## Saturday 26 July 2014

### Montessori Activity: Addition Snake Game

AGE: 5.5 to 6 years

OBJECTIVE(S):

1. To show the possible combinations of 10, emphasizing that in addition, you are making tens.
2. To show that addition and multiplication are of the same concept.
3. To show that no two numbers will add up to be greater than 18.

MATERIALS:

1. 1 box containing 5 sets of colored short bead bars (1-9).
2. 1 box containing 25 golden 10-bars.
4. 1 notched cardboard or plastic counter to act as marker.
5. 1 empty container to contain the used colored bead stairs (the empty black and white bead box may be used for this).
6. 1 mat or felt cloth to work on.

PRESENTATION:

1. Place the black and white bead stair at the upper right hand corner of the mat and arrange them into a triangle with the 1 black bead at the bottom and the 9 bead at the top.

2. Place the notched card below the stair and explain, "This card is to mark where we finished counting."

3. Randomly arrange the colored bead bars (use one of each and an extra 5-bar) in a zig-zag line like a snake.

4. Ask, “How many beads do you think there are in our snake?”

5. Count the beads and insert the marker after the 10th bead has been counted.

6. Place a golden 10-bar next to the colored bead bars.

7. Count the remaining beads of the bead bar, i.e. if a bar of 7 was counted first and bar of 5 second, thus 7 and 3 of the 5 would make 10. The remainder would be 2.

8. Place the black bead of 2 at the end of the 10 bar to hold the place for the remaining beads of the 5 colored bead bar. Remove the colored bead bars you already counted, 7 and 5 into the empty container. Join the snake.

9. Starting from the black bead of 2, count the beads until you reach 10 and mark it with the notched marker. Place a golden 10-bar next to it, count the remainder, place the appropriate black and white bead bar and remove the colored bead bars into the empty container. Join the snake.

10. Continue in the same manner until all the colored bead bars are replaced by golden 10 bead bars. If a black and white bar remains, replace it with the corresponding color bar and return the black and white bead bar back into its stair.

11. Arrange the golden 10-bar vertically, count them and the remaining colored bead bar and say out the answer.

VIDEO DEMONSTRATION:

Basic: Counting 1 bar at a time...

More advance: counting 2 bars at a time...

VERIFICATION:

Place the golden ten-bars in vertical rows. Take the colored bead stair that formed the snake earlier and match it next to the golden ten-bars to make 10. All combinations should be made until all 10s are matched and all bead bars are used.

CONTROL OF ERROR:

The number of bead bars, the colored bead bars should be equal to the number of ten bars, less 1. If a larger black head is desired then make the colored bead bars equal to the 10 bars, less the amount of the black bead used.

1. Place the black and white bead stair at the upper right hand corner of the mat and arrange them into a triangle with the 1 black bead at the bottom and the 9 bead at the top.

2. Place the notched card below the stair and explain, "This card is to mark where we finished counting."

3. Randomly arrange the colored bead bars (use one of each and an extra 5-bar) in a zig-zag line like a snake.

4. Ask, “How many beads do you think there are in our snake?”

5. Count the beads and insert the marker after the 10th bead has been counted.

6. Place a golden 10-bar next to the colored bead bars.

7. Count the remaining beads of the bead bar, i.e. if bars of 1 and 6 were counted first and bar of 7 next, thus 7 and 3 of the white 7-white bar would make 10. The remainder from the  white 7-bar would be 4.

8. Place the black 4-bar at the end of the 10 bar to hold the place for the remaining beads of the white 7-bar. Remove the colored bead bars you already counted, 1, 6 and 7 into the empty container. Join the snake.

9a. Starting from the black 4-bar, count the beads until you reach 10 and mark it with the notched marker. Place a golden 10-bar next to it, count the remainder and place the appropriate black and white 6-bar representing the remainder and remove the colored bead bars into the empty container. Join the snake.

9b. Starting from the black & white 6-bar, count the beads until you reach 10 and mark it with the notched marker. Place a golden 10-bar next to it, count the remainder from the purple 6-bar and place the appropriate black 2-bar next to it, representing the remainder.

9c. Starting from the black 2-bar, count the beads until you reach 10 and mark it with the notched marker.

Place a golden 10-bar next to it, count the remainder from the blue 5-bar and place the appropriate black 1-bar next to it, representing the remainder.

9d. Starting from the black 1-bar, count the beads until you reach 10 and mark it with the notched marker. Place a golden 10-bar next to it, count the remainder from the blue 5-bar and place the appropriate black 1-bar next to it, representing the remainder.

9e. Starting from the black 1-bar, count the beads until you reach 10 and mark it with the notched marker.

Place a golden 10-bar next to it. There is no remainder from the blue 5-bar in this case.

10. Remove the colored bead bars, continue in the same manner until all the colored bead bars are replaced by golden 10 bead bars. (If a black and white bar remains, replace it with the corresponding color bar and return the black and white bead bar back into its stair.)

11. Arrange the golden 10-bar vertically, count them and the remaining colored bead bar and say out the answer, in this case it is 61.

12. To verify the answer, take the colored bead stair that formed the snake earlier from the container and place them next to the golden ten-bars forming combinations of 10. All combinations should be made until all 10s are matched and all bead bars are used.

I tried this with J for the first time on 6 August 2014 (5Y5M1D). He understood the concept, but having difficulty using the markers.

J wanted to do a Montessori activity that does not require him to write. So we tried it again on 25 May 2015 (6Y2M20D). We tried this again on 26 May 2015, so that he got to practise more. He is getting better and better. He likes to have me around when he is working on it, but I need to let him try to take it all the way from the beginning to the end without my supervision.

REFERENCES:

- Shu-Chen Jenny Yen’s On-line Montessori Albums http://faculty.fullerton.edu/syen/mts/math/_link.htm

The Montessori Addition Snake Game is available from Amazon:

 6 August 2014 (5Y5M1D)
 6 August 2014 (5Y5M1D)
 25 May 2015 (6Y2M20D)

### Montessori Activity: Long Chains - Skip Counting

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

OBJECTIVE(S):

1. To give the child a means of counting other than one-by-one.
2. Learn to count in bases other than ten.
3. Preparation for multiplication skill.
4. Development of order, independence, concentration and coordination.
5. Development of a mathematical mind.
6. To get an experience of squaring and cubing in relation of the square of a number to the squares of other numbers and of the cube of a number to the cubes of other numbers.
7. To understand the relation of a square of a number to the squares of other numbers and the cube of a number to the cubes of other numbers.
8. Indirect preparation for multiplication e.g. 5x2=10, etc.

MATERIALS:

1. Chains of 1 in red with corresponding labels in red marked 1.
2. Chains of 2 in green with corresponding labels in green marked 1, 2, 4, 6, and 8.
3. Chains of 3 in pink with corresponding labels in pink marked 1, 2, 3, 6, 9 up to 27.
4. Chains of 4 in yellow with corresponding labels in yellow marked 1, 2, 3, 4, 8, 12 up to 64.
5. Chains of 5 in light blue with corresponding labels in light blue marked 1, 2, 3, 4, 5, 10, 12 up to 125.
6. Chains of 6 in purple with corresponding labels in purple marked 1, 2, 3, 4, 5, 6, 12, 18 up to 216.
7. Chains of 7 in white with corresponding labels in white marked 1, 2, 3, 4, 5, 6, 7, 14, 21 up to 343.
8. Chains of 8 in brown with corresponding labels in brown marked 1, 2, 3, 4, 5, 6, 7, 8, 16, 24 up to 512.
9. Chains of 9 in dark blue with corresponding labels in dark blue marked 1, 2, 3, 4, 5, 6, 7, 8, 9, 18, 27, 36 up to 729.
10. 1 pointer
11. 1 large runner or paper runner

PRESENTATION:

1. Carry the long chains in the same way as the thousand chain.

2. Lay the chain out on a long mat as shown.

3. Gently pull one end of the chain until it is stretched out to its full length down the mat.

4. Bring the squares, cube, and labels to the mat.

5. Slowly fold the chain into 5-squares and draw your child to notice how it looks like a 5-square.

6. Set the squares from the tray on top to show that they are the same and count how many 5-squares there are.

7. Stack the squares and compare to the cube by placing the cube next to it or on top of it to show that they are the same.

8. Straighten out the 5 cube chain.

9. Sort the labels into columns on the tray.

10. Count the beads and lay out labels as you go: “1, 2, 3, 4, 5, 10, 15, 20, 25…” Only the first segment in the chain has a label for each bead, the rest only have a label for the last bead in each segment.

11. When you reach to 25, place the arrow tag as well as a square next to the 25th bead. Repeat this for every 25 (even at the 125th bead)

12. At the 125th bead, place the cube.

13. Walk along the length of the chain from the beginning and read the labels.

15. Then practice counting backwards: 125, 120, 115, 110, 105, 100, 95, 90, 85, 80, 75, 70, 65, 60, 55, 50, 45, 40, 35, 30, 25, 20, 15, 10, 5, 4, 3, 2, 1.

VIDEO DEMONSTRATION:

NOTE:

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

REFERENCES:

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

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