Montessori Activity: Creating 3-Dimensional Pyramid with Colored Bead Stair

Objective:

To provide your child a sensorial experience of building squares and stacking them up into a pyramid with the colored bead stairs.

Materials:

10 each of the color bead stairs from Decanomial Bead Bars set

Additional Information:

C invented this activity by herself today while working on making combinations of 10 with colored bead stairs.

 

Montessori Maths Activity: Numbers & Counters

AGE: From 4 years old (after The Spindle Box has been introduced)

OBJECTIVE(S):

1. To reinforce the knowledge that each number is made up of separate quantities.

2. To reinforce the sequence 1 – 10 and how many separate units go to form each number.

3. To introduce the concept of odd and even numbers.

4. To provide indirect preparation for divisibility of numbers.

MATERIALS:

1. 10 numeral cards (1 – 10)

2. 55 counters of the same color.

3. A straight edge.

PRESENTATION:

Day 1: Cards

1. Name the Numbers and Counters and show where they are kept.

2. Ask the child to lay out a floor mat.

3. Lay out the number cards randomly on the mat and have the child say the numbers out loud.

4. Arrange the number cards in numerical order by saying: “Give me Card 1” and have the child put the Card 1 down. Repeat for the other cards until all the cards are laid out in numerical order.

5. Point to Card 1 and ask: “How many counters should you place under this card?”

6. The child should answer 1 and give you a counter.

7. Put the counter below Card 1 and ask the child to count the counter. Ask: “What comes next?”

8. Repeat for the other numbers placing even numbers in pairs and placing the odd numbers with the last counter under and to the middle of the pair until the child understands. (See diagram above)

9. Explain the concept of odd and even numbers: even numbers are those you can find a friend for each of them two-by-two; odd numbers are those with one left alone and has no friend :-(

Day 2: Odd and Even

1. The child constructs the Numbers and Counters from Day 1’s presentation.

2. Run the tip of your index finger down the middle of each column of pairs; for each row in which your finger strikes an unpaired counter at the end of the column, move the card a little above where it was.

3. Tell the child that the numbers which does not have a friend (i.e. an unpaired counter) are “odd” numbers, because you cannot divide it when you draw your finger down (你不能分割ge3), by saying: “This one does not have a friend, so it is an odd number.”

 

1. Repeat for counters 2 and after you have run your finger through the two counters, tell the child that the numbers with a friend standing two-by-two (i.e. pairs of counters) are “even” numbers, because you can divide it by saying: “This one has a friend, so it is an even number.”

2. Have the child repeat for the remaining counters.

3. Do a Three Period Lesson for odd and even.

4. Once the child is finished, look at all of the cards that are slightly higher than the others (cards 1, 3, 5, 7, 9) and tell the child that these are odd numbers (Stage 1)

5. Point to the other cards (cards 2, 4, 6, 8) and tell the child that these are even numbers (Period 1)

6. Repeatedly ask your child to find one that is odd or even or ask your child whether a particular number is odd or even (Period 2).

7. Point to a number and ask: “What is this?” (Period 3).

VIDEO DEMONSTRATION:

http://www.youtube.com/watch?v=5TA5xdgzRUc

CONTROL OF ERROR:

1. The correct number of counters and numerals are provided.

2. The visual image of the pattern of the counters.

NOTE:

1. Introduce this activity in parallel with the spindle box.

2. On day 1, you put out the pattern until the child get it, and you may stay longer to see if the child need help.

ADDITIONAL INFORMATION:

C tried this again on 1 May 2020 (3Y11M15D). She was able to place the glass stones until 5, however, not exactly in the formation of even and odd numbers. J (3Y7M10D) tried this on 15.10.2012 and 17.10.2012.

REFERENCES:

http://www.infomontessori.com/mathematics/numbers-through-ten-cards-and-counters.htm

http://faculty.fullerton.edu/syen/mts/math/_link.htm

http://www.moteaco.com/albums/casa/casamath.html

 1 May 2020 (3Y11M15D)

Montessori Activity: Short Chains - Skip Counting

AGE: 5.5 and up (after the child who has experience with the Hundred Chain and multiplication)

OBJECTIVE(S):

1. To teach other means of counting other than one-by-one or in bases other than ten.
2. To prepare for multiplication.
3. To understand the relation of a square of a number to the squares of other numbers.

MATERIALS:

1. 1 short chain e.g. yellow 4 chain
2. 1 yellow 4-square
3. 4 yellow 4-bars
4. Corresponding arrow number tags for 4 chains
5. 1 pointer (optional)
6. 1 worksheet (optional)
7. 1 pencil and eraser (optional)
8. 1 mat (optional)

PRESENTATION:

1. Tell the child that this is called 4-chain.
2. Line the 4 bars next to it and show that they are the same.
3. Fold the chain into a square, compare to the square to show that they are the same.
4. Straighten the chain into a line, count and label it: 1, 2, 3, 4, 8, 12, 16
5. Practice counting backwards: 16, 12, 8, 4, 3, 2, 1.
6. Fold it back into a square and label it: 4, 8, 12, 16.

VIDEO DEMONSTRATION:

http://youtu.be/8fd8BPCfpLA

http://youtu.be/WfLzrGVIG74

NOTE:

The child does not need to be shown each of the chains.

REFERENCES:

http://www.montessorialbum.com/montessori/index.php?title=Short_Chains
http://www.infomontessori.com/mathematics/skip-and-counting-skip-counting.htm

ADDITIONAL INFORMATION:

The Montessori Short Chains is available from Amazon:

1. Tell the child this is called the 4 chain.

2.  Line 4-bars next to it and show that they are the same.

3. Fold it into a square and show that they are the same as 4 bars arranged in a square.

4. Compare it to a square and show that they are the same.

5. Straighten the chain, count and label them 1, 2, 3, 4, 8, 12 and 16

6. Do a skip count 4, 8, 12, 16 and count it backwards 16, 12, 8, 4

7. Fold back into a square, skip count 4, 8, 12, 16 and label them.

8. Count backwards 16, 12, 8, 4.

REVISION:

1. Show your child that short chain is represented by the diagram on the worksheet.

2. Count the number of beads in a section and ask your child to write 4 in the first space of _ x _ = _

3. Show your child that the 4 chain is made of 4 sections and ask him to count the sections of the chain and write 4 in the second space of _ x _ = _

4. Ask the child to read the question and write the answer 16.

5. Count each bead from the bottom of the chain i.e. 1, 2, 3, 4, label 4 next to it and write 4 in the worksheet.

6. Continue from the next section and count 5, 6, 7, 8, label 8 next to it and write 8 on the worksheet.

7. Continue in the same manner until all the sections of beads have been counted and the answer written on the worksheet.

12. Explain that when a number chain is folded into a square, the number is "squared", i.e. 4^{2 -} meaning four is squared.  Therefore, explain 4² = 16

Explain the relation between multiplication, addition and squares:

4² = 4 x 4 =16 = 4 + 4 + 4 + 4 

OR 

Present it as follows, showing hat they are all equal to 16, and they mean the same thing, expressed in different ways. 

4² = 16 

4 x 4 = 16

4 + 4 + 4 + 4 = 16

ADDITIONAL INFORMATION:

J (6Y3M11D) tried this for the first time today. He explained to me that 4 x 4 = 16 and it means 4 + 4 + 4, before I explained to it to him. I asked him how he knew. He said that he learned it from his kindergarten. I then expanded further and explained 4² but it was a little difficult for him at the moment.

Montessori Activity: The Exchange Game 2

1 supply box of golden bead material serving as The Bank

 AGE: 5 years old

OBJECTIVE(S):

To demonstrate that 10 units can be exchanged for a ten-bar, 10 ten-bars can be exchanged for a hundred-square, and 10 hundred-squares can be exchanged for a thousand-cube. 

MATERIALS:

1. 1 supply box of golden bead material serving as The Bank
2. 1 tray containing random amount of beads of each type from The Bank
3. 1 mat
4. 2 containers for containing the unit beads

PRESENTATION:

1.     Put some units, ten-bars, hundred-squares and thousand-cubes into a box and say, “What a mess this bank is, I wonder how many beads we have?”

2.     Sort them out in group from right to left the unit beads in a bowl, ten-bars, hundred-squares and thousand-cubes on the mat. 

3.     Ask your child to count the unit beads into an empty bowl and when he reaches the tenth unit, let your child exchange them for a ten-bar, say, “Exchange!” and place it with the other ten-bars.
 

4.     Repeat in the same manner until there are insufficient units to exchange a ten-bar.
 

5.     Ask your child to count the ten-bars and when he reaches the tenth bar, let your child exchange them for a hundred-square, say, “Exchange!” and place it with the other hundred-squares.
 

6.     Repeat until there are insufficient bars to exchange a hundred-square.
 

7.     Ask your child to count the hundred-squares and when he reaches the tenth square, let your child exchange them for a thousand-cube, say, “Exchange!” and place it with the other thousand-cubes.
 

8.     Repeat until there are no more hundred-squares that can be exchanged for a thousand-cube.
 

9.    Ask your child to count the thousand-cubes he has in total now.
 

10.  Show your child that it is very easy to now see how much you have in the bank after exchanging by counting them together.

REFERENCES:
www.montessorialbum.com

ADDITIONAL INFORMATION:

Put some units, ten-bars, hundred-squares and thousand-cubes into a box and say, “What a mess this bank is, I wonder how many beads we have?”

Sort them out in group from left to right the unit beads in a bowl, ten-bars, hundred-squares and thousand-cubes on the mat.

Ask your child to count the unit beads into an empty bowl and

when he reaches the tenth unit, let your child exchange them for a ten-bar, say, “Exchange!” and



place it with the other ten-bars. Repeat in the same manner until there are insufficient units to exchange a ten-bar.



Ask your child to count the ten-bars and when he reaches the tenth bar, let your child exchange them for a hundred-square, say, “Exchange!” and

place it with the other hundred-squares. Repeat until there are insufficient bars to exchange a hundred-square.

Ask your child to count the hundred-squares and when he reaches the tenth square, let your child exchange them for a thousand-cube, say, “Exchange!”



 

place it with the other thousand-cubes. Repeat until there are no more hundred-squares that can be exchanged for a thousand-cube. Ask your child to count the thousand-cubes he has in total now.

Show your child that it is very easy to now see how much you have in the bank after exchanging by counting them together.

 

17 Nov 2014 (5Y8M12D)



J counting the ones and tens with containers, which he picked himself on his own initiative