In which the blue gnome takes away a new lesson
While the other gnomes happily added up piles of gemstones, the blue gnome had slipped off by himself with a handful of gemstones.
He loved all the beautiful colors of the gemstones, but had decided he could do without orange. His plan was to start taking away the orange ones and count how many were left.
He pulled out a handful of gemstones and began taking away the orange ones.
“Let’s see…take away one orange, take away one orange, take away one orange…” he continued for some time.
Soon he had two piles of gemstones. One pile was just orange and the other pile had the rest of the colors. By this time his friends, including Old Dismas, curious where he had gone, were watching quietly.
“Huuuuumph. Subtraction.” said Old Dismas.
Startled, the blue gnome looked up and realized he was no longer alone.
“What’s that?” he said, “I’m just trying to take away the orange ones.”
“What you are doing is called Subtraction. You see how you are taking away one gemstone, and another gemstone and so on? That is called Subtraction. How many gemstones do you have left that are not orange?”
“I’m not sure…I’ll just take away another one and another one…” He realized he was no closer to knowing how many were left.
Now, King Equals came over. The blue gnome hoped he might have a way to help him just as he had helped the green gnome.
“Can you help me?” he asked.
“I certainly can,” replied the King. “I have a gift for you as well,” he said as he pulled out his wand. The King waved his wand at the blue gnome’s chest and suddenly a symbol appeared there. It was one line going side to side.
“Whenever you want to find out how many, just remember to use this sign between each number. And when you have finished, call on me and you will find your answer,” finished King Equals.
The blue gnome looked down at a pile of five gemstones and took away one orange. He wrote the sign in the earth between them. “Five gemstones – one gemstone. King Equals?”
The King approached the gnome and answered, “Four gemstones. Five gemstones take away one gemstone equals four gemstones.”
The blue gnome continued, “Four gemstones – one gemstone. Equals?”
The King answered, “Four gemstones take away one gemstone leaves you with three gemstones.”
Now the blue gnome understood. The little sign took away the gemstones he didn’t want and left him with fewer gemstones. And just like Plus, King Equals' answer told him just how many were left.
“Oh! I get it. Three gemstones take away one gemstone is two gemstones.” He was so relieved that he wouldn’t have to count all those orange gemstones he jumped up and down with glee.
“Excellent work! You have understood well. Because you have also figured out a mystery of counting you too shall have a new name. From this time forth you will be known in Numeria as Minus.” King Equals tapped the shoulder of the gnome, granting him his new name.
“Hah! Of course, Subtraction must be the secret of numbers,” the blue gnome said with pride.
Old Dismas laughed so hard the ground beneath the gnomes shook. “No, my little friend. It is true you are closer, but there is still more to learn. For now, keep practicing with your new symbol.”
The yellow gnome spoke up. “I think I would like to subtract all the blue gemstones from my pile.” So off he went. Minus kept busy taking away the orange gemstones. Plus decided he would keep adding his.
But Red had an idea that just might help him add up more gemstones quicker than any of them imagined. He went off by himself and started making piles.
You can Download Subtraction.pdf here.
The next few weeks will be spent working with Minus. Take this time to really master basic subtraction. For now there will be no borrowing or regrouping. You should continue to review and reinforce lessons on place value to prepare for the next step in subtraction. Use whatever manipulatives you know and love. As stated before in the Gnomes and Gnumbers lessons, they are an essential element in presenting an abstract concept in a concrete way.
For younger children start with a small pile of gemstones in two different colors. For example, three red gemstones and two blue gemstones. Count the whole group-five. Next have the child "take away" the blue gemstones. Ask, "How many are red gemstones are left?" Then "say" the equation, "Five minus Two equals Three." This can then be illustrated in the main lesson book with the equation written below. As you practice, write and illustrate. Switch to using just one color of gemstone. An older child could probably start using just one color. Work up to as large a number as your child is comfortable with. Remember, don't worry about borrowing just yet.
For an older child you can begin working in the orange band of the rainbow. That is, using a base ten set, take the ten rods and practice subtracting tens. For example, fifty minus ten equals forty. The same can be done working in the yellow band, the hundreds. Keep illustrating and recording work in the main lesson book.
Use a chalkboard to practice. Write a subtraction problem. Let's say, 6-4=___. Draw six gemstones. Show your child how to carefully erase four gemstones. The remaining gemstones is the answer. These problems can be copied into the main lesson book.
Revisit the Number Ladder. When we go down the right side, the numbers get smaller. Practice walking down a certain number of steps starting anywhere on the ladder. For example, "What if we start on the fifth rung a step down three rungs. Where are we now?" This could be made into a simple game to race to the bottom by just taking turns rolling a dice and stepping down however many steps each turn.
In one sense, subtraction undoes addition. Helping your child to understand how parts relate to a whole will help them to understand this. Using Cuisenaire rods or Math-U-See blocks would be the best way to illustrate this in a concrete way. If you take a block five units long and line it up with a two unit block and a three unit block, your child can see the relationship between 3+2=5 and 5-3=2 as well as 5-2=3. Working with different lengths and different equations. For example, you can use a four unit block and a one unit block lined up with a five unit block. This will help reinforce the earlier concept of the many ways to add up to a number. To extend this further with an older child, challenge them to use three different lengths to add up to and then take away from a number. For example, 2+2+1=5 and 5-2-2=1 and so on.