Discuss with the people on your table how

Discuss with the people on your table how maths is used in these digital careers? Challenge: Where might prime numbers be used?

Square and cube numbers Prime factor decomposition Percentages and interest Vectors Transformations of shapes Substitution in algebraic formulas Discuss with the people on your table how maths used in these digital careers? Challenge: Where might prime numbers be used? Cyber security in banks

Agree Learning Objectives. WE ARE LEARNING… Prime Decomposition THINGS TO REMEMBER. . . Prime numbers have only 2 factors 1 and itself. YOU WILL BE ABLE TO… All will be able to use a Factor tree to decompose a number into Primes Most will be able to confidently write the answer in Index Notation Some will be able to spot the pattern in the decomposition of Square numbers TRIC… Focussed Key Words. Prime, Decomposition, product P C A R

Agree Learning Objectives WE ARE LEARNING…Prime Decomposition YOU WILL BE ABLE TO… All will be able to use a Factor tree to decompose a number into Prime Most will be able to confidently write the answer in Index Notation Some will be able to spot the pattern in the decomposition of Square numbers THINGS TO REMEMBER. . . Prime numbers have only 2 factors 1 and itself. Key Words…Prime, Decomposition, Product

06 December 2020 Prime Decomposition L. O. To break numbers down into products of their primes

Present new Information • If you use internet banking, you want it to be secure • Banks will code your data using a very long number which is the product of 2 primes • You will have a Prime number assigned and the bank will have another

Present new Information • These are multiplied together to get the code • Even if people hacking the data get the code, they will be unable to get the 2 prime numbers given to you and the bank (which would be needed to get your money!) • This is because the numbers used are so big, a supercomputer would still take years to break it down (The primes used will have over 200 digits each) • Banks change codes every now and then, which effectively resets the process!

Present new Information ‘Prime Decomposition’ • What does this mean? • Prime = Prime numbers • Decomposition = Breaking down • What we will be doing is breaking down bigger numbers into ‘products’ of their Prime factors. • This is done using a ‘factor tree’

Present new Information • Write 120 as a product of its prime factors 120 2 60 2 30 2 15 3 5 120 = 2 x 2 x 3 x 5 = 23 x 5

Present new Information • ‘Prime Decomposition’ Write 80 as a product of its prime factors 2 40 2 20 2 10 5 2 80 = 2 x 2 x 5 = 24 x 5

Construct Meaning • Draw a factor tree for the following numbers: • A) 64 • B) 250 • C) 164

Construct Meaning • Draw a factor tree for the following numbers: • • • A) 64 = 26 B) 250 = 2 x 53 C) 164 = 22 x 41

Apply to demonstrate • Bronze: Using factor trees to break down numbers into their prime factors • Silver: Spotting patterns between the prime factorisation of numbers and their squares. • Gold: Problem Solving: Using very large numbers that are not prime to factorise – much like cyber security experts do for banks.

Bronze Prime decomposition More challenging numbers

Bronze Prime decomposition Because they are doubled the power of two increases by one More challenging numbers a) b) c) d) 5 x 31 2 x 3 x 5 x 7 24 x 3 x 52 x 7 e) 3 x 41 f) 29 g)210 h) 211 a) b) c) d) e) f) g) h) 22 x 5 52 22 x 3 x 5 2 x 32 22 x 52 23 x 5 24 x 5 25 x 5

Silver Prime decomposition

Silver Prime decomposition a) b) c) d) 2 x 3 2 x 5 22 x 3 22 x 5 a) b) c) d) 22 x 32 22 x 52 24 x 32 24 x 52

Gold Prime decomposition

Gold Prime decomposition a) b) c) d) 11 x 17 23 x 29 37 x 89 653 x 761

Present new Information HCF Highest common factor Biggest Same number that goes into it LCM Lowest common Multiple Smallest Same number in the times tables

Present new Information • Find the HCF of 60 and 70 70 60 2 2 30 2 15 3 5 60 = 2 x 3 x 5 = 22 x 3 x 5 35 5 7 70 = 2 x 5 x 7 =2 x 5 x 7 HCF = 2 x 5 = 10

Apply to Demonstrate BRONZE Find the HCF and LCM of these numbers using prime factor trees 1. 6 and 15 2. 20 and 30 3. 14 and 42

Apply to Demonstrate BRONZE 1. HCF =3, LCFM =30 2. HCF =10 LCM =60 3. HCF = 7 LCM =42

Review Write a summary using less than 15 words on what prime decomposition is and how to do it. You can use as many numbers and symbols as you like.

To watch a clip about careers in the digital sector click here: https: //www. youtube. com/watch? v =CIm. Bfu. Ae. Kd 8 For further information, please see http: //www. rsaacademies. org. uk/projects/wow-show-teacherresources/