🎯 Learning Goals

WALT: We Are Learning To apply negative exponents to solve real-world problems and express very small numbers as decimals.

Success Criteria:

✓ I can convert between negative exponents and decimal form
✓ I can solve problems involving very small measurements
✓ I can explain the pattern when exponents become negative
✓ I can apply this knowledge to scientific contexts

📚 Part 1: Understanding Negative Exponents

Answer: ________ × 10⁻⁴ metres

🔬 Part 2: Real-World Applications

🚀 Extension Activities

10² = ______
10¹ = ______
10⁰ = ______
10⁻¹ = ______
10⁻² = ______
10⁻³ = ______

What pattern do you observe?

📋 Differentiation Support

For students needing extra support:

• Use a calculator to check decimal conversions
• Work with a partner for questions 5-7
• Focus on questions 1-4 first, then attempt others

For dyslexic learners:

• Use coloured paper or overlay if needed
• Read questions aloud or use text-to-speech
• Take breaks between sections

Extension for advanced learners:

• Research negative exponents in computer science (bytes, bits)
• Create your own word problems using negative exponents
• Investigate how calculators display very small numbers

📝 Answer Sheet

1. 0.000005 metres

2. 0.000075 metres or 0.0075 cm

3. 10⁻³, 1/1000, 1 ÷ 10³

4. 2 × 10⁻⁴ metres

5. Dust particle: 0.0002 metres, Virus: 0.00000008 metres, Pollen grain: 0.00003 metres

6. Negative exponents simplify the representation of very small numbers, making them easier to read and write.

7. 1.25 mm

8. 10² = 100, 10¹ = 10, 10⁰ = 1, 10⁻¹ = 0.1, 10⁻² = 0.01, 10⁻³ = 0.001

9. Example: The size of a virus is often measured in nanometers (10⁻⁹ meters), which is more manageable than writing out the zeros.