Gnomes and Gnumbers: A Mathematical Tale - Lesson One

    Once upon a time, in the deepest, darkest recesses of the earth, there lived a clan of four greedy gnomes. The first was as blue as a crisp, clear sky.  The second was the shade of a red apple in autumn.  The third was as yellow as the sun and the fourth was greener than a blade of grass.

    Now gnomes are a curious folk.  Burrowing deep in the ground, they build hidden cities that guard the treasures of the earth.  Of course you already knew that, but these gnomes were particularly curious folk.  Not content to work with their fellow earth-dwellers, they wanted to make a name for themselves and build up a treasure greater than any the world had ever known.  So these four miserly gnomes dug and burrowed and tunneled until they reached the middle of the earth where they believed their treasure would remain protected.

    Days and weeks and months went by and the four gnomes came to realize that they had nothing to do but count and sort their mounds and mounds of jewels all the day long. It wasn't long before the gnomes began arguing among themselves about the true owner of the treasure.

    "It is all mine!"  squeaked the small yellow gnome as he scooped great piles of rainbow-colored gems toward himself.  "I am the one who found the way to the middle of the earth.  The jewels belong to me."

    After many days of bickering and quarreling, each of the four gnomes had clearly argued their reason for being the rightful owner of the treasure.  Finally, the red gnome offered a solution.

    "Perhaps if we divide the gems evenly among ourselves..." he timidly suggested. (Having kept some of his wits about him, he realized that the only way for peace and quiet to return to their cavernous home was to share the treasure equally.)

    "But how shall we know if we have divided the treasure evenly?" asked the green gnome.

      The gnomes fell silent, each trying to think of a way to be absolutely certain that their pile was equal to the piles of the other gnomes.

    After what seemed like hours upon hours, the yellow gnome suggested that they take a trip back up through the winding tunnels to the surface of the earth in search of someone with wisdom who could solve their problem.  The others reluctantly agreed and soon they were on their way.

    The gnomes made their way through a tunnel which led to a secret hollow in a magnificent, ancient tree.  Climbing out of the hollow, they tripped over the gnarled feet of the tree and looked around hoping to find someone to direct them to the dwelling place of a wise one who would offer a solution to their problem.  Suddenly a sparkle of brilliant color caught the eye of the green gnome.

    "What is that?" he asked in a whisper.

    The gnomes turned and together discovered a pile of the most beautiful gemstones.

    "They are mine!"  shouted the green gnome.  "I spotted them first!"

    Before he had a chance to dive upon the pile of gems, the red gnome held up his wee hand and interrupted.  "Let us use sticks to count how many gems there are and then we shall share them. Surely this is a great treasure which we must carefully guard."  Then reaching up to the tree above him, he pulled down on a branch and snapped it off.

    "Huuuummmphh!"

"What was that?" asked the blue gnome.

    The other gnomes ignored the deep and unusual sound and went about their work of counting.

    After spreading the gems on the ground, the gnomes laid down the branch next to the first stone.  And when they added a second gem they broke the branch in two.  For the third stone they broke one of the two branches again and saw that they had three stones and three sticks.  Then a fourth gem was moved but the sticks were becoming hard to keep track of and they stopped to find a solution.

    "Let us use two of the pieces of the branch to make the shape of the Letter V.  That looks like the "V" between our thumb and other fingers when we hold up our hand.  That will help us to remember the number five"  suggested one of the gnomes.

    Placing one of the leftover sticks before the V-shaped pair, the gnomes counted four.

    "One before five is four."

    The gnomes continued to count the gems in this way.  The V-shaped formation showed five and then adding a stick after it made six.

    "One after five is six."  The gnomes were rather pleased with themselves.

    Pulling a seventh gem from the group, they decided to break the single stick in half to make seven.  One of those was broken again to make eight.

    "This is getting confusing again," sighed the red gnome.  "What can we do to count so many gemstones?

     "I know," boasted the greedy yellow gnome.  "Let's cross two sticks together, like our arms crossed in front of our chest.  This will remind us that the gems are all mine!"

     The other three were not happy with his solution, but not being able to come up with a better one, they agreed.  It was true, when both hands are crossed together they counted ten fingers. The sticks in the shape of a V were rearranged to form an X.

    "One before ten is nine" said the yellow gnome.

    Again the gnomes continued moving the gems and counting.  The X-shaped sticks by themselves represented ten gems and then one more was added in front of it.

    "One after ten is eleven.  And two after ten is twelve."

    The gnomes were tired and sat down to rest.

    "We have so many more gems to count.  We will most definitely need another branch" announced the yellow gnome.

    And just as he raised his arm to grab the nearest branch..."Huuuummmphh!"  An enormous woody hand swooped down and scooped him up high above the green ceiling of the forest.

LESSON PLANS

According to the age and ability of your child, this lesson could be used over a period of one week or up to one month.  All work should be done in a Main Lesson Book with both stick and block crayons.  Recommended resources and suggested sources are linked below. The lesson plans are suggested for two different age groups.  The ages are only offered as a general estimate but, of course, the parent will be able to best identify the work which will most benefit her own child.

Along with a variety of math-related games and fun, the scope and sequence of the Gnomes and Gnumbers Main Lesson covers the four mathematical processes (addition, subtraction, multiplication and division), counting to 1,000, place value, both horizontal and vertical operations, identifying odd and even numbers, multiplication work up to the 12 times table, mental math, borrowing and carrying work, multiple digit and multiple operation problem solving. 

The original art work can be downloaded and reprinted for use as a visual in telling this story.

The Greedy Gnomes
Download greedy_gnomes.PDF

The Ancient Tree
Download ancient_tree.PDF

Tree Folk
 Download tree_folk.PDF

If you are using this math story with a 5 or 6 year old (or a child with little or no previous math experience), you may want to consider introducing one Roman Numeral per day.  Before you tell this story, go outside with your child and find a stick to use for story time.  The child can break it apart as the gnomes break their stick.  (Rather than breaking a stick, using toothpicks is another option.)  The illustration offered above of the gemstones, sticks and Roman Numerals is a sample page of a Main Lesson Book.  For a young child you will want to demonstrate drawing this page and allow your child to imitate you. 

After the Roman Numerals I through XII are introduced, you will want to spend a few days writing the numbers 1 through 12 on another page of the Main Lesson Book.  Ask your child to draw a different colored gemstone between each number to keep them from running together into one huge number. 

As you work through this introduction you should spend some part of your lesson playing counting games.  Find creative ways of reinforcing number recognition.  Model numbers one through twelve out of modeling beeswax or instead, cut them in salt dough with number cookie cutters, which can be baked and later painted. 

Add movement to your child's learning and take time to play number games.  Toss a bean bag back and forth while taking turns counting the next number.  (Say "One" and toss the bean bag to your child.  He or she will respond "Two" and throw it back to you as you say "Three" and so on.)  The early learning game of Walking the Line can offer another fun exercise in counting.  Mark a line with masking tape or use a grout line on a tile flour.  As your child walks forward, together count forward to twelve and as he or she walks backwards, count the numbers backwards with your child from twelve to one.

If you are using this math story with a 7 or 8 year old (or a child who has a basic understanding of numbers and familiarity with one or two of the four basic math processes), you may be able to tell this story in one day. Have your child complete the entire Main Lesson Book entry of Roman Numerals I through XII on the same or following day.  (As with a younger child, some children will need to imitate your example.  Don't hesitate to draw with your child.) On the following day ask your child to narrate the story as you look at yesterday's drawing in the Main Lesson Book. 

According to the ability of your child, have him write (in crayon) the numbers one through one hundred in his Main Lesson Book.  (You can spread this exercise out of several days if necessary.) Ask him to change colors every tenth number. (For example, 1 through 9 are green, 10-19 are red, 20-29 are blue, etc...) This will help in preparation for learning place value.  Have him separate each number by drawing a gemstone between each number to keep the numbers from running together. 

One day, or if necessary over the course of several days, have your child model the numbers one through twelve using beeswax or use cookie cutters and salt dough and bake.