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I'm Eight

Age 5 to 11 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?''