# Numbers and Shapes

You probably know something about Triangular Numbers etc.

You’re also likely to have come across Square Numbers   etc.

Maybe you’ve explored things like:- 1 + 2 + 3 or 3 + 5 + 7 + 9 or 2 + 4 + 6 + 8 + 10 and 5 + 10 + 15 etc.

THE CHALLENGE IS TO USE NUMBER PATTERNS AND LOOK AT SHAPE NUMBERS

RULES

IN ORDER

Rule A/ Using starting numbers 1 or 2 or 3 or 4 or 5 or 6 So choose one of them now. (e.g. 4)

Rule B/ Going in steps of 1 or 2 or 3 or 4 or 5 or 6 and choose one of these steps. (e.g. 3 so:- 4, 7, 10, 13 etc.)

Rule C/ Using 3 or 4 or 5 or 6 numbers in the set choose again (e.g. 3 so 4, 7, 10)

Rule D/ Add the sequence 4 + 7 + 10 = 21

Rule E/ Look at sequences of Triangular, Square, Pentagonal and hexagonal numbers and see if there’s a match.

YES! 21 is the 6th Triangular number.

SEE WHAT OTHER TRIANGULAR, SQUARE, PENTAGONAL & HEXAGONAL NUMBERS YOU FIND

Here are the first four pentagonal and hexagonal numbers to help you find many more!

etc.       etc.

If you want some help starting here are some examples;

A/Using starting number 3

Going in steps of 2

Using 5 numbers in the set 3 + 5 + 7 + 9 + 11 = 35 the 5th Pentagonal Number

B/ Using starting number 6

Going in steps of 6

Using 3 numbers in the set 6 + 12 + 18 = 36 the 8th Triangular & 6th Square Numbers

We'd love you to share how you've tried this and what you've discovered. You can add a comment below, or you can email us - your work may be featured in the showcase.