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4. Decimal System

#### 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

1. Invite the child to the lesson.
2. Show the child the addition papers.
3. Ask the child to bring the stamp game to the table.
4. Ask the child to also bring two addition papers, two pencils, and two underlays on a tray.
5. Reinforce what the child know by asking him what number the different stamp categories remind him of.
6. “What does this stamp remind you of? Right, a unit bead! What about this one? Yes, a ten bar!” and so on.
7. Write a number such as 5326, ask the child to write it too.
8. Ask the child to make that number with the stamps.
9. Write another number such as 1421, ask the child to write it too.
10.  Ask the child to make the number about an inch below the other one.
11. “It’s like getting two trays of golden beads, but we are using two different numbers made of stamps!”
12. “We’re going to do addition, and I’ll show you how we do it.”
13. Slide the columns of the two different numbers together, starting with the units.
14. Ask the child to count the new number.
15. After the child counts a category, starting with the units, write that number down and ask the child to write it too.
16. Once all the categories are counted and written say:
“We did addition! But there isn’t anything on the papers that says we did addition.”
17. “This is a plus sign, it means we add. We can call it ‘plus.’”
18. “5326 plus 1421 equals 6747.”
1. Invite the child to the lesson.
2. Repeat the same process as before, but you only need one paper this time.
3. “We are going to addition again, but this time we are going to use exchanging.”
4. Say a number such as 3796 and ask the child to write it on the paper.
5. Wait for the child to make the number with stamps.
6. Say another number such as 2176, and ask the child to write it down.
7. Wait for the child to make the number with stamps.
8. With large numbers taking up a lot of space on the table, let the child know that it’s okay to place stamps of the same category in a new, adjacent, column.
9. Ask the child to add the numbers just as before by sliding the columns together and counting the stamps.
10. Once the child counts ten 1 stamps, ask him to stop and exchange them for one 10 stamp.
11. Ask the child to count the unit stamps that are still left on the table, and make sure he writes it down on the paper.
12. Repeat this process for the other categories; watch the child as he makes exchanges and writes the numbers down on the paper.
13. Finish the exercise just as before, only the child is doing it independently. Make sure he writes the plus sign.

#### Exercises

Child works independently.

#### Purpose

To reinforce what was learned with the collective exercises by means of individual work.
Further experience with place value.
To show how to write a problem.

#### Control of Error

Child does not bring work to check for accuracy, but we are watching to see if they get the right answers.

5 to 5 1/2

#### Notes

Child may work with static problems for a couple or few weeks before moving to dynamic.
You may choose to limit the number of thousands so that the child doesn’t go over 9999.
This child is quite skilled in math, and has at least begun memorization and math facts.
Prepare several static addition problems for the child before the lesson so you have a variety of problems to give him.
When the child is working on his own static problems independently, you can go to his table and write the problem for him to solve.