You have had the versatile number line
And you have had the flexible rule,
Let us not forget, however,
There is another marvellous tool.
And what is particularly interesting
Is the way the three are linked
For when we include the grid
We see how beautifully they sync.
Yes, the multifaceted grid is next
On the list of mathematical tools;
It can be made up with a number line
Or perhaps a measurements rule.
On the vertical axis could be the rule
With one on the horizontal as well,
And a simple maneuver across and down
One would its area tell.
Or perhaps it could be a grid
With multiples of numbers from one to five
Showing common multiples and fractions
Making mathematics come alive.
We would also be able to ascertain
A list of consecutive squares
As we proceed along the diagonal
Of those squares we would be aware.
Can’t you see that number grid
Starting with the smallest square?
The square of one then two and three?
Yes! One, four and nine would soon appear.
Next would come sixteen and twenty-five
Then thirty-six and forty-nine
And if we extend the size of that grid
Many more squares we would find.
Or equivalent fractions we should see
As the multiples increase or decrease;
One-third would be equal to three-ninths
As the multiples proceed from the least.
Reduction of fractions would be clear
Just take the opposite direction,
Four-eighths, two-fourths and one-half
Already you should be having fun.
Multiplication would make more sense
As we examine the area model
And division too would fall into line,
The grid would simplify that puzzle.
On the grid you should see the interaction
Between multiplication and division;
Here there is a wonderful attraction
As we process each operation.
One to four along the vertical
And one to three along the horizontal
Produces twelve squares in the area
And there we have our rectangle.
Hence we have a beautiful interplay
Between multiplication and division
Right there on our grid
I trust I have your attention.
One basic thing to keep in mind
When operating division on the grid
The vertical is always the divisor
Never the quotient, math forbids.
So much mathematics on the grid
Hence its multifaceted appeal
And once the teachers take the time
So much on that grid can be revealed.
As I bring this poem to an end
At two other aspects I’ll take a look:
There are subtraction and addition,
I know it doesn’t appear so in your book.
But having mastered these operations
It doesn’t matter with which you start,
So subtracting fractions could come at first
And from the old tradition you could depart.
The grid facilitates both operations
When combined with fractions equivalence;
The Least Common Multiple appears
In a subtraction or addition instance.
One-half, two-fourths, three-sixths
With one-third and two-sixths compared,
From three-sixths two-sixths I take
And presto! One-sixth appears.
Whenever we add or subtract
Our terms must be alike
Hence one-half added to one-third
Becomes five-sixths; that’s right!
By now you should have realised
The multifaceted-ness of the grid,
Combined with the rule and number line
For these three how much do you bid?
You've seen the versatile number line
And you have had the flexible rule
Let us not forget, however,
The grid is a multifaceted tool.
Stewart Russell © 2016