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Exploring Wild & Wonderful Number Patterns

EWWNP means Exploring Wild and Wonderful Number Patterns Created by Yourself! Investigate what happens if we create number patterns using some simple rules.

Sending Cards

This challenge asks you to investigate the total number of cards that would be sent if four children send one to all three others. How many would be sent if there were five children? Six?

Dice and Spinner Numbers

If you had any number of ordinary dice, what are the possible ways of making their totals 6? What would the product of the dice be each time?

What Is Ziffle?

Age 7 to 11
Challenge Level

What Is Ziffle?

There's a planet out in space called Zargon ........

On this planet these areĀ  numbers that are called ziffles
These numbers are ziffles $56, 105, 28, 63, 49$

These numbers are not ziffles: $100, 18, 65, 9, 76$

Only two of these numbers are ziffles: $16, 14, 57, 24, 70$

So what is special about the ziffles?

Why do this problem?

This short problem encourages children to look for patterns and apply knowledge of their times tables and of the properties of numbers.

Possible approach

Encourage the children to look at the sets of numbers in turn and explore their characteristics and properties.

Key questions

Are they all odd in one set and even in the other?
Are they prime numbers?
Are they triangle numbers?
Are they all in the five times table?
How about other tables?

Possible extension

Either you or your pupils could make up their own problem using, for example, multiples of $13$ or another table that they might like to practice.

Possible support

Take an easier table and develop sets of multiples and non multiples to identify.
Use concrete apparatus to explore divisibility such as Multilink cubes.