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: Introduction to the Stamp Game

AGE: 5 years (after the child is familiar with the decimal system, Static Addition With Golden Beads
and Dynamic Addition With Golden Beads)

OBJECTIVE(S):

1. Practice in the function of quantity.
2. Preparation for the four operations with the stamp game.

MATERIALS:

1. Stamp Game.
2. Introduction to Decimal Quantity Tray
3. Large Number Cards
4. 1 mat

PRESENTATION 1:

1. Introduce your child to the stamp game and compare them with the Golden Bead material to show your child the connection.

2. Place the large number cards 1000, 100, 10 and 1 on the table in a row and say, "unit, ten hundred, thousand."

3. Bring the presentation tray, remove the 1000-cube, 100-square, 10-bar and 1-unit and place them below the large number cards respectively.

4. Show the child the green 1 unit stamp and say, "This is 1. It is the same as the unit bead" and place the unit tile below the unit bead.

5. Show the child the blue 10 stamp and have him say 10. Tell the child that this is just like the ten-bar and place the 10-bar next to the 10 tile.

6. Do the same for stamps of 100 and 1000.

7. Do a Three Period Lesson with the 1, 10, 100, and 1000 tiles.

PRESENTATION 2:

1. Show your child that when taking out the unit stamps, they should be placed below the compartment of the unit stamps in a vertical line. For example, place 5 unit stamps under the compartment of the unit stamps. Do the same with tens, hundreds and thousands.

2. Think and write down a number using a two place value numeral, then three, then four for example 30, 500 and 2000 and compose them with the appropriate stamps 3 tens, 5 hundreds, 2 thousands. Ask your child to pick the respective golden beads - unit beads, 10-bars, 100-squares, 1000-cubes as comparison.

3. Have the child read the stamps.

4. Give your child a number and let him try to pick out the appropriate golden beads and then the appropriate stamps.

5. Let your child try to compose a number and let him pick out the appropriate cards and stamps.

6. Remember to have your child put back the tiles into their compartments after each try.

VIDEO DEMONSTRATION:

http://www.youtube.com/watch?v=nE11yCpwzx8
http://www.youtube.com/watch?v=yP_HORLguX8
http://youtu.be/_Skpyo6ifhc

POINTS OF INTEREST:

1. Seeing a new material which represents a familiar concept.
2. Color of the stamps.
3. Numerals on the stamps.
4. Seeing the different categories in the box.
5. Counting the stamps and finding matching symbols.

REFERENCES:
http://www.montessorialbum.com/montessori/index.php?title=Introduction_to_the_Stamp_Game

The stamp game is available from Amazon:

Montessori Activity: Ten Board & Beads (Presentation 3)

AGE: From 4.5 years old (After the child has worked with the teen and the golden bead material for the 45 layout)

OBJECTIVE(S):

1.     To help the child discover that numerals 1 to 9 added to larger numerals can make a variety of numbers.

2.     To teach sequence, the numbers from 11 to 99.

MATERIAL:

1.     1 set of Ten Board

2.     1 set of unit cards with numerals 1 - 9

3.     1 container with 45 golden ten-bars

4.     1 container with 10 or 45 golden unit beads.

PRESENTATION 3 (COUNTING 1 TO 99):

 

1.     Place a unit bead to the right of the Unit Tile 1 and say: “1.”

2.     Add another unit bead and place both to the right of the Tile 2 and say: “2.”

3.     Add another unit bead and place all three next to Tile 3 and say: “3.” Continue up to “9”.

4.     Add another unit bead, but say: “10 units are the same as one ten.” And exchange them for a ten-bar.

5.     Place the ten-bar to the right of the top “10” section on the board and say: “Ten.”

6.     Add a unit bead to the ten-bar, slide the Tile 1 over the zero and say: “This is eleven.”

7.     Add another unit bead to the unit bead and ten-bar, remove Tile 1 and slide in Tile 2 and say: “Twelve.”

8.   Continue to add one bead at a time, using the appropriate tile to form the number on the board and say the number’s name.

9.   Whenever you add the tenth unit bead, exchange the beads for a ten-bar and slide the bars down to the right of the next section on the board.

10.  Encourage the child to complete with the remaining numbers in your presence in the same manner counting all the way to 99.

VIDEO DEMONSTRATION:

http://youtu.be/73l3tZjGRjs

http://youtu.be/rmi86o0E-ng

CONTROL OF ERROR:

The number of beads, correct amounts will use up all 45 of the ten bars and unit beads.

POINTS OF INTEREST:

1.     Learning the number of different combinations that can be made from combining these materials.

2.     Seeing the ten beads on a bead bar and the single units.

3.     The unit beads in the little container.

4.     Watching the quantity of golden bead bars grow from 1 to 9.

5.     Seeing the relationship between the 45 layout and the ten board.

VARIATIONS:

1.     Select numbers and ask the child to provide the quantity

2.     Select quantities and ask the child to provide the correct symbols.



ADDITIONAL INFORMATION:

Although this activity is recommended for children 4.5 years and up, J tried this only for the first time today at 5+ years old (5Y4M7D). We recorded the videos below for memory. He could say the numbers in Chinese very well now, but we are still practicing saying the numbers in English and Danish.

REFERENCES:

http://www.montessorialbum.com/montessori/index.php?title=Tens_Board

http://faculty.fullerton.edu/syen/mts/math/4-3.htm