Wednesday, 2 January 2019

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Montessori Activity: Long Division with Racks & Test Tubes (Single 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 / 5 = ?. Explain that you have 645 cookies (the dividend) and they are to be shared equally among 5 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 5 skittles on the red board representing the divisor 5 in this example. I tell my child that each skittle is the figure of a kid.

4. Explain that each test tube consists of 10 beads. Each red bead represents a hundred. For the dividend of 645, place 6 red beads into the red container.
5. Each blue bead represent a ten. Place 4 blue beads into the blue container.
6. Each green bead represents a unit. Place 5 green beads into the green container.

7. To share the cookies equally among the kids, distribute the red beads from the red container equally among the 5 kids on the board, until you cannot do so anymore without some kids receiving more than the others. You will notice this means each kid will get 1 red bead, thus, explain that each kid gets 100 cookies so far.
8. Write down "1" on the hundredth place of your worksheet, representing that each kid gets 100 cookies so far as shown above (that we are all familiar with from Maths class). Explain that the 1 represents 100 cookies, as it is in the hundredth place.
9. Your child will notice that 1 red bead is left in the red container. In order to share it equally among the 5 kids, tell your child that this red beads needs to be exchanged for 10 blue beads (representing 10 tens). Place the remaining red bead back into the test tube containing the red beads.
10. Place the 10 blue beads from a test tube into the blue container (each test tube contains 10 blue beads). There is now a total of 14 blue beads in the blue container.

11. To share equally among the five kids, distribute the blue beads from the blue container equally among the 5 skittles, until you cannot do so anymore without some kids receiving more than the others. You will notice this means each kid will get 2 blue bead, thus, explain that each kid gets an additional 20 cookies so far.
12. Write down "2" on the tenth place of your worksheet, representing that each kid gets an additional 20 cookies so far as shown above. Explain that the 1 represents 10 cookies, as it is in the tenth place.
13. Your child will notice that 4 blue beads are left in the blue container. In order to share it equally among the 5 kids, tell your child that these blue beads need to be exchanged for 40 green beads (representing ones).
14. Place these 4 remaining blue beads back into the test tube containing the blue beads.
15. Then place 4 test tubes of green beads into the green container (each test tube contains 10 green beads).

16. To share equally among the five kids, distribute the green beads from the green container equally among the 5 skittles, until you cannot do so anymore without some kids receiving more than the others. You will notice this means each kid will get 9 green bead, thus, explain that each kid gets an additional 9 cookies.
17. Write down "9" on the unit place of your worksheet, representing that each kid gets an additional 9 cookies as shown above. Explain that the 1 represents 1 cookie, as it is in the unit place.

18. Summarize by saying that each kid will receive 129 cookies and show the working on the sheet.

Video Demonstration:






https://youtu.be/n3QQfIZFKjA


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 / 5 = ?. Explain that you have 645 cookies (the dividend) and they are to be shared equally among 5 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 5 skittles on the red board representing the divisor 5 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.

7. To share the cookies equally among the kids, distribute the red beads from the red container equally among the 5 kids on the board, until you cannot do so anymore without some kids receiving more than the others. You will notice this means each kid will get 1 red bead, thus, explain that each kid gets 100 cookies so far.


8. Then write down "1" on the hundredth place of your worksheet, representing that each kid gets 100 cookies so far as shown above (that we are all familiar with from Maths class). Explain that the 1 represents 100 cookies, as it is in the hundredth place.



9. Your child will notice that 1 red bead is left in the red container. In order to share it equally among the 5 kids, tell your child that this red beads needs to be exchanged for 10 blue beads (representing 10 tens). Place the remaining red bead back into the test tube containing the red beads.

 10. Place the 10 blue beads from a test tube into the blue container (each test tube contains 10 blue beads). There is now a total of 14 blue beads in the blue container.



 11. To share equally among the five kids, distribute the blue beads from the blue container equally among the 5 skittles, until you cannot do so anymore without some kids receiving more than the others. You will notice this means each kid will get 2 blue bead, thus, explain that each kid gets an additional 20 cookies so far.


12. Then write down "2" on the tenth place of your worksheet, representing that each kid gets an additional 20 cookies so far as shown above. Explain that the 1 represents 10 cookies, as it is in the tenth place.


 13. Your child will notice that 4 blue beads are left in the blue container. In order to share it equally among the 5 kids, tell your child that these blue beads need to be exchanged for 40 green beads (representing ones).

14. Place these 4 remaining blue beads back into the test tube containing the blue beads.

  15. Then place 4 test tubes of green beads into the green container (each test tube contains 10 green beads).



16. To share equally among the five kids, distribute the green beads from the green container equally among the 5 skittles, until you cannot do so anymore without some kids receiving more than the others. You will notice this means each kid will get 9 green bead, thus, explain that each kid gets an additional 9 cookies.

 17. Then write down "9" on the unit place of your worksheet, representing that each kid gets an additional 9 cookies as shown above. Explain that the 1 represents 1 cookie, as it is in the unit place.

18. Summarize by saying that each kid will receive 129 cookies.

Personal Journal:

Boy, it was a long long time since I have done any Maths Montessori activity with our Little FECS. The last time we did was more than 2.5 years ago on 6 April 2016, before our Baby FECS was born. I have been so busy since then with the little baby, and then back to work and then a new full-time job. thereafter, I have lost touch, and it was an uphill task to get started. Also, furthermore, I didn't think that our Little FECS was ready for this when he was 7 years old.

Being a perfectionist, I wanted to wait until I have a full slot of time, before getting into it. Today, I decided that I will start anyway, even if I only have 10 minutes and then continue the following day. It helped. Once I got started, it got easier. So don't be disheartened, if you are feeling just like me. Just get started and continue whenever you can, rather than wait until you have a full slot of time to continue.

Our Little FECS tried this on 2 January 2019 (9Y9M27D). My 2019 new year's resolution is to re-start Montessori Maths activities with Little FECS. 





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