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.