EWWNP means Exploring Wild and Wonderful Number Patterns Created by Yourself! Investigate what happens if we create number patterns using some simple rules.
Find a great variety of ways of asking questions which make 8.
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
While I'm sitting in front of the computer I also have a dice and it is showing a $5$. Rather like this:-
The arrangements usually sit quite well into a rectangular arrangement. So we might call this last one a $3$ by $5$ or a $5$ by $3$ arrangement. Squares are just special rectangles and so we could have a $4$ by $4$ :-
When we have the $3$ by $5$ we can count the dots and see that we have $23$ altogether. Now $3$ times $5$ IS NOT $23$. So we cannot write it as:- $3 x 5= 23$
So we (You) will have to invent another name instead of times and a sign to go with it. Perhaps (because it is convenient on the computer) you may choose "?" BUT you can choose anything that you like!
Now I can write:-
$3 ? 5 = 23$
and when I look at the $2$ by $2$ and the $4$ by $4$ I can write them as:-
$2 ? 2 = 5$ and $4 ? 4 = 25$
If you now look at a bigger arrangement that follows the same kind of pattern you'll find various ways of counting up the number of dots needed.
So let's look at this one $8 ? 4$
Count them up, calculate, or do whatever so that you find out how many there are altogether and we have:- $8 ? 4 = 53$. Invent some more questions of your own and work out the answers.
You probably would know the answer straight away or you'd be able to work it out from things that you knew before. When people learn multiplication tables they often write them out in a big table. So you could explore what happens if you try a similar idea with doing "?" instead of multipliation and make a ?Table instead of a TimesTable.