#### Material

Small wooden squares, all the same size:

Green squares with the symbol 1.

Blue squares with the symbol 10.

Red squares with the symbol 100.

Some green squares with the symbol 1000.

Skittles (for division): 9 green, 9 blue, 9 red and 1 large green.

Some small discs in green, blue, and red.

A compartmented box for all the above.

A tray with squared paper, pencil and ruler.

#### Presentation

##### Short Division Static

- Invite the child to the lesson.
- Ask him to get the stamp game box.
- Tell the child you are going to bring a new underlay and paper.
- Bring the new underlay and short division paper, and a pencil on a tray to the table.
- “I’m going to write a number on this paper and then you can make it with stamps.”
- Write a number such as 3696 and ask the child to make it with the stamps.
- “You did division with the golden beads. Do you remember what division means? That’s right! It means a number is shared equally into smaller numbers!”
- Pick up a green skittle from the box.
- “This is called a skittle, it’s what we’re going to share the number out to.”
- Place a total of three skittles on the left side of the table, each in their own column.
- “We’re going to share to three skittles.”
- Write a 3 to the right of the 3696, leaving a space in between.
- “Do you remember which category we start with when dividing? Right, the largest category!”
- Begin to divide the thousands up, one at a time, placing one 1000 stamp in each of the 3 skittle columns.
- Continue this process for hundreds stamps, right under the 1000 stamp in a column, and let the child begin to place the stamps himself.
- Let the child finish dividing and placing the rest of the stamps.
- “Do you remember how we figured out our answer when dividing with the number beads? Right, we looked at what one tray has. Here, we just need to look at what one skittle has!”
- Count the number with the child to arrive at your answer, such as 1232.
- “To check, let’s count what the other skittles have to be sure that we are right.”
- Count the stamps in the other skittle columns.
- “They are all 1232!”
- “I’ll show you how to write this.”
- Write a division symbol in the empty spot between the dividend and the divisor.
- Write the equals symbol after the divisor and the answer after that, such as 1232.
- “This symbol means divide, we can say ‘divided by.’”
- “3696 divided by 3 equals 1232.”

##### Short Division Dynamic

- Invite the child to the lesson.
- Give the child a number that will require exchanging, such as 3467.
- Repeat the same process as before, but this time with exchanges.
- Once the child has finished exchanging, he should have a remained, such as 2.
- “We have some left that we can’t share.”
- “I’ll show you how to write it.”
- Write the answer 1155 followed by ‘r.’
- “This r. means remainder. What was our remainder? Right, just 2!”
- Read the paper “3467 divided by 3 equals 1155 with a remainder of 2.”

##### Long Division Two Digit Divisor

- Invite the child to the lesson.
- Repeat the same process as before, but we will use a two digit divisor and we will introduce the blue skittles which represent 10.
- Ask the child to write a number such as 3657.
- “We are going to divide it 23 times!”
- Introduce the blue skittles.
- “We are going to give the green skittles 10 times less than the blue skittles.”
- Start sharing out the stamps, 100 stamp for blue is a 10 stamp for green, and making exchanges.
- Hand off to the child.
- Conclude the exercise the same as the previous exercises.

##### Long Division Three Digit Divisor with a 0 in the Middle

- Invite the child to the lesson.
- Repeat the same process as two digit divisor, but this time we are using a three digit divisor with a 0 in the middle.
- “Can you write 5259?”
- Ask the child to make this number with stamps.
- “We are going to divide by 203.”
- Ask the child to write the division symbol followed by 203.
- “That’s a big number! We will use the red skittles, too. Each red skittle represents 100, right? You know that!”
- “We will use this blue circle here. This blue circle represents 0. No one is home!”
- “The three green skittles are the same as before. Together, this is 203!”
- “Remember, blue is 10 times less than red, and green is 10 times less than blue.”
- Start the sharing out process to emphasize that ‘no one is home at blue.’
- 1000 at red, is 0 at blue, but 10 at green, as the tens spot would have 100 had the divisor not had a 0 in the tens spot.
- Hand it off to the child and ask him to share the rest out.
- Conclude the exercises the same as the previous exercises.

##### Three Digit Divisor with a 0 in the Units

- Invite the child to the lesson.
- Repeat the same process as before, but this time we are using a 0 in the units.
- Ask the child to write a number such as 5289 and ask him to make that number in stamps.
- “We are going to divide by 230. Can you write that?”
- Place 2 red skittles, 3 blue skittles, and a green circle.
- “This time our units is just a zero.”
- “Remember, blue gets 10 times less than red, and green gets 10 times less than blue.”
- Ask the child to share it out.
- Once the child realizes there is a remainder, say:

“Oh you’re right, you’re done sharing out, but how do we know the answer? We normally look at our units place for our answer, but this time, the units place is a 0 and has no stamps!” - “Well, the green skittle is just 10 times less than blue. Can you figure out what the answer is?”
- “Right! 22! Can you write that? Make sure you count the remainder and write that, too!”

#### Exercises

Child works independently.

#### Purpose

To reinforce and consolidate the understanding acquired in collective exercises by means of individual work.

Further experience with place value.

To show how to write a problem and then to check it.

#### Control of Error

The child may be shown how to check his answers by means of reverse operation.

#### Age

5 to 5 1/2

#### Notes

These exercises are nice, as the child gets to collect his papers of math problems and take them home.

This individual work allows a child to not be held up by his friends as he would be in collective exercises.

Eventually through independent work, the child will discover the need to deal with remainders which are very large.