In which EVEN gnomes make an ODD discovery.
The yellow gnome held his eyes closed tightly as the woody hand lifted him up, high above the treetops. Suddenly everything was still and quiet except for the steady sound of a groaning wind that was blowing his pointed hat directly behind his head. Mustering up enough courage to open just one eye, the gnome saw before him a tree that looked like a man. Or was it a man who looked like a tree? As these questions danced in his head, the Tree Man spoke,
“You have taken that which does not belong to you” he groaned in his deep, woodsy voice.
“I…I’m...I’m sure I don’t know what you mean, thank you,” replied the gnome, hoping that being polite would help matters.
The gnome was completely confused by the Tree Man’s strange words and, wondering what had happened to his three friends far below, he ignored the woeful words of the Tree Man and begged to be returned to the ground.
“Please, put me down on the ground with my friends. I am a gnome, an earth-dweller, and it is not natural for me to be suspended at such great heights.”
With that the gnome heard the familiar groan that had sounded when the branch had been snapped from the tree.
“Huuuummmphh! And neither is it natural for my ancient branches to be broken into bits” replied the Tree Man.
With these words he lowered his enormous wooden hand and soon the gnome was safely back on the ground with his three companions. Suddenly the Tree Man took a step forward into a clearing and the four gnomes could plainly see his enormous stature.
Before they had a chance to speak, the Tree Man addressed them,
“I am Old Dismas. I have lived in these woods since it came to be. When the earth was still young, a wizard cast an enchantment on my wood,
Whosoever shall harm and tear thee asunder, shall forever count until he hath discovered the secret of numbers.
With those words, Old Dismas left the gnomes in the clearing. The earth groaned under the weight of his steps and the quaking sound of the forest floor echoed throughout the woods.
"What are we to do? Oh dear! Oh me! We've brought a terrible enchantment upon ourselves!" cried the blue gnome.
"It sounds as if we will have to find something to count. The Ancient Tree said that the enchantment will not break until we discover the secret of numbers. What shall we count?"
The gnomes confusedly looked around until they again spotted the mountain of gemstones.
The four gnomes approached the huge mountain of gemstones and noticed that there were small baskets scattered around the ground. Each of them grabbed one and collected as many gems as he could fit in his basket.
After their baskets were filled to the brim, the green gnome asked, "Now what do we do?"
"How about we break a branch off that tree over there and use the sticks to count our gemstones" replied the blue gnome, with a look of enthusiasm.
"No!" shouted the other three. "Don't you remember? That's what got us in this mess in the first place!"
The four gnomes didn't know what to do, so they emptied their baskets of gemstones and began spreading them on the ground in order to count. The blue and green gnomes decided to sort their gemstones into pairs of two, but soon the blue gnome became frustrated.
"Well now, this is rather ODD. Every time I try to sort my gems in pairs, I always find one left over."
The green gnome continued his work of sorting and soon matched each gemstone perfectly in pairs. Upon seeing his success, the blue gnome grumbled,
"Now, that is not EVEN fair. You do not have any left over. How is it that when I match my gemstones in pairs I always have one left over and you are able to match every last one?"
"Yes, it is ODD when a group has one left over and for this reason we call those numbers ODD. How many gemstones have you counted?" asked Old Dismas.
"Eleven" replied the blue gnome. "Is eleven an ODD number?"
"Yes" answered the Ancient Tree. "And how many gemstones have you counted?" he then asked the green gnome.
"Twelve. Twelve gemstones" answered the gnome. "Twelve is an EVEN number then because all of my gems have a partner. That's it! I've discovered the secret of numbers!" The silly green gnome began dancing around his sorted gemstones.
"Not so fast," laughed Old Dismas. "The secret is far deeper than the discovery of ODD and EVEN. But don't lose hope. There is someone here to help you."
And suddenly a King dressed in purple was standing before them.
To Be Continued...
This lesson continues the story from Lesson 1 and introduces the concept of odd and even numbers. If your child has not yet mastered the material presented in Lesson 1, wait before continuing with Lesson 2. Regardless, remember to practice and review Roman Numerals throughout the week. If your child is interested, introduce further Roman Numerals such as L equals 50 and C equals 100. Use your child's work in the Main Lesson Book as a springboard for review. By creating a Main Lesson Book, your child is writing and illustrating his own Math book!
If you are continuing with a 5 to 6 year old, rely heavily on the manipulatives (the gemstones) to teach this concept. Talk to your child about the things around her that naturally exist in pairs: two eyes, two ears, two feet, two socks or shoes. Then proceed to group the gemstones in pairs of two. Fill up the miniature baskets with gemstones (keep it under 10 for a young child) and ask him to sort them in pairs. If one is left over you can make a game of saying, like the blue gnome, "Well, isn't this ODD!" Point out that when all the gemstones have a partner, they are all EVEN. Make an Odd Number and Even Number page in your child's Main Lesson Book modeled after the sample page in the story. Draw with your child if he is having trouble expressing these concepts in writing and allow your child to spend a few days on his page if necessary. Young children learn best by imitation.
If you're working with a 7 to 8 year old, repeat the above activity and review it each day. Create and add the Even and Odd Number pages in the Main Lesson Book. Encourage your child to decorate his page with a border that reflects the story or concept learned. Remember, these pages are to be approached as works of art. When your child has grasped the concepts of even and odd, continue the work by using the blackboard. Write a random number and ask your child to tell you if it is even or odd. Allow her to use the gemstones to find the answer.
Continue to combine movement with your child's learning. Games of bean bag toss are a fun way to practice numbers. This week, play games of Even and Odd toss. As you toss the bean bag to your child say, "One!" and as your child catches it, he responds, "Three!" Continue through the odd numbers as he is able and then try the even numbers. Weather permitting, take your lessons outside. Use stones or acorns and sidewalk chalk to make number pictures on the ground.
Beginning this week we are going to concentrate on a different number each week. Don't skip this activity, even if your child knows his numbers well and can work basic math equations. We're going to be considering the concrete reality behind the very abstract idea of numbers. This week we'll begin with Number 1.
Consider the world and its Creator. What exists that expresses oneness? Some answers could be one God, one sun, one moon, one nose, etc... (Remember these answers are taken from the experience of a young child. There is no need to correct him and point out that the sun is a star and there are many in the universe, etc...) Ask your child to make a Number 1 page in his Main Lesson Book.