# Prime Factorisation using 'Sigma Prime'

**CURRICULUM AREAS COVERED**

Ages 11-13

- Finding prime factors
- Prime factorisation

**HOW TO PLAY**

Use your **divisibility strategies** and **prime factorisation** skills to 'fire' prime number missiles at the incoming 'alien' invader. Each alien appear randomly at the top of the screen, displaying a number value that needs to be decomposed/factorised to 1. Click on the alien and select the correct prime factor.

By selecting (firing) prime number missiles at the alien, your aim is to divide its value down to 1 and so destroy it! But take care, you must only hit an alien with its prime factors. If you hit an alien with a prime that is not a factor, ‘Remainder Rubble’ will rain down.

As Remainder Rubble accumulates at the bottom of the screen, it pushes Sigma Prime closer and closer to the lethal Laser Wire at the top of the screen – one touch of this deadly barrier spells disaster, and ends the game!

*The goal of this game is to protect the remote moonbase, Sigma Prime from marauding alien invaders. Stay alert for surprise appearances by alien Motherships - giant vessels that glide across the top and are worth big points if you manage to bring them down!*

*The aliens attack in waves. As the waves progress, the aliens become faster and tougher to destroy. Fortunately, after each wave, any Remainder Rubble is cleared from play so you always start a new wave back on the ground.*

When you destroy an alien with a value consisting of two or more prime numbers, the corresponding factor tree appears in the ‘Analysis’ column on the right of the play area so you can see exactly how you brought the alien down!

**SCORING INFORMATION**

There are 2 modes to this game. Complete the relevant mode and beat the Target Score to earn a medal (**B**ronze, **S**ilver, **G**old).

**Mode 1: Sigma Prime Lite - Finding Prime Factors >>**Target Score >>> 40,000 (**B**), 120,000 (**S**), 400,000 (**G**)**Mode 2:****Sigma Prime - Prime Factorisation****>>**Target Score >>> 40,000 (**B**), 120,000 (**S**), 400,000 (**G**)

**SCORING INFORMATION**

Sigma Prime features 22 unique attack waves. Before a game begins, you have the option to start play from any wave reached previously – though note that skipping the earlier waves will reduce your score and make medals harder to earn! If you beat all 22 waves, the game will ‘loop’ back to the start – but now with the aliens faster than before!

The scoring increases as your progress from one wave to next:

At the end of each wave, you receive a bonus. The bonus is proportional to how far Sigma Prime has been pushed up the screen by Remainder Rubble, and is also multiplied by the wave number.

**'End of wave' bonus points **= 1000 × (percentage distance from Laser Wire) × (wave number)

So, if Sigma Prime ends a wave:

- at ground level (i.e. it has not been pushed up the screen at all), you get the full bonus
- pushed halfway up the screen, you get half the bonus
- almost touching the Laser Wire, you get next to no bonus at all!

**MATHS STRATEGIES**

- Even numbers end in 0, 2, 4, 6 or 8. They are divisible by 2
- Numbers that end in 0 or 5 have 5 as a prime factor salvo
- If a number ends in 0 then its divisible by 10 so hit it with a 2, 5
- If a numbers ends in 00 then its divisible by 100 so hit it with a 2, 5, 2, 5 salvo
- If the sum of the digits of a number is a multiple of 3 then the number itself is divisible by 3
- If the sum of the digits of a number is divisible by 9 then the number itself is divisible by 9
- Learn the squares of the prime numbers in the game: 2² = 4, 3² = 9, 5² = 25
- Learn the cubes of some of the prime numbers: 2³ = 8, 3³ = 27, 5³ = 125
- Any number in this sequence can be destroyed by 2s only: 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096,…
- And any number in this sequence can be destroyed by 3s only: 3, 9, 27, 81, 243, 729,…

**OTHER BASIC STRATEGIES**

- When a new wave starts, familiarise yourself with which primes correspond to which buttons as quickly as possible
- Try to destroy aliens as quickly as you can after they appear – if you let the alien hordes build up, you can get overwhelmed quickly
- Remember: you don’t need to destroy the Motherships to complete a wave. Although they’re worth big points, if you’re struggling it’s better to focus on the aliens
- Learn basic divisibility tricks to get in some early hits, reducing your alien enemies to more manageable quantities
- When an alien appears, if its number is small enough then try to work out all of its prime factors and destroy it with a quick salvo of shots. For example, if an alien appears with 25 on it then fire off two 5s in quick succession – this will destroy it because 25 = 5 × 5
- Similarly, learn standard finishes – for example, 2, 2, 3 will finish off a 12 because 2 × 2 × 3 = 12
- Aliens attack at different speeds so take this into account when deciding which ones to target and exactly when to fire