The Cube Land Saga – Book 1 – Addition and Subtraction decomposition and regrouping

Chapter One

Once upon a time there was a land called Cube Land. It was ruled by the King of the Cubes.

Cube Land was a Northern Kingdom, and had other Kingdoms all around it. The Kingdom that lay to the south of it was known to be full of restless cubes that liked to fight and make war. (More about that in Book Two.)

There were A LOT of cubes in Cube Land. Too many in fact.***

(Can you count how many cubes there are in YOUR Cube Land?)

Chapter Two

One day the King decided to sort out his Kingdom. He decided to split his Kingdom into two different parts. He made rules for each of the new parts, and gave the lands new names.

“The first shall be called the Ones Land. The second shall be called the Tens Land.” The King proclaimed. “And the rule will be that from now on, there can only be 9 or less Ones cubes in Ones Land at any time. All others must get into groups of ten and go and live in Tens Land.” The King thought for a minute, and then said: – “And there shall be a line to divide the two new lands.”

“But how will we know which group of ten we are in once we get to the other side?” asked his people.

“You will all be attached together into a line of ten, and you will not be able to become loose again until you cross the border into Ones Land.”

All the Cubes thought the King was brilliant. They all sorted themselves out into groups of ten, and the ones who could form a line of ten became attached to each other, and left for Tens Land. There were 9 or less ones left in Ones Land. ***

(Can you sort out the Cubes you have in front of you into Ones Land and tens Land?)

Chapter Three

After a few days the people noticed that Tens Land was kind of crowded. There were A LOT of Tens in Tens Land. They said to the King: –

“Your Majesty, we are too crowded! Can you help us?”

The King thought for a while and then decided.

The King decided to sort out his Kingdom again. He decided to split his Kingdom into THREE different parts. He made rules for each of the new parts, and gave the lands new names.

“The first shall be called the Ones Land. The second shall be called the Tens Land, and the third shall be called the Hundreds Land.” The King proclaimed. “And the rule will be that from now on, there can only be 9 or less Ones cubes in Ones Land at any time, and only 9 or less lines of ten in Tens Land. All others must get into groups of hundreds and go and live in Hundreds Land.” The king thought for a minute, and then said: – “And there shall now be lines to divide the three Lands, so that everyone will know where to be.”

“But how will we know which group of a hundred we are in once we get to the other side?” asked his people.

“Ten lines of Ten will be attached together into a square shape, and you will not be able to become loose again until you cross the border into Tens Land. All other rules still apply.”

All the Cubes thought the King was brilliant. They all sorted themselves out into groups of hundreds and the ones who could form ten lines of ten became a square of a hundred. Following the King’s rule 9 or less lines of ten were left in Tens Land, and there 9 or less left in Ones Land. ***

(Can you sort out the Cubes you have in front of you into Ones Land, Tens Land and Hundreds Land?)

Chapter Four

After a while. the Hundreds Land became very crowded. There were A LOT of Hundreds in Hundreds Land. They said to the King: –

“Your Majesty, we are too crowded! Can you help us?”

The King thought for a while and then decided.

The King decided to sort out his Kingdom yet again. He decided to split his Kingdom into FOUR different parts. He made rules for each of the new parts, and gave the lands new names.

“The first shall be called the Ones Land. The second shall be called the Tens Land, and the third shall be called the Hundreds Land. The fourth shall be called the Thousands Land.” The King proclaimed. ‘ And the rule will be that from now on, there can only be 9 or less ones cubes in Ones Land at any time, 9 or less lines of ten in Tens Land, and 9 or less hundred squares in Hundreds Land. All others must get into groups of thousands and go and live in Thousands Land.” The King thought for a minute, and then said: – “And there shall be lines to divide the three Lands, so that everyone will know where to be.”

“But how will we know which group of thousand we belong to in once we get to the other side?” asked his people.

“Ten squares of a hundred will be attached together into a box shape, and you will not be able to become loose again until you cross the border into Hundreds Land. All other rules still apply.”

All the Cubes thought the King was brilliant. They all sorted themselves out into groups of thousands. Following the King’s rule, 9 or less Squares of a hundred in Hundreds Land, 9 or less lines of ten were left in Tens Land, and there were 9 or less left in Ones Land. ***

(Can you sort out the Cubes you have in front of you into Ones Land, Tens Land, Hundreds Land, and Thousands Land?)

Q & A

1. What do you think happened next? And then?… And then?
2. How do you think the King solved the problem that came next? And the next? And the next?
3. How many ones can be in Ones Land?
4. How many lines of ten can be in Tens Land?
5. How many squares of a hundred can be in Hundreds Land?
6. How many boxes of a thousand can be in Thousands Land?