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Monday, October 31, 2016

The Multifaceted Grid



Image result for images for got an idea

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. 


Image result for images for multiplication grids showing from 1 to 5

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.

Image result for images for a number grid showing squares

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.

Image result for images of a grid showing equivalent fractions

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.

Image result for images for a number grid showing division

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.

Image result for images for number grids showing multiples
 
Hence we have a beautiful interplay
Between multiplication and division
Right there on our grid
I trust I have your attention.

Image result for images for the area model for multiplication

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.

Image result for images for adding fractions on a grid

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!

Image result for images for the aha

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

Saturday, October 29, 2016

This Same Jesus



Image result for images for Acts 1:11

He was a carpenter’s son
It’s written in the book
But he was far more than that
If you take more than just a look.

In the beginning was the Word
And the world was created by him,
This same Word gave up his life
To save mankind from sin.

It was not taken from him
As some may dare to believe
But he took on himself our death
That his life we may receive.

The fulfillment of the Law
And spoken of by the prophets
This same Jesus
Is the world’s most widely discussed topic.

Image result for images for the little town of Bethlehem
Born of the Virgin Mary
In the little spoken of town,
This same Jesus whom angels worship
For us gave up his heavenly crown.

He led a life of poverty
Though all the world was his
And relinquished all in his Father’s care
And not a single step did he miss.

From heaven’s palatial splendor
To a world in which he had no home
Came this same Jesus
To rescue his sheep that roam.

His life was a perfect walk
Though many his teachings balked
Yet no man spoke as Jesus talked
Even though the Pharisees had him stalked.

Image result for images of the River Jordan

Baptized in the muddy Jordan
By the Baptist we know as John
And right there in that same river
The world’s greatest ministry had dawned.

Next was his trek to the desert
By the devil to be tempted
For there is nothing that we face
From which he could have been exempted.

The devil would hit his hardest,
The three temptations were his best shots,
Over each Jesus was triumphant
Defeating all three of the devil’s plots.

He chose a motley group
The disciples he called his crew,
A selection that baffled the world
But in the end only one dropped through.

Image result for images of the wedding canaan of Galilee

His miracles could not be disputed
They were authentic to say the least,
The last would be his ascension
The first was at a wedding feast.

He walked on water and fed thousands
And some followed for the bread and fish
But those that feasted on his words
He exceeded their greatest wish.

His teachings were unparalleled
And he taught as one having authority,
Not as the Scribes and the Pharisees
That advocated insularity.

His parables were soul searching
Of the earth but heavenly defined
And though the disciples oft didn’t grasp
He would explain their ultimate design.

Image result for images of the Holy Scriptures

Not a single book has he written
But he is the greatest co-author ever,
Sixty-six books of the written word
That the Holy Spirit has pulled together.

His lifestyle was simplicity
He cared not for the things of this world
Yet he traversed it with humility
As he walked as the Living Word.

He resigned to his Father’s will
Though life’s path was rugged and steep
And identified with hurting people
When at a tomb he would weep.

The beasts of the field had holes
The birds of the air had their nests
But this same Jesus creator of everything
Owned no place for his head to rest.

He slept often in the wild
Where to his heavenly Father he prayed,
Not my will he had resigned
When he viewed that horrid day.

Image result for images of the Garden Of Gethsemane 
  
In the garden of Gethsemane
His sweat seemed mingled with blood
As he mentally prepared himself
For the cross and our ultimate good.

The cross that beckoned from eternity
The cross on which his blood was spilt
The blood of the spotless Son of God
Shed to pardon us from sin and guilt.

A contemptuous miscarriage of justice
Fitted into Almighty God’s plan
As they sentenced him to crucifixion
The price for the redemption of man.

The creator crucified by his subjects
Their own lifeline they thought to sever
But glory hallelujah this same Jesus
Arose from the grave triumphant
And now is alive forever.

Image result for images of the second coming

He will come again for his own
Those whom the Father has promised him,
Those that call to him for salvation
Those that have been saved from sin.

This same Jesus, yes, this same Jesus
Once dead but now alive forever
Will come again he assures us
To gather his redeemed together.

Are you ready?  Are you ready?
Are you ready for that day to come?
Are you ready?  Are you ready?
Are you ready for the return of God’s Son?

Stewart Russell © 2016

Tuesday, October 25, 2016

Just a Problem Solving Idea for the Lower Juniors



 Image result for images for apples

Please note that in the following exercise the focus is not on the answer to the question but the information related to the question.  This problem solving exercise is treated as though it were a Comprehension exercise.  Hence the children are encouraged to familiarize themselves with the story.
 
Sam bought 8 apples for $4.00.  He gave his sister 3 apples and ate 2.  He had $8.00 left.

They may discuss the following:
·      From whom do you think Sam may have received the money?
·      Where do you think he bought the apples?
·      Why do you think he shared with his sister?
·      Could it have been a school day?  Why do you think so?
·      What are some other questions we could ask about this story?

What are the facts in the problem?
A.            Sam bought 8 apples.
B.            He paid $4.00 for the apples.
C.            He gave his sister 3 of the apples.
D.           He ate 2 of the apples.
E.            He had $8.00 left.

Here are some questions to think about.

Task:
Write under each question item the facts that relate to that question.
If none off the facts relate to a question leave the space blank.

1.   How much money did Sam have at first?
Facts:



2.   How much money did he have left?
Facts:



3.   How many apples did Sam have left?
Facts:



4.   What would be the cost of 3 apples?
Facts:




5.   How many apples were spoilt?
Facts:




6.   How much money did Sam have the day before?
Facts:




 Stewart Russell (c) 2016