Materials Needed

• Pens, pencils, and eraser
• Notebook or lined paper
• A ruler
• Basic scientific calculator (optional, but good for practice)
• Colored highlighters

Learning Objectives

By the end of this lesson, you will be able to:

• Use BIDMAS/BODMAS to solve multi-step equations correctly.
• Round numbers to a specific number of decimal places and significant figures.
• Convert fluently between Fractions, Decimals, and Percentages (FDP).
• Identify and apply basic algebraic substitution.

1. Introduction: The "Missing Million" Hook (5-10 mins)

Scenario: Imagine you are a video game developer. Your game has a glitch: instead of giving players 100 gold coins, the code calculates 10 + 5 × 2. Some players are getting 30 coins, and others are getting 20. If 1 million players use this, and you give out 10 extra coins by mistake, you lose 10 million gold pieces!

The Question: Who is right? (10 + 5) × 2 = 30 or 10 + (5 × 2) = 20?

(Hint: Math has a "Law of the Land" called BIDMAS that tells us exactly which order to follow so everyone gets the same answer!)

2. "I Do": The Rules of the Game (15 mins)

The Order of Operations (BIDMAS)

To solve any math "sentence," follow this hierarchy:

1. Brackets
2. Indices (Powers like ² or ³)
3. Division and Multiplication (Left to right)
4. Addition and Subtraction (Left to right)

Example: 20 - 3² + (4 × 2)
1. Brackets first: 4 × 2 = 8 → 20 - 3² + 8
2. Indices next: 3² = 9 → 20 - 9 + 8
3. Subtract and Add: 11 + 8 = 19.

Rounding for Reality

In GCSE math, we often round to Decimal Places (dp). Look at the digit to the right of your cut-off point. "5 or more, let it soar; 4 or less, let it rest."

Example: Round 7.468 to 2dp. The 3rd decimal is 8 (big!), so the 6 becomes a 7. Answer: 7.47.

3. "We Do": Guided Practice (15 mins)

Let's try these together. Talk through your steps out loud!

1. BIDMAS Check: What is 5 + 2 × 10? (Wait... do we add or multiply first? Multiply!)
2. The FDP Bridge: If a pizza has 10 slices and you eat 3, what is that as a fraction? (3/10). As a decimal? (0.3). As a percentage? (30%).
3. Basic Algebra: If x = 5, what is 3x + 4? (Remember, 3x means 3 times x!)

4. "You Do": Foundation GCSE Kick-Starter Quiz (20 mins)

Instructions: Complete this questionnaire to check your understanding. Show your working out for every question!

5. Conclusion & Success Criteria (10 mins)

Check your work:

• Did you follow BIDMAS? (Question 1 should be 14, not 6!)
• Did you remember units? (Question 6 needs "cm")
• Did you show your steps? (In GCSE, the "method" gets you marks even if the final answer is wrong!)

Real-World Recap: Why do we need rounding? (Example: You can't pay someone £5.333333; you have to round to £5.33!).

Differentiation & Adaptations

For a Challenge (Extension): Try to round 0.00456 to 2 significant figures. (Answer: 0.0046). Create your own BIDMAS puzzle where the answer must be exactly 100.

For Extra Support (Scaffolding): Use a calculator to check the arithmetic, but write down the order of steps first. Use a 100-square grid to visualize the Fractions/Percentages questions.

Success Criteria