Prime Factor Decomposition
This is a set of resources for students learing Higher mathematics about prime numbers. The video from Playback Schools gives a good understanding and practical example of the importance of primes. Co primes are introduced and various resources that provide the basic principles of prime factor decompostion using the branch method.
Resouces are also included for the teacher to gain a more comprehensive knowledge about the study of primes over history.
Extension material is include with challenges and questions on primes to keep the most able busy whilst others are finishing off the standard quesitons.
Wresting with Primes
Gives an amusing historical background to prime numbers. It shows how any non prime number can be made by multiplying primes together. It compares the finding of larger primes with the factorisation of them. It then shows how prime numbers are used in internet security by producing two prime numbers, multiplying them together and sending them to the person who puts their credit card details into a web page.
The solution is incredibly difficult (which takes a long time even for the fastest computers) but very simple for the creator of the two prime numbers used originally. This is known as RSA and it the core of all encrypted of information.
GAIM Activities: Investigations
Open Investigations 21-30 and then find the Co-Primes sheet. This worksheet defines co-primes as two hole numbers that have no common factor apart from 1.
Then it has a number of questions for students to find sets of co-primes. This is useful for Higher students who are learning about primes and gives a deeper understanding about primes.
Number and Algebra 4 - Nuffield Foundation
Starting on page 41 is an introduction to prime and composite numbers and introduces the branch method of finding the prime factors of a composite number. Several exercises are available for students that are graduated. Excellent work for higher students.
2010 Senior Mathematics Challenge
On page 3 of this document (question no) 15 is an interesting challenge to stretch the most able in the class and keep them quite for a while.
The Mathematics Curriculum: Number
Section 10.4 starting on page 107 gives a thorough background on primes and I advise to watch the 'Wresting with Primes' before. This resource is for the teacher and only the most advanced and self motivated and enthusiastic student.
It covers deep concepts including Fermat primes and other famous mathematicians as primes have been deeply studied in history and this knowledge helps the teacher to give the significance of prime numbers to higher pupils.
Challenges
Open the 2011 challenge and on page 1 is no 3. Prime Directive. Use this challenge to test your higher students of their understanding and skills in prime numbers.