Thursday, 3 January 2019

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Montessori Activity: Long Division with Racks & Test Tubes (Double Digit Divisor)


Age: 7.5 years old

Objective: To teach  the concept and method of division in a concrete way

Materials:

The Montessori Long Division set consists of:
1. 7 test tube racks
2. 3 white racks for the groups of units.
3. 3 grey racks for the groups of hundreds.
4. 1 black rack for the thousands.
5. Each rack has 10 test tubes.
6. Each test tube holds 10 beads of the relevant hierarchical colors from units to millions.
7. 7 containers colored on the outside that correspond to the colors of the racks and on the inside that correspond to the colors of the bead.

Presentation:

1. Set up the materials that is shown above:
- Count the number of beads in a test tube with your child - there should be 10 each.
- Explain that each set of test tubes represent the different categories of numbers i.e. red for hundreds, blue for tens and green for ones.
- Similarly introduce the 4 boards to the child i.e. one of the green boards for thousands, red board for hundreds, blue board for tens and the other green board for ones.

2. Write down the division problem, e.g. 645 / 15 = ?. Explain that you have 645 cookies (the dividend) and they are to be shared equally among 15 kids (the single digit divisor). How many cookies will each kid get? Explain that the concept of division is about sharing equally.


3. The skittles are used to represent the divisor. Place 1 skittle on the blue board and 5 skittles on the green board representing the divisor 15 in this example. I tell my child that each skittle is the figure of a kid.

4. Each test tube consists of 10 beads. Each red bead represents a hundred. For 645, place 6 red beads into the red container.

5. Each blue bead represent a ten. For 645, place 4 blue beads into the blue container.

6. Each green bead represents a unit. For 645, place 5 green beads into the green container. The beads above represent the dividend 645.

7. To share the cookies equally among the 15 kids, distribute the red beads from the red container and the blue beads from the blue containers at the same time.

8. You will need to exchange 2 red beads for 20 blue beads in order to distribute them equally among the 15 kids on the blue and green boards, until you cannot do so anymore without some kids receiving more than the others. Count only the red beads. You will notice this means each kid will get 4 red beads.
9. Then write down "4" on the tenth place of your worksheet. Count all the beads on the board - they will add up to 45. Write down "60" in your working sheet.

10. Clear the boards of the beads back into the respective test tubes.

11. Distribute the remaining blue beads and the green beads in the containers equally to the skittles.  You will need to exchange 1 blue beads for 10 green beads in order to do so. Count only the blue beads on the board. You will notice this means each kid will get 3 blue beads.
12. Then write down "3" on the unit place of your worksheet. Count all the beads on the board - they will add up to 45. Write down "45" in your working sheet. You will notice that there is no remainder and the containers are now completely empty.

13. Summarize by saying that each of the 15 kids will receive 43 cookies.

Video Demonstration:


References:
https://www.montessoricommons.cc/long-division

Picture Illustration:

1. Set up the materials that is shown above:
- Count the number of beads in a test tube with your child - there should be 10 each.
- Explain that each set of test tubes represent the different categories of numbers i.e. red for hundreds, blue for tens and green for ones.
- Similarly introduce the 4 boards to the child i.e. one of the green boards for thousands, red board for hundreds, blue board for tens and the other green board for ones.

2. Write down the division problem, e.g. 645 / 15 = ?. Explain that you have 645 cookies (the dividend) and they are to be shared equally among 15 kids (the single digit divisor). How many cookies will each kid get? Explain that the concept of division is about sharing equally.

3. The skittles are used to represent the divisor. Place 1 skittle on the blue board and 5 skittles on the green board representing the divisor 15 in this example. I tell my child that each skittle is the figure of a kid.

 4. Each test tube consists of 10 beads. Each red bead represents a hundred. For 645, place 6 red beads into the red container.

 5. Each blue bead represent a ten. For 645, place 4 blue beads into the blue container.

 6. Each green bead represents a unit. For 645, place 5 green beads into the green container.

The beads in the containers above represent the dividend 645 (or the "cookies").


7. To share the cookies equally among the kids, distribute the red beads from the red container and the blue beads from the blue container at the same time.


8. You will need to exchange 2 red beads for 20 blue beads in order to distribute them equally among the 15 kids on the blue and green boards, until you cannot do so anymore without some kids receiving more than the others. Count only the red beads. You will notice this means each kid will get 4 red beads.



9. Then write down "4" on the tenth place of your worksheet. Count all the beads on the board - they will add up to 45. Write down "60" in your working sheet.

 10. Clear the boards of the beads back into the respective test tubes.

 11. Distribute the remaining blue beads and the green beads in the containers equally to the skittles.  You will need to exchange 1 blue beads for 10 green beads in order to do so. Count only the blue beads on the board. You will notice this means each kid will get 3 blue beads.

 12. Then write down "3" on the unit place of your worksheet. Count all the beads on the board - they will add up to 45. Write down "45" in your working sheet. You will notice that there is no remainder and the containers are now completely empty.

13. Summarize by saying that each of the 15 kids will receive 43 cookies.

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