Montessori Activity: Stamp Game - Dynamic Subtraction

AGE: 5.5 years (after the child is familiar with the decimal system, Static Subtraction With Golden Beads and Dynamic Subtraction With Golden Beads)

OBJECTIVE(S):

To teach subtraction without using golden beads.

MATERIALS:

1. Stamp Game
2. Subtraction worksheet
3. Pencil and eraser
4. 1 mat (optional)

PRESENTATION:

1. Read the equation:

                  7325
                - 5956
                --------
                        ?      
                --------

2. Arrange the stamps showing the minuend e.g. 7325

3. Point to the unit place value and explain that it is not possible to subtract 6 from 5 without exchanging the stamps.

4. Exchange 1 blue ten stamp with 10 green unit stamps from the bank and place the 10 green unit stamps together with the unit stamps.

5. Keep track of the exchange by counting the remaining blue ten stamps (now 1) and green unit stamps (now 15).

6. Indicate on the worksheet by crossing out the number 2 in the ten place value with 1 and writing 1 in front of the 5 unit place value indicating that there are now 15 unit stamps.

7.  Subtract 6 green unit stamps from the now 15 green unit stamps and return them to the bank.

8. Count the remainder and write the answer 9 in the unit place value.

9. Point to the ten place value and explain that it is not possible to subract 5 from 1 without exchanging.

10. Exchange 1 red hundred stamp with 10 blue ten stamps from the bank and place the 10 blue ten stamps together with the ten stamps.

11. Keep track of the exchange by counting the remaining red hundred stamps (now 2) and blue ten stamps (now 11).

12. Indicate the change on the worksheet by crossing out the number 3 in the hundred place value with 2 and writing 1 in front of the 1 ten place value indicating that there are now 11 ten stamps.

13. Subtract 5 blue ten stamps from the now 11 blue ten stamps and return them to the bank.

14. Count the remainder and write the answer 6 in the ten place value.

15. Point to the hundred place value and explain that it is not possible to subract 9 from 2 without exchanging.

16. Exchange 1 green thousand stamp with 10 red hundred stamps from the bank and place the 10 red hundred stamps together with the hundred stamps.

17. Ask your child to keep track of the exchange by counting the remaining green thousand stamps (now 6) and red hundred stamps (now 12).

18. Indicate on the worksheet by crossing out the number 7 in the thousand place value with 6 and writing 1 in front of the 2 hundred place value indicating that there are now 6 green thousand stamps and 12 red hundred stamps.

19. Subtract 9 red hundred stamps from the now 12 red hundred stamps and return them to the bank.

20. Count the remainder and write the answer 3 in the hundred place value.

21. Subtract 5 green thousand stamps from the now 6 thousand stamps and return them to the bank.

22. Count the remainder and write the answer 1 in the thousand place value.

23. Read out the question and the answer again and verify by counting the stamps:

                  7325
                - 5956               
                --------
                  1369        
                --------

VIDEO DEMONSTRATION:

ADDITIONAL INFORMATION:

Our Little FECS (5Y11M20D) tried this for the first time today 25 Feb 2015. He was very tired and still jet lagged from our trip back from Singapore. He understood the concept, but required step-by-step prompting. It was a little wasted work. I will have repeat this again.

Our Little FECS tried this again on 17 August 2015 (6Y5M11D). He was able to do the first sum, but found it a little challenging with 703 - . For a moment, he got stuck with the "0" in 703. But this time around, it has been better than the first time, and practice makes perfect. He found division with remainer easier than dynamic subtraction.

REFERENCES:
http://www.montessorialbum.com/montessori/index.php?title=Addition_With_the_Stamp_Game

The stamp game is available from Amazon:

1. Read the equation

2. Arrange the stamps showing the minuend e.g. 7325

3. Point to the unit place value and explain that it is not possible to subtract 6 from 5 without exchanging.
4. Exchange 1 blue ten stamp with 10 green unit stamps from the bank and place the 10 green unit stamps together with the unit stamps.

5. Keep track of the exchange by counting the remaining blue ten stamps (now 1) and green unit stamps (now 15).

6. Indicate on the worksheet by crossing out the number 2 in the ten place value with 1 and writing 1 in front of the 5 unit place value indicating that there are now 1 blue ten stamps and 15 green unit stamps.

7.  Subtract 6 green unit stamps from the 15 green unit stamps and return them to the bank.

8. Count the remainder units and write the answer 9 in the unit place value

9. Point to the ten place value and explain that it is not possible to subract 5 from 1 without exchanging.
10. Exchange 1 red hundred stamp with 10 blue ten stamps from the bank and place the 10 blue ten stamps together with the ten stamps.

11.  Keep track of the exchange by counting the remaining red hundred stamps (now 2) and blue ten stamps (now 11).

12. Indicate the change on the worksheet by crossing out the number 3 in the hundred place value with 2 and writing 1 in front of the 1 ten place value indicating that there are now 2 red hundred stamps and 11 blue ten stamps.

13. Subtract 5 blue ten stamps from the now 11 blue ten stamps and return them to the bank.

14. Count the remainder and write the answer 6 in the ten place value.

15. Point to the hundred place value and explain that it is not possible to subract 9 from 2 without exchanging.
16. Exchange 1 green thousand stamp with 10 red hundred stamps from the bank and place the 10 red hundred stamps together with the hundred stamps.

17. Keep track of the exchange by counting the remaining green thousand stamps (now 6) and red hundred stamps (now 12).

18. Indicate the change on the worksheet by crossing out the number 7 in the thousand place value with 6 and writing 1 in front of the 2 hundred place value indicating that there are now 6 green thousand stamps and 12 red hundred stamps.

19. Subtract 9 red hundred stamps from the now 12 red hundred stamps and return them to the bank.

20. Count the remainder and write the answer 3 in the hundred place value.

21. Subtract 5 green thousand stamps from the now 6 green thousand stamps and return them to the bank. 

22. Count the remainder and write the answer 1 in the thousand place value.

 

23. Read out the question and the answer derived again and verify by counting the stamps i.e. 1369.

25 Feb 2015 (5Y11M20D) - Our Little FECS tried this for the first time today

15.4.2015 (6Y1M10D) - Our Little FECS got it right without much supervision today :-)

Montessori Activity: Division Board - Static Division (Without Remainder)

AGE: 5.5 years (after the child is familiar with the Addition, Subtraction, Multiplication Stamp Game)

OBJECTIVE(S):

To illustrate the concept of division in a concrete and easy to understand way.

MATERIALS:

1. Division Board
2. Division worksheet
3. Pencil and eraser
4. 1 mat (optional)

PRESENTATION:

1. Read the question i.e. 16 ÷ 4 = ?

2. Pretend that the skittles represent people and the beads represent green apples.

3. Explain that 16 is called the dividend [红利] and it represents the total number of "apples" to be shared.

4. Explain that 4 is called the divisor [除数] and it represents the number of people to share the apples equally.

5. Explain that you are trying to find out how many "apples" each "person" will have, and the answer to this is called the quotient [商数].

6. Count out 16 beads (representing the "apples") and put them into a small bowl.

7. Place 4 skittles (you can also use LEGO figurines) across the top of the board, counting as you go along, and say, "these are people to share those apples in the bowl."

8. Distribute the beads ("apples") from the bowl to each skittle one at a time until there are no beads remaining in the bowl.

9.  Ask your child to count the beads ("apples") under each skittle ("person") and your child should answer 4. Explain that this is the quotient and it means that each person will get 4 "apples".

10. Ask your child to repeat the question, count and write the answer 4 on the paper i.e. 16 ÷ 4 = 4.

11. Invite your child to try the next question.

TIPS:

Start with an easy question first i.e. 8 ÷ 2.

VIDEO DEMONSTRATION:

https://youtu.be/wjvfV0Q4AIs

ADDITIONAL INFORMATION:

Over breakfast this morning, Daddy practised division with our Little FECS (5Y10M2D) using LEGO figurines and 4-in-a-line game chips. J is grasping the concept well, but still needed practice counting out the answer. J asked how much the figurines are wearing funny costume. We explained that it was because they are celebrating "Fastelavn" - a Danish tradition once a year, whereby the children turned up in kindergarten in fancy-dress.

Substituting with LEGO

Montessori Album has a fantastic idea - if you don't have this Montessori materials, not to worry, you can use LEGO man and LEGO - see here:

http://www.montessorialbum.com/montessori/index.php?title=Division_Board

REFERENCES:

http://www.montessorialbum.com/montessori/index.php?title=Division_Board
http://www.infomontessori.com/mathematics/tables-of-arithmetic-unit-division-board.htm
Shu-Chen Jenny Yen's On-line Montessori Album

The division board is available from Amazon:

 

0. Bring the tray over and set up materials as shown above

1. Read the question i.e. 16 ÷ 4 = ?
2. Pretend that the skittles represent people and the beads represent green apples.
3. Explain that 16 is called the dividend and it represents the total number of "apples" to be shared.
4. Explain that 4 is called the divisor and it represents the number of "people" to share the "apples" equally.
5. Explain that you are trying to find out how many "apples" each "person" will have, and the answer to this is called the quotient.

6. Count out 16 beads (representing the "apples") and put them into a small bowl.

7. Place 4 skittles (you can also use LEGO figurines) across the top of the board, counting as you go along, and say, "these are people to share those apples in the bowl."

8. Distribute the beads ("apples") from the bowl to each skittle one at a time until there are no beads remaining in the bowl.

8.  Ask your child to count the beads ("apples") under each skittle ("person") and your child should answer 4. Explain that this is the quotient and it means that each person will get 4 "apples".

10. Ask your child to repeat the question, count and write the answer 4 on the paper i.e. 16 ÷ 4 = 4.
11. Invite your child to try the next question.

You can also use LEGO figures and LEGO bricks in place of the skittles and beads respectively.

If you don't have the division board, don't worry, but keep it simple like the above placing the LEGO bricks directly on the table below each LEGO figure.

If you have the 4-in-a-line game at home, you can also use its chips in place of the beads or...

any other counters such as smileys in place of the beads :-)

You can also use coins, teaching how to share money equally among the LEGO figures.

Here are more pictures of Division using LEGO figures and 4-in-a-line chips

26 Jan 2015 (5Y10M21D) - J trying out the division board with LEGO and 4-in-a-line game chips with Daddy over breakfast this morning

11 Aug 2015 (6Y5M6D) - Division without remainder