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Year 8 Term 1 Week 2 Maths - Multiples, Factors and Prime Numbers

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Introduction

This week, we’re exploring factors, multiples, and prime numbers, three key building blocks of number theory. You’ll learn how to find them, spot patterns, and see how they’re used in real life, from packaging in factories to creating secure online passwords.


Real World Application

Manufacturers and event organisers use factors, multiples, and prime numbers in practical ways every day. Factors help them divide products evenly into boxes or groups without leftovers, while multiples make it easy to plan quantities and schedules. For example, if a factory packs drinks in boxes of 12, knowing the multiples of 12 ensures they order stock in the right amounts. Prime numbers are also crucial in cybersecurity, where they are used to create secure codes that protect online transactions and personal data.


Day 1


What am I learning today?

I am learning to understand what factors are and to be able to find all the factors of a number and recognise factor pairs.


What is a factor?


A factor is a number that divides another number exactly with no remainder. Factors help simplify fractions, work out equal groups, and solve puzzles.


a number or quantity that when multiplied with another produces a given number or expression.

Game

Play Mathplayground: Find the factors. Try all three levels.


Learn

Watch Fuse school - Factors and Multiples.

Task

In your journal:

  • Write the heading Factors

  • Write a definition for the term factors

  • Give at least three examples

  • List all factors of the following numbers: 12, 24, 36, 60. Write them in pairs.


I am finding this hard, help!

That's Ok! First of all, I want you to take a five-minute break and do something active or creative, no screen time!


Welcome back!

Now I was hoping you could work through BBC KS3 BiteSize: Factors, stop at the end of the factors section, do not go onto multiples. If you feel too frustrated or stressed, come back tomorrow, but it would be amazing if you could give it a try today.


Conclusion

You can now confidently list the factors of any number. Tomorrow, we’ll look at multiples and see how they link with factors.


Day 2


What am I learning today?

I am learning to understand what multiples are and to find the first few multiples of a given number. I will also learn to recognise common multiples.


What is a Multiple?

You learned about multiples in the Fuse School video yesterday. Rewatch that if you need to. Multiples are what you get when you multiply a number by an integer. They’re used in everything from timetables to arranging seats in rows without gaps.


a number that may be divided by another a certain number of times without a remainder.

Game

Play Hit the Button on TopMarks. You can decide how hard the game is going to be; the hardest level is times tables up to 12 and mixed.


Learn

Complete Khan Academy: Pre-algebra Unit 1. Stop at the end of Quiz 1.


Task

In your journal:

  • Write the heading Multiples

  • Write a definition for the term multiple

  • Give at least three examples

  • Find the first five multiples of: 7, 8, and 12. Then, find the common multiples of 6 and 8 up to 50.


Conclusion

You can now spot multiples and common multiples. Tomorrow, we’ll focus on prime numbers and why they’re special.


Day 3


What am I learning today?

I am learning to define and identify prime numbers.


What is a Prime Number?

Prime numbers are special; they can only be divided exactly by 1 and themselves. They’re key to encryption and data security.


a whole number greater than 1 that cannot be exactly divided by any whole number other than itself and 1.

Game


Learn

Watch Maths with Mr J - Prime Numbers.


Task

In your journal:

  • Write the heading Prime Numbers

  • Write a definition for the term prime number

  • List all prime numbers between 1 and 30. Highlight those that are also factors of 60.

  • Complete MEP Maths Year 8 2.1.


Conclusion

You can now identify prime numbers and understand why they’re unique. Tomorrow, we’ll put factors, multiples, and primes together using factor trees.


Day 4


What am I learning today?

I am learning to break a number into its prime factors using a factor tree.


What are Factor Trees?

Prime factors are the building blocks of numbers. Using factor trees, we can break down any number into the primes that make it.


Game

Play this Wordwall game.


Learn

Go to Blooket and play the game solo, yes you get two games today!


Learn about prime factorisation on Khan Academy: Pre-algebra unit 1 Prime Factorization. Go right to the end of the unit test.


Notice the spelling difference - factorisation is UK English Spelling and factorization is USA English.


Task


Conclusion

You can now break numbers into prime factors — a skill that’s essential for simplifying fractions and solving more complex problems later on. Tomorrow, you’ll complete a real-world project using all of this week’s skills.


Day 5 - Project


What am I learning today?

I am learning to apply factors, multiples, and prime numbers to solve a real-world problem. I am also learning to work logically and to organise information.


Introduction

You’re in charge of planning how food is packaged and sold at a music festival. You’ll use factors to pack boxes, multiples to work out quantities, and primes to add a bit of security to your ticket system.


Task – The Festival Food Stall Challenge

  • Choose 3 food items to sell (e.g., hot dogs, drinks, cakes), and write these into your journal.

  • Decide how many fit in a box (this number must be a factor of your total stock), and write this next to each food.

  • Work out how many full boxes you can make for:

    • 120 hot dogs

    • 96 drinks

    • 72 cakes

  • Find a multiple of 12 that would allow you to restock without leftovers.

  • Choose a prime number as your special discount code for the day.

  • Present your answers clearly, with factor trees for each stock number.


Conclusion

This week, you’ve learned to find factors, multiples, and prime numbers — and used them to solve practical problems. Next week, we’ll look at fractions, decimals, and percentages.



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