In which the gnomes learn the VALUE of their PLACE.
By this time the clearing was littered with baskets thrown here and there. Some were filled with gemstones and others had been toppled over. The mountain of gemstones was still high above the gnomes, but gems were now scattered everywhere, some in even numbered piles and some mismatched in odd groupings. The gnomes knew that they must continue counting in order to find the secret of numbers, but they were getting more and more frustrated the longer they tried to count. And while they were happy that Old Dismas had explained the difference between odd and even numbers, they still knew that there were far more gemstones than they were able to count on their own.
The gnomes were surprised when they suddenly saw a purple-clad king come out from behind the great trunk legs of Old Dismas.
"There is someone here for you to meet," the Ancient Tree announced to the gnomes.
The king stepped out in the clearing. He was an odd looking fellow, almost as wide as he was tall. He was dressed in purple robes that seemed to reflect every color imaginable and, instead of a crown, he wore a pointed cap trimmed in gold.
Careful not to trip over the gemstones and baskets, he began,
"I am King Equals, King of all Numeria. It was my ancestor who cast the enchantment on the Ancient Tree long, long ago...the enchantment that you have brought upon yourselves because of your greed. And he who cast the enchantment was a great wizard king, one who knew the secret of numbers that you so eagerly seek to discover."
The gnomes didn't know what to say. Who was this King Equals and what did he want from them? Finally the red gnome replied,
"We know the enchantment. Old Dismas explained it to us. And we know we must count until we discover the secret of numbers. But these gemstones are far too many for us and when we count we soon become confused. Can you help us?"
King Equals nodded his head and pulled a magic wand out from beneath his purple cape.
"You're a wizard too?" gasped the green gnome.
"Well, of course. And I can offer you a very simple way to solve your problem. If you want to find the solution to keeping track of the numbers you count, you must repeat this verse with me,
Regal old yellow gnomes buy itchy vests.
Simply repeat this verse and the solution will present itself to you."
The gnomes were convinced that King Equals was a fool, but they soon decided that since they had no better plan there was no harm in trying the verse, as silly as it seemed. Together they began repeating the strange words,
"Regal old yellow gnomes buy itchy vests....Regal old yellow gnomes buy itchy vests....Regal old yellow gnomes buy itchy vests..."
Suddenly a radiant light broke through the tops of the trees and shone upon the mountain of gemstones. And then there was a most beautiful sight. The reflection of the gemstones created a brilliant rainbow and a a prism of color filled the sky. Red, orange, yellow, green, blue, indigo, and violet.
Still awestruck by the exquisite color surrounding them, the gnomes were confused by the words, "Only nine of each kind can fit in one band." And anticipating their confusion, the King began to demonstrate.
"Do you see this first band of red? We call this band Units. Each gemstone represents one unit. And we can fill the red band with nine of them."
King Equals picked up a basket and filled it with 9 sparkling gemstones and carefully laid them in the red band of color.
"But there are many more than nine gemstones, Your Majesty. How can this possibly help us? We have a mountain of gemstones to count" remarked the confused green gnome.
"Ah, but don't you see these other bands? There are many places within which you may count. When we fill up the red Units we move on to the orange band. This band is called Tens."
"Oh! I know what ten is. We counted ten and made up a symbol for it in the shape of an X using branches from...Oh. Sorry Dismas. I'm sure it was not pleasant to have your branches broken off" admitted the yellow gnome with great regret.
The Ancient Tree lowered his heavy head and offered a gentle smile.
As he said this, the King carefully lined up the gemstones in groups of ten and placed them in the orange band of color.
"Now remember, only nine of each kind can fit in one band. So once we have nine groups of ten in the Tens place, we must move on to the yellow band of color. We call this the Hundreds."
Beginning to understand the sorting game, the gnomes began gathering gemstones once again in their baskets. When they filled the Hundreds with nine groups of one hundred gemstones, they moved on to the green. King Equals went on to explain that the green band was called Thousands and the numbers continued far past that. There were blue Ten Thousands, indigo Hundred Thousands and a place in the violet band for a number called Millions. The gnomes continued their work, and stopped only to notice that King Equals had opened his purple cape to reveal a funny little symbol made up of two lines on his chest.
"Excuse me, Your Majesty, but what is that symbol you wear on your chest? Is it some sort of royal family crest?" asked the red gnome.
"Oh, it is much more than that. Much more. But that story if for another time. For now, continue your counting and fill this rainbow with gemstones. Soon you will learn the purpose of the symbol I wear upon my chest" answered the King.
The gnomes whispered among themselves, "Well, I sure hope that mysterious symbol can help us discover the secret of numbers!"
Of course, you know that Ancient Trees can hear the softest, most faintest sound in the forest. And hearing the musings of the silly gnomes, Old Dismas let out a laugh that shook the forest floor.
There is no need to move on to this lesson until the concepts introduced in the previous two lessons have been mastered. Move at your child's pace. The Gnomes and Gnumbers lessons are archived in chronological order on this page for your convenience.
You will need to assemble a Rainbow Tray for this lesson, as well as collect a set of numerals. If you already have a set of moveable numerals like the ones shown in the picture above, use them. If not, and purchasing a set is not in your budget, spend one afternoon baking a set with your child. The easy salt dough recipe is here and a set of cutters can be purchased. Another option is to model the numerals with modeling beeswax (Suppliers are linked on the right sidebar.) or Sculpey Clay.
If you already own a Base Ten set, you can make use of it for place value work. If not, you can download the Ten Bar and Hundred Flat files below. These were made using Do-A-Dot markers on graph paper. Donna Young's site offers graph paper files for download if your child would like to make a set of base ten gemstones. The graph paper used here is the 10 x 14 size.
You can download the story and artwork by clicking on the links below.
Lesson Three Story
King Equals Picture
King Equals Coloring Page
Main Lesson Book Sample, Rainbow
Gemstone Ten Bars (Print out 2 copies on card stock. Laminate before cutting, if desired.)
Gemstone Hundred Flat (Print out 9 copies on card stock. Laminate before cutting, if desired.)
Presenting the Rainbow
We have chosen to present the rainbow in its true order of colors rather than the simplified version used in many children's songs and books. Red, Orange, Yellow, Green, Blue, Indigo, and Violet. Have fun with the mnemonic device created by Marybeth Foss, Regal old yellow gnomes buy itchy vests, for memorizing the colors of the rainbow and their order.
After reading the story and presenting this lesson on place value, have your child use the gemstones to practice identifying the place value of each numeral in a larger number. Depending on the age and ability of the child, you will want to go as high as he or she is able. A younger child may only understand up to the hundreds place, while an older child will enjoy discovering a million.
Ask your child to illustrate a place value page in the Main Lesson Book. The sample rainbow page offered above can be used as a model for your child.
There are three place value activities that you can play this week using the Rainbow Tray and gemstones. First start by filling a small basket with gemstones. For instance, if your basket is filled with 23 gemstones, your child will count nine gemstones and, reminding him that only nine of each kind can be placed in each band, will then cross over to the Tens color band. The remaining 20 should be grouped in two sets of ten gemstones. Then show your child how to swap out 10 gemstones for a ten bar. Continue in this way until your child understands the concept.
Next, make a 2 or 3-digit number (or larger for an older child) using the moveable numerals. For instance, arrange the numerals so that they show 45. Ask you child to build this number with the gemstone materials or a Base 10 set next to the Rainbow Tray and then place the numerals in the correct strips of color on the tray.
Another fun activity is to sort gemstones in different sizes of cups. Begin with 10 small bathroom-sized cups and ask your child to fill each with 10 gemstones. When ten small cups are filled, they can be poured into a larger 8 ounce cup, representing 100 (pictured here). Ten of these 8-ounce cups can then be poured into a large 32-ounce cup to represent 1,000. This tactile experience gives the child the opportunity to see and feel these numbers. The goal is to bring the abstract into the realm of the concrete.
Fun and Movement
Add movement by playing games of rainbow bean bag toss. Say "Red" and toss your child a bean bag. He should respond by saying, "Orange" and then toss the bag back to you. Continue in order to memorize the sequence of the colors in the rainbow.
Don't forget to review the concepts covered in the previous lessons. Together read your child's entries in the Main Lesson Book and discuss each page. Practice Roman Numerals at least one day this week and use the bean bags to play a game of toss, using odd and even counting as the rhythm.
If you feel that your child would benefit from math sheet review, there is a wonderful math worksheet generator online called The Math Worksheet Site. You can get a subscription for only $2.50 per month. (The price is reduced depending on the length of your subscription.) The subscription gives you unlimited use of the site and allows you to create custom math worksheets for your child. The site is very easy to use. Consider creating sheets on Roman Numerals, odd and even counting, and place value for your child.
This week we will continue our study of numbers by concentrating on the Number Two. Ask your child to consider the world around him and find thing that exist in pairs of two. Possible responses might be two eyes, two ears, two lights (the sun and moon), two feet, etc...
Gemstone Fun for the Little Ones
Nicholas Foss came up with a fun activity for the little ones. Using rainbow-colored craft sticks, he sorted the different colored gemstones on each stick and made the pattern of a rainbow. Since these were not glued down, a young child can repeat this activity many times.
This week we are adding the element of form drawing. This exercise in creating rhythmic patterns prepares a young child for handwriting and improves handwriting for the older child. When presenting these running forms, allow your child to first practice in a shallow tray of sand or cornmeal. Tracing the form with a finger in the air also helps the child in learning to imitate the pattern. Your child should use stick crayons when drawing the forms. Later in this main lesson we will be painting the geometric shapes and practice in form drawing will help in preparing the child for this activity.
One running form will be introduced each week for a period of nine weeks and we will be using the art of story telling to capture the attention and interest. Read the following story to your child as an introduction to the first running form. If your child has not had much practice in drawing, it may be a good idea to spend some time practicing standing forms such as squares, triangles, circles, rectangles and stars. Draw with your child and allow her to imitate you. Don't hesitate to draw a form for a young child, allowing her to trace your work. Soon they will learn the movement and pattern and be able to work independently.
Our form drawing tale will be centered on the story of King Equals and how he brought peace to the Kingdom of Numeria. Read this story to your child and practice drawing the form before making a main lesson book page (a sample page is shown here). Perhaps after practicing the form each day, the child can draw it in the Main Lesson Book on Friday. Encourage your child to draw this form with a continuous and uninterrupted movement. Have fun with the colors. You can use these forms to practice memorizing the order of the colors of the rainbow too.
The Story of the Great King Equals
Once upon a time there was a sad prince who lived in a great stone castle in a divided kingdom. For many years his ancestors ruled the kingdom in peace; but one day, in the furthest part of the kingdom, a great treasure was discovered in hidden cave. Ever since that day the people of the kingdom argued and quarreled over the question of who was the rightful owner of the cave and the great treasure. As the prince looked out through the parapets of the great stone castle, he longed for the day when his family's great kingdom would be one again.
At this point show your child the sample page of the running form pictured above. (Download great_king_equals.Story 1.PDF
) These lines resemble the parapet of a castle wall. Practice drawing this form each day, retelling the story each time. By the end of the week your child should be able to narrate the story himself as he works on mastering this form.
Now is a good time to add a few mathematically themed read-alouds. Living math goes hand-in-hand with Living Books. Here are a few titles for this week: