Download Types of numbers - investigation

Types of numbers - investigation
Task 1
Task 1
Is your current age
Is your current age
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a prime number
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a prime number
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a Fibonacci number
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a Fibonacci number
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a square number
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a square number
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a triangular number
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a triangular number
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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
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a prime number
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a prime number
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a Fibonacci number
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a Fibonacci number
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a square number
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a square number
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a triangular number
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a triangular number
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a happy number?
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a happy number?
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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!
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e.g. 31 becomes 32 + 12 = 9 + 1 = 10
10 becomes 12 + 02 = 1
10 is happy!
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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, …
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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, …
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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.
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