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Types of numbers - investigation Task 1 Task 1 Is your current age Is your current age • a prime number • a prime number • a Fibonacci number • a Fibonacci number • a square number • a square number • a triangular number • a triangular number • a happy number? • a happy number? Task 2 Task 2 How old will you be when your age is next How old will you be when your age is next • a prime number • a prime number • a Fibonacci number • a Fibonacci number • a square number • a square number • a triangular number • a triangular number • a happy number? • a happy number? © www.teachitmaths.co.uk 2016 26174 Page 1 of 4 Types of numbers - investigation Hints Hints A prime number has only two factors – the number 1 and itself. 2 is the smallest prime number. A prime number has only two factors – the number 1 and itself. 2 is the smallest prime number. A Fibonacci number comes from the Fibonacci sequence. The rule is ‘add the two previous numbers to get the next’. The Fibonacci sequence starts like this 1, 1, 2, … A Fibonacci number comes from the Fibonacci sequence. The rule is ‘add the two previous numbers to get the next’. The Fibonacci sequence starts like this 1, 1, 2, … A square number is the result of multiplying another number by itself. A square number will make a square shape, e.g. 9 is a square number and 9 dots can be arranged in a square (with 3 dots in each row.) A square number is the result of multiplying another number by itself. A square number will make a square shape, e.g. 9 is a square number and 9 dots can be arranged in a square (with 3 dots in each row.) A triangular number will make a triangle shape! A triangular number will make a triangle shape! A happy number is happy if the sums of the squares of its digits can be added together to make 1. Keep going until you end up with a single digit answer – hopefully 1! A happy number is happy if the sums of the squares of its digits can be added together to make 1. Keep going until you end up with a single digit answer – hopefully 1! e.g. 31 becomes 32 + 12 = 9 + 1 = 10 10 becomes 12 + 02 = 1 10 is happy! © www.teachitmaths.co.uk 2016 e.g. 31 becomes 32 + 12 = 9 + 1 = 10 10 becomes 12 + 02 = 1 10 is happy! 26174 Page 2 of 4 Types of numbers - investigation The number sequences The number sequences Prime numbers 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, … 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, … Fibonacci numbers 0, 1, 1, 2, 3, 5, 8, 13, 21, … Triangular numbers Square numbers Square numbers 1, 4, 9, 16, 25, … Happy numbers 1, 7, 10, 13, 19, 23, 28, … © www.teachitmaths.co.uk 2016 Triangular numbers 1, 3, 6, 10, 15, 21, 28, … 1, 4, 9, 16, 25, … Fibonacci numbers 0, 1, 1, 2, 3, 5, 8, 13, 21, … 1, 3, 6, 10, 15, 21, 28, … Prime numbers Happy numbers 1, 7, 10, 13, 19, 23, 28, … 26174 Page 3 of 4 Types of numbers - investigation Teacher notes Designed to be used A5 size, each student sheet is duplicated so they will print 2 per A4 sheet. This investigation works best if students discover the answers for themselves. If they need to find information on the different number types then they should use the internet. If internet access is not available, then provide students with the hints sheet. If more help is required give out the lists of numbers. Extension Students could work out the next part of each sequence up to 100. © www.teachitmaths.co.uk 2016 26174 Page 4 of 4