 4 → x/3 = 6 → x = 18
  5. x/6 − 1 = 5 → x/6 = 6 → x = 36
  6. x/10 − 5 = 5 → x/10 = 10 → x = 100

Watch for: the classic error is undoing the multiplication first — 2x + 4 = 10 read as x + 4 = 5. Every solution here is a whole number, and every one can be checked by substitution in one line. Insist on the check; it is the success criterion for Lesson 5.

📋 Teacher Planning Snapshot

Ngā Whāinga Ako — Learning Intentions

Fluency practice for Lesson 5: a graded set of two-step equations.

Ngā Paearu Angitū — Success Criteria

  • ✅ I can solve a two-step equation by undoing the constant first, then the coefficient.
  • ✅ I can show every step with both sides written out.
  • ✅ I can check my solution by substitution and say whether it works.

Differentiation & Inclusion

Ākonga who lose the order should write the two steps as a plan before solving: "undo + 4, then undo × 2". Part 2 is harder than Part 1 because the division is written as a fraction; some ākonga will need it read aloud as "x divided by 2". Extension: ask for a two-step equation whose answer is 7.