The Multifaceted Grid

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