Cracking the Code

---

Curriculum Alignment

Subject: Mathematics
Year Level: Year 9
Australian Curriculum Strand:

• Number and Algebra
• Sub-strand: Algebra
• Content Descriptors:
  • ACMNA175: Extend and apply the index laws to variables, using positive integer indices and the zero index.
  • ACMNA177: Solve problems involving linear equations, including those derived from formulas.
  • ACMNA210: Apply the associative, commutative and distributive laws to aid mental and written computation and algebraic reasoning.

---

Duration

30 minutes

---

Learning Intention

WALT (We Are Learning To):

• Understand and apply inverse operations to solve algebraic problems
• Apply BODMAS rules to simplify and evaluate algebraic expressions

---

Success Criteria

By the end of the lesson, students will be able to:
✅ Identify and use inverse operations to rearrange and solve algebraic equations
✅ Accurately simplify expressions using BODMAS in the correct order
✅ Explain each step of their working out clearly, using correct mathematical language

---

Resources

• Mini whiteboard and markers
• Printed dyslexia-friendly maths sheets (OpenDyslexic Font, size 14+)
• Algebra tiles (physical or paper-based set)
• ‘Mystery Equation’ cards (for extension)
• Calculator (optional)
• Timer or stopwatch
• Coloured pencils (for grouping and ordering operations visually)

---

Lesson Sequence

1. Warm-Up: BODMAS Sprint (5 minutes)

Purpose: Activate prior knowledge of order of operations

Instructions:

• Provide a list of five mixed algebraic expressions on the mini whiteboard.
• Explain that students need to solve as quickly and accurately as possible following BODMAS:
  • Brackets
  • Orders (indices)
  • Division and Multiplication (left to right)
  • Addition and Subtraction (left to right)

Example Questions:

1. 2 + 3 × 4
2. (6 + 9) ÷ 3
3. 2² + 10 ÷ 2
4. 15 – 5 × 2 + 1
5. (8 – 4)² + 7

Differentiation:
✔ For students with dyslexia, provide printed expressions in larger font with steps colour-coded (brackets in blue, orders in red, etc.)
✔ Use algebra tiles to model one problem physically if required

---

2. Mini-Workshop: Inverse Operation Magic (10 minutes)

Purpose: Introduce and explore the concept of inverse operations in algebra

Direct Instruction (3 min):

• Explain: Inverse operations are opposite mathematical actions. Addition ↔ Subtraction, Multiplication ↔ Division.
• Use a number machine diagram to show how inverse operations “undo” each other.
• Demonstrate a simple equation like:
  • x + 5 = 12
  • Subtract 5 from both sides → x = 7

Guided Practice (7 min):

• Solve 3 problems together on the board:
  1. x – 3 = 9
  2. 4x = 20
  3. x/5 = 6

Student Task:

• Student uses their whiteboard to solve a new problem using inverse operations:
  2x + 3 = 11
• Think-Pair-Share (even if 1:1, student can explain aloud or journal their thinking steps)

Differentiation:
✔ Use visual inverse operation flip cards (green = operation, red = inverse operation)
✔ Allow calculator for those who struggle with mental arithmetic

---

3. Challenge Zone: Decode the Message (10 minutes)

Purpose: Apply BODMAS and inverse operation skills together

Activity:

• Hand out the ‘Algebra Decoder Sheet’ (dyslexia-friendly formatting)
• Sheet includes 4 equations where each solution matches a letter
• Example:
  • Solve: 3(x – 2) = 9
  • x = 5 → Letter E
• Once solved, the student decodes a hidden message (e.g., “MATHS IS FUN”)

Differentiation:
✔ Provide partially worked examples based on student readiness
✔ Offer diagrams for visual learners to ‘see’ the flow of operations
✔ Provide oral instructions for students with reading difficulties

---

Extension Task (Advanced Learner Option)

“Mystery Equation Cards” (with real-world algebra scenarios):

• Student selects a card like:
  “If 3 pens and 2 notebooks cost $18, and each pen costs $2, how much does one notebook cost?”
• Must form an equation and solve it using inverse operations and BODMAS

Bonus Challenge:

• Create your own multiplication-based algebra problem and challenge the teacher to solve it!

---

Differentiation Strategies

Learner Type	Strategy
Dyslexia-Friendly	Use OpenDyslexic font, coloured symbol cards, reduce reading load
EAL (English as an Additional Language)	Use icons for operation symbols, provide bilingual glossaries (if available)
Visual Learners	Use algebra tiles, colour-code BODMAS steps
Struggling Learners	Break questions into smaller steps; offer oral explanations
Advanced Learners	Use multi-step real-life problems; introduce simultaneous equations

---

Assessment for Learning (AfL)

During the lesson:

• Use mini whiteboards for immediate responses & working out
• Observe problem-solving thinking aloud
• Ask scaffolded questions, e.g. “What is the inverse of this operation?” or “What comes first in BODMAS here?”
• End with a reflective prompt:
  “What was the trickiest part and how did you overcome it?”

---

Teacher Reflection (Post-Lesson Prompt)

• Did the student demonstrate understanding of inverse operations independently?
• Could they apply BODMAS without prompting?
• What misconceptions arose and how were they addressed?
• What will I plan next to build on this knowledge?

---

🎉 Celebrate success & effort, not just the right answers. Use humour, colour, and mini-competitions to keep the energy high—even in 1:1 settings!

“Learning algebra is like cracking a secret code. Once you know the pattern, unlocking answers feels amazing!”