Year 8 Term 1 Week 3 Maths - LCM, HCF, Index Notation and Standard Form

Introduction

This week, we’ll explore how factors and multiples lead to more powerful number tools: Lowest Common Multiple (LCM) and Highest Common Factor (HCF). We’ll also look at index notation for repeated multiplication and standard form, which helps us write very large and very small numbers simply.

Real-World Application – Why This Maths Matters

Scientists, engineers, and organisers use LCM, HCF, index notation, and standard form every day. The LCM helps with scheduling, like working out when two traffic lights or train services will line up again. The HCF is useful for dividing things into the largest equal groups, such as sharing equipment or packaging products without leftovers. Index notation makes repeated multiplication quick and neat, especially in physics and computing, where powers of 10 are common. Standard form allows us to handle huge numbers, like the distance between planets, and tiny numbers, like the size of bacteria, without writing endless zeros.

Day 1 – Lowest Common Multiple (LCM)

What am I learning today?

I am learning to understand what LCM means and to use multiples and prime factorisation to find the LCM of two numbers.

What Does LCM Mean?

The Lowest Common Multiple (LCM) of two numbers is the smallest number that both divide evenly into. It helps solve problems with repeating cycles, like when buses, lights, or machines line up again.

Game

Play the Prime Number Wordwall.

Learn

Watch Maths with Mr J: GCF and LCM. Greatest common factor (GCF) is another name for the highest common factor (HCF).

Task

In your journal:

• Write the title LCM

• Write a definition for LCM

• Find the LCM of:

  6 and 8

  12 and 15

  9 and 21

Day 2 – Highest Common Factor (HCF)

What am I learning today?

I am learning to understand what HCF means and to use factorisation to find the HCF of two numbers.

What is the HCF

The Highest Common Factor (HCF) is the biggest number that divides into both numbers. It’s useful for sharing things into the largest equal groups.

Game

Play the Blooket HCF and LCM Review.

Learn

Watch Maths Genie: Finding HCF and LCM. This is a longer video. If you are confident, watch the first few examples. If you need a bit more practice, please watch it all.

Task

In your journal:

• Write the title HCF

• Write a definition for HCF

• Find the HCF of:

  12 and 18

  20 and 50

  81 and 63

• Complete MEP Maths Year 8 2.4.

Conclusion

You can now find the HCF of pairs of numbers. Tomorrow, we’ll move on to index notation.

Day 3 – Index Notation

What am I learning today?

I am learning to write repeated multiplication in index form and to understand square numbers, cube numbers, and powers of 10.

What is Index Notation?

Index notation (also called powers or exponents) is a way of writing repeated multiplication.

For example, 24=2×2×2×2=162^4 = 2 × 2 × 2 × 2 = 1624=2×2×2×2=16.

This makes calculations shorter and neater.

Game

Play the Blooket solo game.

Learn

Work through Khan Academy: Pre-algebra Unit 5 - The meaning of Exponents. Do not go any further!

Task

In your journal:

• Write the heading Index Notation

• Write these in index notation and calculate:

  3 × 3 × 3

  2 × 2 × 2 × 2 × 2

  10 × 10 × 10

  5² and 4³

• Complete MEP Maths Year 8 2.3.

Conclusion

You can now use index notation to simplify repeated multiplication. Tomorrow, we’ll learn how to use standard form.

Day 4 – Standard Form

What am I learning today?

I am learning to write very large and very small numbers in standard form and how to convert between ordinary numbers and standard form.

What is standard form?

Standard form is a way of writing numbers that are extremely large or small in a clear format.

Game

Play the Wordwall Indicies Game.

Learn

Work through BBC Bitesize: Introducing Standard Index Form.

Watch Standard Form by Beyond Revision.

Task

In your journal:

• Write the heading Standard Form.

• Write a definition

• Convert into standard form:

  56,000

  0.0047

  1,230,000

  0.00092

Conclusion

You can now write numbers in standard form, which is often used in science and engineering. Tomorrow, you’ll complete a real-world project that ties this week’s skills together.

Day 5 – Project: Science and Space Challenge

What am I learning today?

I am learning to apply LCM, HCF, index notation, and standard form in real-life contexts.

Introduction

From planning timetables to measuring the universe, this week’s maths is everywhere. Today you’ll solve a challenge combining all four skills.

Task – Science and Space Challenge

1. Two planets orbit a star: Planet A every 20 days, Planet B every 30 days. After how many days will they align again? (Use LCM).

2. A company is making science kits with 84 pencils and 108 erasers. They want equal packs with no leftovers. What is the largest pack size? (Use HCF).

3. Rewrite these numbers in index notation:

   • 2 × 2 × 2 × 2 × 2

   • 10 × 10 × 10 × 10

4. The distance from Earth to the Sun is 149,600,000 km. Write this in standard form.

5. A bacterium is 0.000023 m in length. Write this in standard form.

   
   

Conclusion

This week, you’ve mastered LCM, HCF, index notation, and standard form, skills that help in maths, science, and technology. Next week, we’ll build on this knowledge by moving into algebraic expressions and equations.