### 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.

### 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?

### Month Mania

Can you design a new shape for the twenty-eight squares and arrange the numbers in a logical way? What patterns do you notice?

# I'm Eight

##### Stage: 1, 2, 3 and 4 Challenge Level:

When I went into a classroom earlier this week a child rushed up to tell me she was 8 that day!

Well, Happy Birthday to everyone who has a birthday today!

If you are 8 then this could be for you, but if it is another number then you just change the 8 to whatever your age is today.

There is not a lot to say to introduce this challenge. It's really just to find a great variety of ways of asking questions which make $8$.

Things like $6 + 2$, $22 - 14$, etc.

But you need to get examples that use all the different mathematical ideas that you know about.

$1$) So you could show some multiplications and some divisions.

$2$) If you know about fractions then you can add or subtract numbers involving fractions. You could also ask questions like "What is half of $16$?''; "What is four-fifths of 10?'' and so on.

$3$) If you've come across decimals then do a few of those also, perhaps using all the four rules [addition, subtraction, multiplication and division].

And so on.

Use whatever mathematics you know to find as many different ways of getting the answer $8$.

You may find some patterns that would go on for ever and ever. If you do, just put down a few, and then see if you can describe how the pattern works.

So if you're $8$ years old maybe you'll write something like this:

$16 \div 2$, $8 \div 1$, $4 + 4$, $2 + 6$, $9 - 1$, $12 - 4$

$1 + 1 + 1 + 1 + 1 + 1 + 1 + 1, 2 + 2 + 2 + 2$

$15 - 3 - 2 - 1 - 1, 5 + 3 + 6 - 3 - 3$

and so on.

But if you're much much older you may write something like:-

$4 \sin (\pi/2) + \sqrt{5^2 - 3^2}$

Whatever your age, and whatever ones you get caught up with, have a look at the ways that you can make new ones that have a similar pattern.

Your "What would happen if ...?'' questions may be a little different from our usual ones.

The 8 year old might ask "I wonder what would happen if I tried to use multiplication and addition to make 8?''

The much older person (17 years old perhaps) may well ask "I wonder what would happen if I used matrices?''

The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice. More information on many of our other activities can be found here.
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