## Monday 26 January 2015

### 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:

VIDEO DEMONSTRATION:

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

## Sunday 25 January 2015

### J Summary (5Y10M20D) - Making Snowman

25 Jan 2015 (5Y10M20D) - This was the first time my Mr.FECS made a snowman, since our Little FECS was born, but firstly our Little FECS said it looked too Chinese... (but hey, you are a Chinese too, Little FECS!)

and secondly... er... it was this mini size :-)... blame it on the quality of the snow, but at least we could tick off our family tradition calendar for having built a snowman during winter this year ;-)

Then we continued our walk/sledge...

and we found a huge snowman... built by others... er... so we couldn't really blame it on the quality of the snow anymore... :-(

Then we gave this snowman our carrot as nose, so that we could say that we contributed to building part if it :-)

Then we continued walking/sledging...

before the snow melts away...

Time to go home... good bye to the last bit of sunshine...

Walking past the old windmill...

with the ducks keeping us company :-)

No time to make dinner, so we had snack dinner instead with Daddy's favorite homemade 100% real tomato soup all done in 23 mins made from the Phillips soupmaker (which I got from Florian for my Christmas present) and topped with various non-cooked toppings chopped while the soup was cooking in the soup maker and a quick 15 mins oven salmon dish. Nothing fanciful, but super healthy and dinner is made :-)

## Saturday 24 January 2015

### Montessori Activity: Stamp Game - Static Division (Without Exchanging and 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. Stamp Game
2. Division worksheet
3. Pencil and eraser
4. 1 mat (optional)

PRESENTATION:

1. Read the question i.e. 4824 ÷ 2 = ?

2. Explain that 4824 is called the dividend and it represents the total number of apples to be shared.

3. Explain that 2 is called the divisor and it represents the number of people to share the apples equally.

4. Explain that you are trying to find out how many apples each person will get, and the answer to this is called the quotient.

5. Arrange 4 unit stamps, 2 ten stamps, 8 hundred stamps and 4 thousand stamps each in a vertical line representing 4824 "apples" in this case.

6. Place 2 skittles side-by-side on the desk representing the divisor/people i.e. 2 in this case.

7. Share the 4 thousand stamps, 8 hundred stamps, 2 ten stamps and 4 unit stamps equally among the 2 skittles by placing each thousand stamp one at a time under each skittle until no thousand stamps are left, followed by the hundred stamps, ten stamps and unit stamps in the same manner, until no stamps are left.

8.  Ask your child to count the stamps under each skittle and your child should answer 2412. Explain that this is the quotient and it means that each person will get 2412 apples.

9. Ask your child to repeat saying the question, count and write the answer 2412 on the paper i.e. 4824 ÷ 2 = 2412.

10. Invite your child to try the next question, this time have a problem with 3 divisor/people sharing the apples i.e. 396 ÷ 3 = ?

TIPS:

VIDEO DEMONSTRATION:

Static Division
http://youtu.be/CYHMRLpsOs0

Long Division (With exchanging, but without remainder)
http://youtu.be/fCDNoyBMHnk

Our Little FECS was intrigued by the skittles of the stamp game. He thought that we could play chess with it. He asked to try out the activity with the skittles. I thought that it was too early to present the division stamp game, which makes use of the skittles. I have so far only presented the addition stamp game and the multiplication board. I have not presented the multiplication stamp game to him, nor the division board. Nevertheless by his insistence, I decided to give it a try and demonstrated the division stamp game.

He (5Y10M19D) tried this for the first time today 24 Jan 2015. I presented the simplest division first - 8 ÷ 2 = 4 and to my surprise, before I started presenting it with the stamps and the skittles, he blah out the answer 4. We simply verify his answer with the presentation after that. I tried the next few questions 6 ÷ 2 and 9 ÷ 3, and he was able to say out the answer mentally without using the stamp game. He was able to solve all the questions. He got answer to 24 ÷ 2 wrong, saying that it is 14, instead of 12. But we used the stamp game to show that the answer was 14. We went on through the whole worksheet, and finishing off with division with thousand place value without remainder. I am not sure where he learned it from. It said it was from me, but I haven't introduce to him yet. His kindergarten only taught them numbers 1-10. So I think it could be the iPad app on division that he has been playing with that gave him his foundation for division - https://itunes.apple.com/us/app/montessori-mathemagics-dynamic/id870703884?mt=8

It also seemed there is a growth spurt with regards to Maths for kids between 5 to 6 years old. Just one year ago, he would be struggling to even get the place value correct and struggling to count 1-100. What a difference one year has made, and I didn't think that I have done much to really help him. It perhaps shows that when the child's mind is developed and ready, it will be easy for the child to learn and thus would be the time to present him with these various arithmetic concepts. I will be introducing the division board to him next.

Substituting with LEGO

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_With_the_Stamp_Game

http://homeschoolingsonshine.blogspot.dk/2015/03/long-division-with-regrouping.html

The stamp game is available from Amazon:

 1. Read the question i.e. 4824 ÷ 2 = ? 2. Explain that 4824 is called the dividend and it represents the total number of "apples" to be shared. 3. Explain that 2 is called the divisor and it represents the number of "people" to share the apples equally. 4. Explain that you are trying to find out how many apples each person will get, and the answer to this is called the quotient.

 5. Arrange 4 unit stamps, 2 ten stamps, 8 hundred stamps and 4 thousand stamps each in a vertical line representing 4824 "apples" in this case. 6. Place 2 skittles side-by-side on the desk representing the divisor/people i.e. 2 in this case.
 7. Share the 4 thousand stamps, 8 hundred stamps, 2 ten stamps and 4 unit stamps equally among the 2 skittles by placing each thousand stamp one at a time under each skittle until no thousand stamps are left, followed by the hundred stamps, ten stamps and unit stamps in the same manner, until no stamps are left.

 8.  Ask your child to count the stamps under each skittle and your child should answer 2412. Explain that this is the quotient and it means that each person will get 2412 apples.

 9. Ask your child to repeat saying the question, count and write the answer 2412 on the paper i.e. 4824 ÷ 2 = 2412. 10. Invite your child to try the next question.

### Old Medals

26 Jan 2015 (5Y10M21D) - Don't throw away your old medals... it could be an inspiration to your children. Our Little FECS is currently crazy about medals, esp. Daddy's medals collected when Daddy was a child. He asked for them, asked questions about them and could not wait for us to retrieve it from the store room. It inspired our Little FECS to strive like Daddy. My medals are all in Singapore, and I didn't even know where they are. Good that Daddy kept his :-)

Our Little FECS found a special place in his playroom to hang Daddy's medals by himself.... aaawwww... melts my heart :-)

I have been wanting to throw away the medals during spring cleaning of our home, but our "Garang guni*" man stopped me. Thank goodness I didn't :-)

* Singlish expression for someone who keeps everything

## Friday 23 January 2015

### Montessori Activity: Stamp Game - Dynamic Addition

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

OBJECTIVE(S):

MATERIALS:

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

PRESENTATION:

1. Read the first equation i.e.

2535
+1566
--------
?
--------

2. Arrange the stamps showing the first addend e.g. 2535

3. Use a ruler to make a divider under the first addend.

4. Arrange the stamps showing the second addend e.g. 1566

5. Remove the ruler divider.

7. Count the unit stamps and stop when you have counted 10.

8. Put the 10 unit stamps into the units compartment and take out 1 ten stamp. Place the ten stamp after the other stamps in the tens column.

9. Count the remaining units and write down the answer on the paper.

10.  Count the ten stamps and stop when you have counted 10.

11. Put the 10 ten stamps into the tens compartment and take out 1 hundred stamp. Place the hundred stamp after the other stamps in the hundreds column.

12. Count the remaining tens and write down the answer on the paper.

13.  Count the hundred stamps and stop when you have counted 10.

14. Put the 10 hundred stamps into the hundreds compartment and take out 1 thousand stamp. Place the thousand stamp after the other stamps in the thousand column.

15. Count the remaining hundreds and write down the answer on the paper.

16. Count the thousands and write down the answer on the paper.

17. Ask your child to say the question, count and write the answer on the paper (if this is not written down along the way earlier), for e.g.

2535
+1566
--------
4101
--------

17. Invite your child to try the next question.

VIDEO DEMONSTRATION:

Our Little FECS (5Y10M18D) tried this for the first time today 23 Jan 2015. Since he is very familiar with place value through the other Montessori exercises prior to this, we went straight to the thousand place value. He is getting a grasp of the concept, but needs guidance and reminders through the steps. For example, he would put back the 10 units, but take a hundred stamp, during the exchange. We need to repeat more exercises with exchanges and I need to learn to be patient and be more encouraging. Like most children, he prefers the stamp game to the golden beads, as he finds it easier to take the stamps than to take the golden beads. But I would not discount the golden beads and jump straight to stamp fame, as the golden bead materials sets a very good foundation step for children. Our Little FECS are also intrigued by the skittles in the stamp game - he thought it is for playing chess (he is currently crazy about playing chess at the moment), but I told him that it is for division, and we haven't reach there yet.

REFERENCES:

The stamp game is available from Amazon:

 2. Arrange the stamps showing the first addend e.g. 2535
 3. Use a ruler to make a divider under the first addend. 4. Arrange the stamps showing the second addend e.g. 1566
 5. Remove the ruler divider. 6.  Move the second addend up to join the first addend.
 7. Count the unit stamps and stop when you have counted 10 and...
 exchange the 10 unit stamps for 1 ten stamp.
 8. Put the 10 unit stamps into the units compartment and take out 1 ten stamp from the tens compartment. Place the ten stamp after the other stamps in the tens column. 9. Count the remaining units and...
 write down the answer on the paper.
 10.  Count the ten stamps and stop when you have counted 10 and...
 exchange the 10 ten stamps for 1 hundred stamp.
 11. Put the 10 ten stamps into the tens compartment and take out 1 hundred stamp. Place the hundred stamp after the other stamps in the hundreds column. 12. Count the remaining tens and...
 write down the answer on the paper. In this case, it is zero remaining.
 13.  Count the hundred stamps and stop when you have counted 10 and...
 exchange the 10 hundred stamps for a 1 thousand stamp.
﻿
 14. Put the 10 hundred stamps into the hundreds compartment and take out 1 thousand stamp. Place the thousand stamp after the other stamps in the thousands column. 15. Count the remaining hundreds and...

 and write down the answer on the paper.

 16. Count the thousands and write down the answer on the paper.

 17. Ask your child to repeat saying the question, count and write the answer on the paper (if this is not written down along the way earlier).

 23 Jan 2015 (5Y10M18D) - Trying out the Dynamic Addition Stamp Game for the first time