MATHEMATICS

SEQUENTIAL SNAKE GAME

Julien Jutras

UMC - January 2015

The Canadian Montessori Teacher Education Institute MAKING TEN

Age: 3 ½ + Materials: A box with ten compartments each containing: a number of coloured bead bars from 1 to 9, a number of ten bars from the bank, a counter notched to fit between the beads of a bead bar, a mat, paper, and colour pencils Presentation:

1. Invite a child to work with the coloured bead bars with you. Show him where to find the activity on the shelf and invite him to bring it to a table. Once seated, invite him to place the container at the top of the table and to unroll the mat.

2. Remove a ten bar from the container and place it vertically on the mat in front of the child. Invite him to count the ten bar with the counter. He will count to 10 and tell you “this is 10.”

2. then say, "Let us find out how many kinds of coloured bead bars we can put together to make 10."

3. Invite the child to pick any coloured bead bar from the box. If the child chooses a 5 bar, indicate for him to place it next to the ten bar and count one till five.

4. Invite him to count the remaining beads, (in this case: five) and to get the coloured bead bar to match, in this case five. Invite him to count both blue bead bars to verify. Declare: “Oh! Five and five make ten. Would you like to find another combination?”

5. Invite the child to select another ten bar and place it vertically beside the previous, he will then choose a different coloured bead bar.

6. Invite to count the bead bar, to count the remaining beads and to get the coloured bead bar to match with the remainder until another ten has been made. Again declare: “Ah! Two and eight make ten!”

7. Invite to continue until many coloured bead bars are combined to form ten. 8. Invite the child to use a colouring sheet to record his results. 9. When complete, invite him to return the activity to the shelf and tell him he can

make tens anytime he would like.

Direct Aim:

To make combinations of ten using the coloured bead bars

Indirect Aim: • To give the child an intuition of addition and multiplication • Build mathematical and logical thinking • Begin the progression of grouping numbers into tens internally • Preparation for further work with coloured bead bars

Language:

Introducing the concept of making tens and stating the tens made

Point of Interest:

The colourful bead bars, working with golden beads, figuring out the bead bars (numbers) that make ten, colouring and recording the work, counting the beads, and the pattern made by the bead bars side by side

Control of Error: • Unable to remember the quantities of the coloured bead bars • Not understanding the concept • Loosing count and/or becoming frustrated • The teacher-guide for the first presentation (or so)

3 Activities Before: 1. Short bead stair 2. Spindle box 3. Number rods 3 Activities After: 1. Snake game 2. Addition and subtraction with the colored beads 3. Associativity

MAKING TEN - Presentation

5 & 5 make 10 2 & 8 make 10 3 & 7 make 10

4 & 6 make 10 1 & 9 make 10 6 & 4 make 10 and so forth…

The Canadian Montessori Teacher Education Institute

THE SNAKE GAME

Age: 4 + Materials: A box with divisions containing: a quantity of coloured bead bars (1 – 9), one set of black and white beads (from one through five, the beads are black and from six to nine, the beads are black and one white, a bead is added for each number over five. For instance, seven has five black beads and two white beads and 9 has five black beads and four white beads), and a quantity of ten bars. A notched counter, a mat (or felt), and a small dish.

LEVEL ONE: GOLDEN BEADS TO COLOURED BEADS

Presentation: 1. Ask the child if she has ever seen a snake before and ask her how it moves

then invite her to make a beautiful golden snake with you. Show her where the activity is kept on the shelf and invite her to bring it to a table. Once seated, invite her to place the box either between herself and the teacher guide or at the top of the table (easily accessible for both) and to unroll the mat. Invite her to open the box and admire what you see inside. Ask: “What do you see?” She can tell you about what is inside the box (making sure she remembers the previous work with the bead bars).

2. Invite the child to make a golden snake with four to five ten bars in a zigzag line.

2. Say, "You remember making ten, let’s find out how many combinations of tens we can make here with the coloured bead bars and completely substitute this golden snake for a coloured snake.”

3. Invite the child to pick out any coloured bead bar from the box. If the child gets a yellow four bar, starting from the left (head of the snake), to place it next to the first ten bar and count it leaving the marker in place at the point where the counting till ten was stopped.

4. Invite to count the remaining beads, (in this case: six) and invite the child to get the coloured bead bar to match, in this case six. Count both yellow and purple bead bars to verify the total. Declare: “Oh! Four and six make ten. Let’s keep going with your snake, but before we do we have to make an even trade. You said 4 and 6 made ten right? Well since we took the 4 and the 6 and made 10 we have to put our ten away. Let’s put it into the empty container you brought.” Allow her to place the ten bar into the container. then say: “Okay, that’s fair! Let’s keep going.” Invite her to repeat this process until reaching the end (or tail) of the snake.

5. Once all the coloured bead bars have replaced the ten bars and the golden snake has been completely replaced by a coloured snake say: “Wow, Look at you! You have changed the golden snake into a coloured snake! Let’s make sure you were fair in your trading. You remember making tens right? Let’s take

all the ten bars from the container and see if they make even tens with the coloured snake. You can start with the largest bead bar in the container.”

6. She will know how to make tens from the previous activity and can check her work independently. You are just there watching.

7. Once complete, ask: “Were you fair? Did they all make tens?” 8. Invite her to replace the bead bars to the box and to make another snake. If

she declines, invite her to return the activity to the shelf and to make a golden snake anytime. After you have worked with her a few times and she is successful, you can show her the snake cards so she can work independently.

Direct Aim:

To replace a golden snake (ten bars) with a coloured snake (coloured bead bars), making combinations of ten

Indirect Aim: • To develop the internalisation of the combinations of numbers that make ten • Preparation for addition and multiplication

Language:

In counting and making the combinations

Point of Interest: Making a snake with coloured bead bars, using the counter, watching the golden snake change into a colourful snake, in checking own work

Control of Error: • The number of bead bars (the coloured bead bars should be equal to the

number of ten bars) • Making tens to check own work in end • The teacher-guide in the first few presentations

SNAKE GAME (1ST Level) - Presentation

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LEVEL TWO: COLOURED BEADS TO GOLDEN BEADS

Presentation: 1. Invite a child to make a snake. He will know what he needs to get from the

shelf. Once seated, tell him: “Today we will make a colourful snake!” and invite him to take “the head” from the box filled with coloured bead bars (he may choose any colour he would like. He can place it down on the mat for the head.

2. Next, tell him: “My turn” and choose the colour bead bar that would make ten. Ex. If the child gets a white seven bar, invite him to put “the head” of his snake on the left of the mat and you choose the pink three bar and place it next to his.

3. “Your turn” and have him choose the next bead bar. To make the combination, you pick the quantity needed to make ten from what he chooses. Continue in this manner: “your turn, my turn”; until you have a zigzag snake. At the end, you can pick out the last bead bar to complete the combination and you could invite him to place it next to the previous one. “This is the “tail” of your snake”.

4. Say, "Let us find out if we can change this coloured snake into a golden snake.” Invite him to count the bead bars with counter moving from left to right, till he can make a combination of ten, leaving the counter in place. Invite him to get one golden ten bar to replace the beads that make ten. Invite him to put those coloured bead bars in the empty container.

5. Continue in this manner until all the coloured bead bars have been counted and replaced by the ten bars. The coloured snake has been completely replaced by a golden snake. Say: “Wow, look at you! You have changed a coloured snake into a golden snake! I wonder if you traded fairly, you remember how to check right?”

6. He will know to place the ten bars in vertical rows and to select the longest coloured bead bar from all the bead bars in the container and to place it next to the ten bar.

8. He will continue until all combinations are made with coloured bead bars and the dish empty. Ask him “Were you fair?”

9. Invite him to make another coloured snake. If he declines he can tidy up and replace the activity on the shelf. Invite him to let you know anytime he would like to build a coloured snake. Once you have worked a few times with him and he has been successful, invite him to use the snake cards and to work independently.

Direct Aim:

To change a coloured snake into a golden snake (trading combinations of ten for ten bars)

Indirect Aim: • To develop the internalisation of the combinations of numbers that make ten • Preparation for addition and multiplication

Language:

In counting and making the combinations

Point of Interest: Making a snake with coloured bead bars, using the counter, watching the coloured snake change into a golden snake, in checking own work Control of Error:

• The number of bead bars (the coloured bead bars should be equal to the number of ten bars)

• Making tens to check own work in end • The teacher-guide in the first few presentations

SNAKE GAME (2nd Level) - Presentation

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LEVEL THREE: INTRODUCTION TO A REMAINDER (WITH THE BLACK AND WHITE BEADS)

Presentation: 1. Invite a child to build a coloured snake. He will know what he needs to prepare

from previous activities. He may choose a Snake Card appropriate for this activity, if he wishes. Once seated, invite him to take “the head” from the box filled with coloured bead bars. He may choose any coloured bead bar he would like.

2. To make the combination, you pick out the next bead bar to make ten. Continue in this manner, the child has a turn, you have a turn, making a zigzag snake with different coloured bead bars making combinations of ten. At the end of the snake, invite him to pick out any coloured bead bar and to place it next to the previous one. “This is the “tail” of your snake, a rattlesnake tail”.

4. Tell him today he will need the black and white beads. Invite him to lay out the black and white bead bars on the mat in a triangular display (stair pattern or triangle).

5. Say, "Let us find out if we can change this coloured snake into a golden snake.” Invite him to count the bead bars with counter moving from left to right, until he can make a combination of ten, leaving the counter in place. Invite him to get one golden ten bar to replace the beads that make ten. Invite him to put those coloured bead bars in the empty container. He will know how to replace the coloured beads with ten bars from the previous activity.

6. Continue in this manner until all the coloured bead bars have been counted until the last combination. When the child reaches the “tail” of the snake, invite him to count the quantity of beads. Ask him if he can replace the remaining beads with a ten bar. He will not be able to, so invite him to replace it with one of the black and white bars. The coloured snake has been completely replaced by a golden snake and it has a black or black and white “rattlesnake tail”

7. Ask the child if he thinks that the golden snake with this “special tail” has the same length of the coloured snake? Invite him to verify. He will know how to verify his work.

8. When he gets to the black and white (or black) bead bar, invite him to place the remaining coloured bead bar beside it and ask: “Is it the same?” His answer will be yes.

9. Invite him to make another coloured snake. If he declines, invite him to tidy up his work and to replace it on the shelf. Invite him to build a rattlesnake anytime. You may offer him the snake cards so he can work independently.

Direct Aim:

To change a coloured snake into a golden snake (trading combinations of ten for ten bars) with a remainder (using the black and white bead bars)

Indirect Aim: • To develop the internalisation of the combinations of numbers that make ten • Preparation for addition and multiplication • Introducing a remainder

Language:

In counting, making the combinations, and explanation of the rattlesnake tail

Point of Interest: Having a rattlesnake tail, the remainder, using the black and white bead bars, making a snake with coloured bead bars, using the counter, watching the colourful snake change into a golden snake, in checking own work Control of Error:

• The number of bead bars (the coloured bead bars should be equal to the number of ten bars)

• Making tens to check own work in end • The teacher-guide in the first few presentations

SNAKE GAME (3rd Level ) - Presentation

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LEVEL FOUR: THE COMPLETE SNAKE GAME Presentation:

1. Invite a child to build a coloured snake. She will know what she needs from

previous activities. Once seated, invite her to build the black and white stair (or triangle.) When done, tell her it is her turn to build a coloured snake and invite her to take “the head” from the box filled with coloured bead bars.

2. Tell her that you won’t build this snake but that you just would like one turn. Choose the second bead bar so that it does not make a combination of ten and allow the child to finish building her snake. (Many times the child is use to making tens and will continue to do so, but through choosing the second bead bar you are insuring that the snake will not make combinations of ten, this time.)

3. Say, "Let us find out if we can change this coloured snake into a golden snake.” Invite her to count the bead bars with counter moving from left to right, until she can make a combination of ten, leaving the counter in place.

4. As soon as she has reached ten, invite her to place a counter or stopper after the tenth bead and to count the remaining beads in the bar, (ex. if a white seven bar was counted first and light blue five bar second, thus 7 and only 3 of the light blue five bar would make a combination of ten, but with a remainder of 2). Invite her to select the black bead bar of two from the black and white bead stair and place next to the light blue five bar. Remove the coloured bead bars, the white seven bar and the light blue five bar and put them into the empty container and to get one golden ten bar to replace the coloured bead bars.

5. Tell the child to begin counting from the black and white (or black) bead bar. Count the beads until ten is reached, to count the remainder if any, then to place the appropriate black and white bead bar at the end. Invite her to remove the coloured bead bars by replacing them with one golden ten bar. She will place the coloured beads into the container but tell her: “We never place the black and white beads in the container, they must always go back to their spot in the stair.” Invite her to return it to the stair (or triangle.)

6. Continue in this manner until all the coloured bead bars have been counted until she reaches the “tail” of the snake. The coloured snake has been completely replaced by a golden snake and it may or may not have a black or black and white “rattlesnake tail”

7. Ask the child if she thinks that the golden snake is the same length as the coloured snake. Invite her to verify.

8. Continue until all combinations of ten are made with coloured bead bars. She will know how to do this from previous activities.

9. There is another way to verify. Invite her to get all the coloured bead bars from the container and to sort them on the mat by categories, such as all dark blue nine bars together, all brown eight bars together, etc. Take one golden ten bar from the golden snake and place it on the mat in a vertical manner. Invite the child to make the combination with the coloured bead bars starting with the longest one. For example, place the dark blue nine bar next to the golden ten bar and show the child that one more bead is needed to make them equal. Then place the one red one bead at the end of the dark blue nine bar.

10. Invite her to continue until all tens are made by combining coloured bead bars even the black or black and white beads bar.

Direct Aim:

To change a coloured snake into a golden snake (trading combinations of ten for ten bars) including exchange and a remainder

Indirect Aim: • To develop the internalization of the combinations of numbers that make ten • Preparation for addition and multiplication

Language:

In counting, making the combinations, and explaining the remainder and trading (if needed)

Point of Interest: The remainder, having the combinations not make exact tens, using the black and white bead bars, having a rattlesnake tail, making a snake with coloured bead bars, using the counters, watching the coloured snake change into a golden snake, in checking own work Control of Error:

• The number of coloured bead bars (the coloured bead bars should be equal to the number of ten bars)

• Making tens to check own work in end • The teacher-guide in the first few presentations • Forgetting and placing the black and white (or black) bead bars into the

container instead of back to their stair, thus throwing off verification in the end Extension: Invite the child to use the Snake Cards available for this level of work 3 Activities Before: 1. Previous levels of the snake game 2. Making ten 3. Short bead stair 3 Activities After: 1. Addition with coloured beads 2. Multiplication with coloured beads 3. Subtraction with the coloured beads

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2nd

3rd

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2nd

3rd

SNAKE GAME (4th Level ) - Presentation

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The counter stops here as the Child sees 7 & 3 make a 10.

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The counter stops here as the Child sees 2 & 8 make a 10.

Take away the beads and replace the reminder ‘2’ with the B&W beads from the trangle.

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SNAKE GAME – 4th Level (Con’t)

Take away the beads and replace the reminder ‘2’ with the B&W beads from the trangle.

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The Canadian Montessori Teacher Education Institute

PROPERTY OF ASSOCIATIVITY OF NUMBERS

Age: 5 +

Materials: A box containing 10 short bead stairs, addition and equals and parenthesis signs, associativity equation slips, prepared paper, and a pencil for recording Presentation:

1. Invite a child to work with the coloured beads and invite him to bring the box to the table. Return to the shelf with the child and show him where the associativity slips are kept. Invite him to bring a few to the table.

2. Once seated, invite the child to open the box. Inside he should find the coloured beads and the mathematical symbols needed for the activity.

3. Invite him to read the first slip and to remove the corresponding coloured beads from the box. Remind him to use the proper symbols between the coloured beads, like on the slip with the numbers.

4. Once done, invite him to make another line and tell him this will be his “working line”. Tell him he will not need the mathematical signs this time.

5. Now, invite the child to “find groups of ten” (like 7 and 3, or 6 and 4, etc...) using the working line. Invite him to bring them together below (in a horizontal manner).

6. Next, invite him to bring ten bars (as many as needed) to replace the coloured beads that make ten.

7. Once he has placed all the coloured beads bars under beside the ten bars (making ten), invite him to bring the tens together with any coloured beads remaining in a vertical manner at the tip of the equation after the equal sign. Ask him to read his answer. Now, invite him to flip the associativity slip over to check his work. Invite the child to record his work on the prepared paper.

8. After which, invite him to return the beads and symbols to the box and to begin again with the next slip. When done, invite him to use this activity anytime he would like.

Direct Aim: To begin working with larger addition and to continue to build skills in making tens and to assist his mind in becoming skilled to detect what makes 10 in long addition

Indirect Aim: • Strengthening counting skills • Building mathematical logical thinking • Memorization of simple addition • Fostering abstract thinking • Introduction to working in an algebraic manner

Language:

Introducing the activity and materials to the child

Point of Interest: The coloured beads, the mathematical symbols, working with numerous numbers in addition, making tens, detecting swiftly what numbers make combinations of 10, and recording his work

Control of Error: • The answer written on the back of the slip • The teacher-guide (for the introduction)

3 Activities Before: 1. Bead chains 2. Division board 3. Snake game 3 Activities After: 1. Disassociativity 2. 1000 chain 3. Abstract simple addition (without materials)

3 + 5 + 7 + 8 + 5 =

3 + 5 + 7 + 8 + 5 =

In the note book:

3 + 5 + 7 + 8 + 5 = 28

6 + 9 + 3 + 4 + 1 = 9 + 5 + 1 + 5 + 7 = 4 + 3 + 5 + 7 + 6 = 4 + 2 + 9 + 8 + 6 = 9 + 5 + 2 + 8 + 1 = 3 + 1 + 7 + 9 + 5 = 9 + 4 + 1 + 3 + 6 = 8 + 9 + 2 + 4 + 1 = 5 + 8 + 5 + 8 + 2 = 4 + 3 + 9 + 7 + 6 = 9 + 2 + 2 + 8 + 1 = 4 + 1 + 8 + 9 + 6 = 1 + 5 + 2 + 8 + 9 = 1 + 2 + 9 + 8 + 6 = 2 + 5 + 2 + 8 + 5 = 4 + 2 + 7 + 8 + 3 = 8 + 5 + 2 + 8 + 2 = 4 + 3 + 9 + 7 + 6 = 9 + 6 + 2 + 4 + 1 =

ASSOCIATIVITY ASSOCIATIVITY Answer: Answer:

ASSOCIATIVITY ASSOCIATIVITY Answer: Answer:

ASSOCIATIVITY ASSOCIATIVITY Answer: Answer:

ASSOCIATIVITY ASSOCIATIVITY Answer: Answer:

ASSOCIATIVITY ASSOCIATIVITY Answer: Answer:

ASSOCIATIVITY ASSOCIATIVITY Answer: Answer:

ASSOCIATIVITY ASSOCIATIVITY Answer: Answer:

ASSOCIATIVITY ASSOCIATIVITY Answer: Answer:

ASSOCIATIVITY ASSOCIATIVITY Answer: Answer:

ASSOCIATIVITY ASSOCIATIVITY Answer: Answer:

The Canadian Montessori Teacher Education Institute

PROPERTY OF DISASSOCIATIVITY OF NUMBERS

Age: 5 + Materials: A box containing 10 short bead stairs, addition and equals and parenthesis signs, disassociativity equation slips, prepared paper, and a pencil for recording Presentation:

1. Invite a child to work with the coloured beads and invite her to bring the box to the table. Return to the shelf with the child and show her where the disassociativity slips are kept. Invite her to bring a few to the table.

2. Once seated, invite the child to open the box. Inside she will find the coloured beads and the mathematical symbols needed for the activity.

3. Invite her to read the first slip and to remove the corresponding coloured beads from the box, she will know what to do from the previous activity.

4. Once done, remind her to make another line, this will be her “working line”. 5. Now, invite the child to “find groups of ten” using the working line. Invite her to

bring them together below (in a horizontal manner). 6. If there are any tens already made, she can bring them down like before. Most

of the coloured beads will not make tens without exchanging the beads for smaller quantities. She should know what to do from previous activities, but if she needs assistance, ask questions to bring the answers out from the child. “Oh, you said you need a two bead bar and a three bead bar. Do you see anything here that would make those? What can we do?” Etc…

7. Once she has exchanged the needed beads, she can continue to make tens in this manner. Once she has completed all the necessary exchanges she can place the ten bars under each combination that makes 10. Then invite her to bring the tens together with any coloured beads remaining in a vertical manner at the tip of the equal sign at the end of the equation. Ask her to read her answer. Now, invite her to flip the disassociativity slip over to check her work. Invite the child to record her work on the prepared paper.

8. Invite her to return the beads and symbols to the box and to begin again with the next slip. When done, invite her to use this activity anytime.

Direct Aim: Making tens through exchanging a minimum of beads to answer an equation

Indirect Aim:

• To strengthen making tens • Building mathematical thinking • Memorization of simple addition facts • Fostering abstract thinking • Introduction to algebraic equations

Language:

Introducing the activity and materials to the child

Point of Interest: The coloured bead, exchanging to make tens, the mathematical symbols, and recording the work and detecting what makes ten among all the sets of beads given

Control of Error: • Placing an incorrect bead • The answer written on the back of the slip • The teacher-guide (for the introduction)

3 Activities Before: 1. Associativity 2. Bead chains 3. Snake game 3 Activities After: 1. 1000 chain 2. Abstract simple addition (without materials) 3. Abstract simple multiplication (without materials)

3 + 9 + 9 + 8 + 5 =

3 + 9 + 9 + 8 + 5 =

In the note book:

3 + 9 + 9 + 8 + 5 = 34

3 + 9 + 9 + 8 + 5 = 7 + 9 + 2 + 4 + 9 = 2 + 5 + 6 + 9 + 5 = 6 + 9 + 3 + 5 + 8 = 6 + 5 + 7 + 9 + 5 = 3 + 9 + 3 + 8 + 1 = 2 + 9 + 7 + 9 + 7 = 1 + 8 + 5 + 7 + 9 = 4 + 5 + 7 + 8 + 7 = 5 + 9 + 3 + 6 + 9 = 9 + 5 + 7 + 6 + 3 = 6 + 3 + 3 + 5 + 8 = 4 + 5 + 7 + 8 + 7 = 5 + 9 + 3 + 6 + 9 = 4 + 2 + 7 + 9 + 7 = 9 + 5 + 3 + 6 + 8 = 3 + 5 + 7 + 8 + 7 = 3 + 9 + 8 + 6 + 5 =

DISSOCIATIVITY DISSOCIATIVITY Answer: Answer: DISSOCIATIVITY DISSOCIATIVITY Answer: Answer: DISSOCIATIVITY DISSOCIATIVITY Answer: Answer: DISSOCIATIVITY DISSOCIATIVITY Answer: Answer: DISSOCIATIVITY DISSOCIATIVITY Answer: Answer: DISSOCIATIVITY DISSOCIATIVITY Answer: Answer: DISSOCIATIVITY DISSOCIATIVITY Answer: Answer: DISSOCIATIVITY DISSOCIATIVITY Answer: Answer: DISSOCIATIVITY DISSOCIATIVITY Answer: Answer: