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1. How would you teach numbers 0 to 10 to a child according to Montessori method?
Explain all the exercises in the group briefly in your own words.
Montessori approach is quite different and one of the easiest ways to teaching the concept of
numbers to the children in the early years of life. In Montessori education, they provide many
appropriate ways to the children for exploring the world of mathematics. The math journey
commences in the child‟s life with concrete experiences and then leads the child towards
abstractions. The opportunities of learning and teaching the mathematics are found very easily
from the daily life of the child. It is said that the child‟s brain is like a sponge, he greedily
absorbs all what is shown and taught to him.
It would be very surprising to know that the child starts learning mathematics from the very early
age of his life, even though from the age of toddler. Teaching the Mathematics to the child in the
early years of life is not taken as a daunting task in the Montessori Education. The basic and
chief task of teaching to the child through Montessori education is to make the concept very clear
and comprehensible.
In Montessori education numbers are taught in the various ways so that the children may learn
them with perfection because the perfection in the child‟s life, was the basic motive of Maria
Montessori . We should make mathematics as a part of everyday activity for the children.
Learning can be a great fun for the children if taught playfully. It has been widely observed and
understood that children can learn faster and quickly when visual teaching practices are used.
There are countless activities which can make the math as a fun for not only toddlers but also
kids (4 to 6 years old)
It is scientifically proved that the little children are naturally attracted to the science of numbers.
Mathematics, like language, is the product of the human intellect. It can be clearly said that
human beings have a mathematical mind. Montessori took this idea, that the human has a
mathematical mind, from the French philosopher Pascal. Children mind is always ready to
estimate the quantity of the things, similarity, difference, patterns, to make order, sequence in
things and to control error in everyday life.
Indirect Preparation of Number
Understanding of numbers develops through experiences with concrete objects, which are used
in EPL Exercises because it contributes effectively in the development of mathematical mind.
EPL are the everyday household activities. The child is naturally attracted to these activities as
these experiences are essential part for full development and self dependence. By taking the
participation in these activities, the child becomes a responsible and helping member of the
society who can deal with the problems of everyday living. Along with it, at the unconscious
level, practicing these activities forms the essential patterns in the nervous system that leads to
the conceptual development of “order”, “concentration”, “coordination”, and
“independence”, which are all crucial elements of mathematical mindset. These skills are
learned by the child through EPL, without even knowing.
Order is one of the basic elements for math, as we cannot do any mathematics task without the
capacity of sequencing and ordering. Similarly, ability to the concentration on a task is also
essential for math as it helps develop logical thinking and problem solving. EPL also gives
children good eye-coordination and controlled movements, which are required to do work
effectively with the math materials present in a Montessori classroom and at home.
There are different ways and materials of teaching numbers to the kids in Montessori,
The Number Rods (The Red Rods)
Sandpaper Numbers
The Spindle Boxes
Number Cards and Counters
Memory Game
Actions Game
Number Poems and Rhymes
Math Area
Number Rods - Ten rods, grated in length, the shortest rod being ten centimeters in length, and
each succeeding rod increasing by the length of the first, with the longest rod being one meter.
These rods prepare the child for 1-10 counting.
Number Rods
Number Rod Variation - Using the same object children can count out the objects onto each
section of the rods.
Sandpaper Numerals - Numeral symbols 0-9 in sandpaper. These help the child with
recognition of numerals 0-9.
Sandpaper Numerals
Association of Rods and Numerals - Number rods and numeral cards 1-10. Children associate
the number rod quantity with the number symbol. Children gain a growing understanding of
sequence as they work with association exercises.
Association of Rods and Numerals
Small Number Rods - These can also be used for simple addition along with Bead Stair
Addition when the child is ready to work with simple addition. I placed the photo here as an
extension work wih the Small Number Rods.
Small Number Rods
Addition with Small Number Rods
Spindle Boxes - A child counts out the quantity of spindles in their hand and places each set of
spindles into the appropriate rectangular section. The Spindle Box indirectly helps to develop the
idea that each quantity can be made up of loose units taken together as one set. They also begin
to learn the concept of zero as an empty set.
Extensions 1-10 - These are additional exercises that can be added to the Math shelves to
provide practice in associating quantity and symbol. I change these monthly according to unit
studies to enhance those as well.
Apples 1-10
Smiles 1-10
Pumpkins 1-10
Fish Bubbles
Cards and Counters - A set of numerals 1-10 and 55 plastic discs. The layout of the counters is
what makes this counting work different. Children will count out the discs in pairs under the
numeral. When all the discs are counted out, point out that some of the numerals have a disc that
doesn't have a partner. Those numbers are called odd numbers. The discs which all have partners
are called even numbers.
Cards and Counters
Memory Game - A small basket with slips of paper each with a numeral from 0-10 written on it.
55 small similar objects such as buttons, seashells, or tiny pebbles. This exercise can be done
with two, three, or four children. Each child chooses a number. Explain that they are to keep
their number a secret. Ask them to look at their number, remember it, and bring that many
objects from the basket of objects that is on the shelf. You can also provide small trays in which
the children can use to count out their objects. When all the children have returned to the mat
have them take turns to read their number and count out their objects.
Short Bead Stair - A set of small numeral cards from 1-9 and one set of bead stair beads. These
beads provide exercise in counting. The bead stair will be used in later math exercises such as the
teen board and the snake game.
Short Bead Stair
Short Bead Stair
Introduction Tray - Golden Beads - Two felt green squares, one red felt square, and one blue
felt square are needed along with one unit bead, one ten bar, one one hundred square, and one
thousand cube. This work helps the children to learn the language of the decimal system and
progresses with association of symbol and quantities.
Introduction Tray - Golden Bead Material
Introduction Tray - Quantity and Symbol
Tens Tray - Using the golden beads in amounts of ten units, ten 10's, ten 100's, and one
thousand, children are helped to see that ten of one category builds one of the next category (ten
units make one ten bar).
Exchange Game - Manipulation of beads between catergories
Nine's Tray - Tray containing: nine units, nine 10's, nine 100's, nine 1,000's, and four squares of
felt. Nine units beads are placed onto a green felt square. Say to the child, "If I had one more
unit, that would make one ten." Place blue felt square on the mat and put one ten on it. Remove
units and green felt. Continue with remaining bead material.
Association of Quantity and Numeral
Horizontal Layout
Composition of Numbers - Need a set of small numerals, Nine's Tray or the Bank, unit
container, empty tray, place value paper pages and colored pencils.
Tens Tray
Association of Symbol and Quantity - Using the golden bead material, this is a sample of one
of the presentations combining quantity and symbol.
Association of Quantity and Symbol
Composition of Numbers
Operations with the Golden Bead Bead Materials - Using the golden beads, the concept and
process of addition, subtraction, multiplication, and division are taught.
Operations with the Stamp Game - The Stamp Game leads the child into a more abstract way
of performing the basic operations of addition, subtraction, multiplication, and division.
Teen Board - Helps children to recognize numbers 11-19 in quantity and symbol as well as
reinforces the concepts of place value. Prior learning to this work is the Short Bead Stair. This
can be presented after the Introduction Tray.
Ten Board - Presents to the child the names of the decades and counting from 1-99.
100 Board - Aids the child in the development of number concepts and logical thought,
recognition of numbers 1-100, and provides exercise in counting to 100 with the symbols. Prior
Learning: Teen Board, Ten Board, and the 100 Chain, all of which can be presented
simultaneously with 100 Board.
Addition with Golden Beads
Addition with Golden Beads (completed)
Stamp Game - Addition
Stamp Game - Addition (continued)
Stamp Game - Addition (completed)
Addition and Subtraction Cards
Teen Board
Teen Numbers
Ten Board
Ten Board (mixed numbers)
100 Board
Bead Chain Cabinet - Beautiful cabinet of color coded chains, squares, cubes, and number
cooresponding number tiles.
Squares of Numbers - Children are introduced to skip counting. The five ssquare chainis made
up of all fives and when you fold it, it makes a five square. Children count out each set adding a
number tile to each. They roll out the register tape and write the numbers along the paper.
Cubes of Numbers - Same as the Squares of Numbers, but now children find out about the
cubes of numbers withthe colored chains.
Bead Chain Cabinet
Squares of Numbers
Squares of Numbers
Cubes of Numbers
Memorization of Facts - Learned through mateirals such as the Snake Game, Short bead Stair,
Addition and Subtraction Strip Boards, and Charts.
Snake Game
Strip Board
Multiplication and Division - Learned through Bead Bar Exercises, Boards, and Charts.
Bead Bars
Bead Bars
Multiplication Board
Division Board
Fractions
Clock
Money
Fractions
Fraction Skittles (I make a set of paper ones that the children can cut and make a chart of
fractions to take home)
Clock
Money (There are many ways you can introduce and teach simple money concepts to the
children, just be sure to have real money available.)
2. What do you know about the decimal system? How would you enable children to
count any quantity and identify numerals till 9999?
Introduction to quantity
Materials 1
- A tray containing 1 golden bead unit, 1 golden ten-bar, 1
golden hundred square and 1 thousand cube.
- A small mat for the table.
Presentation 1
1. Invite a child to come and work with you. Bring him to the shelf, name the lesson and
have him bring the material over to the shelf.
2. Have him unroll the small mat onto the table.
3. Take the unit, feel it, and name it. “This is a unit.”
4. Give it to the child to feel and name it.
5. Have him place it on the right side of the small mat.
6. Repeat for the ten-bar.
7. When the child places it onto the small mat, count the beads.
8. Place the ten-bar vertically to the left of the unit.
9. Repeat for the hundred square.
10. Lay it on the mat to the left of the ten-bar.
11. Use the ten-bar to count how many tens are in the hundred.
12. Repeat for the thousand cube.
13. Place it to the left of the hundred square and use the hundred to count how many
hundreds are in a thousand.
14. Do a Three-Period Lesson for them.
15. End the 2nd Period with the categories in the correct order: (from left to right) thousand,
hundred, ten, unit.
16. For the 3rd Period, point to each category and ask the child to name it.
17. Show the child how to put the material away, making sure the beads are placed in the
correct order on the tray.
Materials 2
- A mat
- A supply box with unit beads, ten-bars, hundred square and thousand cube with beads drawn on
them.
- A tray as in Presention 1
- A tray with a dish on it.
Presentation 2
1. Invite a child to come and work with you. Have him bring the material over to the table.
2. Have him unroll a mat and have him bring over the material.
3. Compair the material in the box to the mterial that is on the tray that was used in
Presentation1. This will show the child that units and tens are the same.
4. Take out a hundred from the box and comapir it to the hundred on the tray.
5. Tell the child that the hundred on the tray is made of beads but the hundred in the box has
beads drawn on it. But explain that they are still both hundreds.
6. Put the hundred from the box at the top of the mat.
7. Repeat and discuss for the thousand.
8. Place the thousand from the box above the hundred at the top of the mat.
9. Take the material out of the box and set it up as shown :
Thousand Cubes
Hundred Squares
Ten Bars
Bowl with units
This mat is called the Supply May
10. Have the child bring over a small mat and place it far away from the supply mat.
11. Have him also bring over a tray with a small dish on it and have him place it onto the
small mat.
12. Sit next to the small mat with the child.
13. Ask the child for a precise amount of units, such as 5 units.
14. Have the child go over to the supply mat with the tray and count out 5 units. Have him
place these units into the dish on the tray. If needed, go with the child.
15. Have the child bring the material over to the small mat and have him count it to check.
16. Repeat by giving the child other amounts to get, such as : 4 tens, or 7 hundreds, or 5
thousands.
17. After some time, you place an amount of material onto the tray and have the child count
to tell you how much there is.
18. Repeat this until the child seems comfortable with this exercise.
19. When the child can work well with one catergory, introduce two categories such as 4
units ans 2 tens. Continue like this for three categories and then four categories.
Purpose
Direct
To introduce the child to the concept of the decimal system.
To make the child familiar with the names and relative sizes of the categories
To help the child with the difference in bulk between e.g. 6 units and 6 thousands.
Control of Error
The directress and the child‟s own knowledge
3. Explain addition and multiplication exercise in your own words?
Learning mathematical concepts in a Montessori classroom begins concretely and progresses
towards the abstract. They are developed from simple to complex. Process is taught first and
facts come later. Order, coordination, concentration, and independence are experienced by the
child using these materials. The math activities are organized into five groups.
The activities in the Math area are not to be implemented at a set pace. Providing the child with
the materials at precisely the right challenge level will enable the child to demonstrate his
development to the teacher through his progress. A child that is able to grasp such math concepts
as addition and subtraction demonstrates the successful use of the math materials. The materials
are so beautifully designed and appropriate for each child during his sensitive periods of learning
math. Mathematical apparatus provides the necessary stimulation for the child to learn math
concepts more readily.
Addition
Materials
- 3 boxes with sets of small cards, including 9 units, 9 tens, 9 hundreds and 3 thousands.
- 1 box with a set of large cards from 1 to 9000.
- An ample quantity of loose unit beads, ten-bars, hundred squares and thousand cubes.
- 3 trays and 3 little bowls for the loose beads.
- 1 larger tray with one extra bowl.
Notes
When you give the cards or have the children read the numbers always start with the units.
Static Addition
Presentation
1. Invite a minimum of three children to come and work with you. Have them unroll three
large mats and have them bring the materials.
2. Have one child lay out the large cards as explained in Introduction to Symbols.
3. Have another child lay out the beads for the “supply mat”.
4. Have the children place three small mats between the two large mats.
5. Have the children set up their set of small cards as with the large cards but only having
1000-3000.
6. On the third large mat, have the children place three trays.
7. Ask the three children to take their trays to the small mats.
8. Tell the first child to get the cards for: 2 units, 3 tens, 2 hundreds, and 3 thousand. Have
the children place each card at the bottom of their tray. See diagram:
9. Have the second child take the cards for: 2 units, 1 ten, 3 hundreds, and 2 thousands.
10. Have the third child take the cards for: 1 units, 2 tens, 5 hundreds, and 3 thousands.
11. Have the children bring their trays back to the large empty mat and have the children sit
on the opposite side as the directress.
12. Review with each child how many units, tens, hundreds, and thousands are on his cards
before sending them one by one to the Supply Mat to get the appropriate beads on their
trays.
13. Once each child has returned, check what each child got by having him count his beads:
units, tens, hundreds, thousands.
14. Once the first child has checked, have him supper-impose his cards (as shown in the
Formation of Numbers).
15. Have the child read with you that this child has 2 units, 3 tens, 2, hundreds, and 3
thousand. Then say, “So he has 3232 beads.”
16. Repeat after each child has verified his beads.
17. Tell the children that you are going to get something very special. Bring back a large
scarf and place it on the directress tray.
18. Tell the children that we are going to see how many beads we all have if we put them
together.
19. Ask each child, one by one, to gently place their beads anywhere on the tray.
20. Say, “Wow, we have a lot of beads.” To reinforce this idea, lift the scarf by the four
corners to show that it is heavy.
21. Tell the children that we are now going to count how many beads we have altogether.
22. Ask the first child to take out all of the units and to place it in the directress‟ dish.
23. Have each child take out the tens, hundreds, and thousands and place them to the side of
the directress tray.
24. Remove the cloth.
25. Have the first child count the units and then go to the large mat to get the appropriate
number card. Have him place the card below the unit dish.
26. Have the second child count the tens. Have him get the appropriate number card from the
large mat and place it below the ten-bar pile.
27. Repeat for the hundreds and thousands.
28. Have a child superimpose the cards together.
29. Tell the children that when we put all of the beads together we had (as you point have the
children say with you): “7 units, 9 tens, 7 hundreds, 6 thousands.”
30. Then say, “So altogether we have: six thousand, seven hundred, and ninety-seven beads.”
31. As you tell the children, collect their small cards, keeping them superimposed and place
them in the top right corner of the mat. “So we put 3232, and 2312, and 1253 all together
and when we did this we got (move 6797 below the small cards) 6797.
32. “And you have just done addition!”
33. Do several examples of Static Addition before moving on to Dynamic Addition.
Dynamic Addition
Presentation
1. The presentation begins exactly as in Static Addition but have the children take cards for
a problem where they will have to carry over. These numbers could be: 3323, 2456,
1345.
2. Repeat all the steps through 23 as above but there is no need for the scarf this time.
3. When the first child counts the units and reaches 10, point this out and have him
exchange ten units for a ten-bar. Have him count the rest of the units and then go get the
card for that amount. (4)
4. Repeat for the tens, hundreds, and thousands, changng when needed.
5. Finish the exercise as for Static Addition.
Exercise
Children who are secure in both Static and Dynamic Addition can work without the teacher.
Purpose
Direct
To give the impression of the nature of addition, that is of two or more small numbers coming
together to form one larger number.
Control of Error
Initially the Directress, and later on, the child when he knows the process.
Age
4 – 5 years
Multiplication
Materials
- As for addition
Presentation
Static Multiplication
1. Invite three children to come and work with you.
2. Have them set up the materials as for addition.
3. Have each child take the same number with the cards, but do not tell them so. For
example: 1223
4. The presentation is exactly the same as in addition. Do not tell the children they have the
same numbers until the end.
5. Once you have found the total number of beads, collect each child‟s small cards and
place them as you had done in addition.
6. Have the children notice that they had the same amount of beads.
7. Tell them that in this case we only need one of the cards (give the two other children back
their small cards) and because they each had the same amount of beads and there are 3
children (count them to show this), we can show this with a special 3 card.
8. Place this special card to the right of the small card and the large number cards to the
right of that.
9. Say, “When we take 1223 three times, it equals 3669.
10. “And you have just done multiplication!”
11. Repeat a few times with the child.
Dynamic Multiplication
Same as with Dynamic Addition.
Purpose
Direct
To give the impression of the nature of multiplication, that it is an addition in which the
quantities added are not different, as in addition, but in fact are all alike.
Control of Error
Initially the Directress, later the child‟s own understanding.
Age
4 – 5 years
4. Explain how would you give the concepts of subtraction and division?
Substraction
Materials
As for addition, but including a fourth set of small cards to 9000 and a small mat to put those
cards on.
Notes
Specify the vocabulary: minuend, subtrahend, and the different.
Static Substraction
Presentation
1. Invite three children to come and work with you.
2. Set up the material as in Addition, including the new set of cards. This new mat should be
placed next to the large mat with the large number cards.
3. Take the directress tray and with the children, go over to the Supply Mat.
4. Ask one child to put 7 units into the dish on the tray.
5. Ask another child to place 8 tens onto the tray.
6. Ask another child to place 7 hundreds on the tray.
7. Ask another child to place 9 thousands on the tray.
8. Emphasize that you have a lot of beads on your tray.
9. Take the tray back to the large mat.
10. Ask each child to count the units, tens, hundreds, and thousands. Have each child get the
corresponding card after each is counted.
11. Supper impose the cards to get: 7879
12. Have each child take their trays to the small mats and tell them each what to get. For
example:
3 units, 2 tens, 4 hundreds, and 3 thousands
2 units, 4 tens, 5 hundreds, and 6 thousands
1 unit, 3 tens, 4 hundreds, and 5 thousands
13. Tell the first child that you are going to give him some of your beads.
14. Ask his how many units his card asks for. (3)
15. Have him count three from the directress‟s tray and place it into his own dish.
16. Repeat for the tens, hundreds, and thousands.
17. Have the child superimpose his cards and read it with the others: 3 units, 4 tens, 2
hundreds, and 3 thousands. Then read, 3423
18. Ask, “Do I still have 7879?” No!
19. Move the cards 7879 up to the top left corner of the mat.
20. Ask one child to count how many beads you have left and choose the new small cards to
mark each set of beads.
21. Have the child superimpose the cards to read: 4456.
22. Say, “So let‟s see what we did here. We started off with 7879 but then I gave some
away.” (Ask for the first child‟s cards and place them below 7879.) “I gave away 3423.
And in the end, (place the new total below 3423) I ended up with…4456 beads.”
23. “And this is called subtraction!"
24. Give the cards back to the child to replace and have him give you back the beads.
25. Beginning at when you started with 7879 beads, repeat the subtraction for the second
child.
26. Once done, begin again at 7879 and repeat the subtraction with the third child.
27. Once each child has had a turn, say: “What we have just done is subtraction. I had a lot of
beads and you took some from me so I no longer had the same amount of beads.”
Dynamic Substraction
1. Done as in the above presentation.
2. The only different is you will have to change, just as in Dynamic Addition.
Multiple Substraction
This is done in the same way as in the above presentation but this time, the first child will take
some of your beads away, the second will take from what is left of the directress tray, and the
third child will take from what is left after that.
(Photo shows this in process.)
After the first quantity is taken from the original pile, place the large number cards at the top left
corner of the mat. Place the small cards from the child below it. Keep placing the cards in this
manner after each child take some of the beads away.
(See photo to the side)
Purpose
Direct
To give the impression of the nature of subtraction and how it differs from addition, in this case:
- One starts with a capital and people come to fetch from it, by bringing an empty tray and the
demand expressed in small cards.
- One has to break up a unit of the larger category into ten of the smaller one.
- A larger quantity is divided into 2 or more smaller different ones.
- Generally something is left over for the one who had the original number.
Control of Error
The directress verifies at first. Then she shows that if all the smaller numbers that were taken
away are added together, they should amount to the original number.
Age
4-5 years
Division
Materials
- As for addition, but all small cards are laid out to 9000.
Static Division
1. Have three children come and work with you.
2. Have them set up the material.
3. Bring over the directress tray to the supply mat and ask for 9 units, 3 ten, 9 hundred, and
3 thousand.
4. Bring the tray back over to the mat.
5. Ask the first child to count the units and to then bring the card over for 9 units.
6. Ask the next child to count the tens and to then bring over the card.
7. Repeat for the hundreds and thousands.
8. Ask one child to place all of the cards together and as a group, read out 9 units, 3 ten, 9
hundred, 3 thousand.
9. Super-impose the cards.
10. Tell them that you want to give them all some of your beads and you want to be fair and
give them each the same amount.
11. Say that in division, we always start with the thousands.
12. Start by giving each child 1 thousand. Say, “I don‟t have any more thousands to give.”
13. Have each child count how many thousands they have to check if each child has the same
amount of thousands.
14. Have the children go over to their card mat and get the card for 1 thousand.
15. Repeat for the hundreds. They should all have 3 hundreds.
16. Repeat for the tens. They should all have 1 ten.
17. Repeat for the units. They should all have 3 units.
18. Emphasis that you gave each of them the same amount. “Did you get the same amount?”
19. Have each child place his cards together and read out loud the number the child has.
20. Place the large cards at the top left of the mat.
21. Say that because they each have the same amount, you only need one of their cards.
22. Discuss that because there are three children, you gave each one of them the same
amount, to three children.
23. Take out a 3 from your small dish and place it to the left of the large cards.
24. Then place one of the children‟s cards to the right of the 3.
25. Then, out loud, and as you point to each number say, “3939 divided by 3 is 1313.”
Dynamic Division
1. Begin by telling the children that division is different than the other operations. We must
start with the thousands.
2. Move over to the supply tray and ask each child in turn to place 6 units, 2 tens, 5
hundreds, and 4 thousands onto the directress tray.
3. Give each child 1 thousand and have them get the card.
4. Have a child exchange the last thousand for 10 hundreds.
5. Give each child 1 thousand until they all have 5 hundreds.
6. Look at the 2 tens and notice that you cannot give each child a ten. Ask one child to
exchange a ten for 10 units.
7. Ask another child to do the same for the other ten.
8. Count all of the units. (26)
9. Give each child a unit until they all have 8 units. Discuss Have then get the correct cards.
10. Have them place their cards together and read what each child has.
11. Notice how they all have the same number.
12. Lay out all of the children‟s cards under the large cards.
13. Read 4526 divided by 3 is 1508.
14. Look at the remaining units and say, “But we have a remainder of 2. Place the two units
in the dish to the right of 1508.
15. Reread: “4526 divided by 3 is 1508 with a remainder of 2.”
Long Division
1. Bring the directress tray over to the supply mat with the children.
2. Ask for 2568 in material.
3. Bring the tray back over to the working mat with the children.
4. Count out the numbers of each and ask the children to bring the corresponding cards
over.
5. Tell the children that today we are not going to divide by 3 as we have been. We will be
dividing by 12. Show the fact that one child is going to represent the tens by giving the
first child a blue ribbon and the two other children a green ribbon because they represent
units.
6. Ask the first child to go ask nine of their friends if they would come over for just a
moment.
7. Count them all (including the first child) and say that because these nine children all have
to go back to work, the first child will represent them all.
8. Give the first child the thousand block and give the other two children each 1 hundred
because “the first child represents ten people so he has ten times as many hundreds.”
9. Give the other thousand to the first child and each of the other children a hundred square.
Have them get the cards.
10. Give the first child a hundred square and the other two children a ten bar.
11. Have then get the appropriate cards.
12. Repeat in this way until all of the beads have been shared appropriately.
13. Have each child count what they have and choose the correct cards to show the number:
2140, 214, 214.
14. Roll out the long red mat and have the first child re-invite his nine friends to sit behind
the red mat.
15. Discuss how you want to give each of their friends some of your beads but you can‟t
because you only have 2 thousands.
16. Divide the 2140 by ten, exchanging when necessary.
17. Once it has been divided equally among himself and his nine friends, have him count
what he has and have him choose the new correct cards for what he has left on his tray:
214
18. Look at the two other children sitting next to this first child and notice that they too have
214.
19. Then look at the nine friends and check if they all have 214. Say, “You all have the same
amount!”
20. Then place 12 (explain because you are dividing the total by 12 people) to the right of the
large cards reading 2568 and 214 to the right of the 12.
21. Read out loud: 2568 divided by 12 is 214.
22. Excuse the nine friends and have the three children replace the material.
Purpose
Short Division
To give the impression of the nature of division. Here a large quantity is divided into a number
of smaller equal quantities.
Long Division
To show the child how the quantities are distributed in long division. He learns how the divisor is
always grouped and how the answer is always the share of one person.
Control of Error
The directress verifies at first. Then she shows that if all the smaller numbers that were taken
away are added together, they should amount to the original number.
Age
4 1/2 - 5 years
5. What are teens and tens boards? Explain their purpose and usage.
Teens: Quantity
Materials
- One short bead stair – 1 red, 2 green, 3 pink, 4 yellow, 5 light blue, 6 purple, 7 white, 8 brown,
9 dark blue.
- Nine bars of ten.
Presentation
Stage A
Have the child bring over the material to the table.
Unroll the little cloth and take out each bead bar, having the child count the beads on
each.
Once all of the bead bars have been placed on the cloth, ask for bead bar 1.
Have him choose it, count it, and place it at the bottom left corner of the cloth.
Ask for 2. Have the child repeat as before, placing it directly above bead bar 1 and
centered. Bring attention to the color.
Repeat for bead bar 3, 4, 5, 6, 7, 8, and
Take out the ten-bars and review these with the child.
Place a ten-bar vertically at the top of the cloth.
Place the one-bar directly to the right of the ten-bar.
Count with the child, beginning with at the bottom of the ten-bar and adding, as you point
to the one-bar: “Eleve
Take out the ten-bars and review these with the child.
Place a ten-bar vertically at the top of the cloth.
Place the one-bar directly to the right of the ten-bar.
Count with the child, beginning with at the bottom of the ten-bar and adding, as you point
to the one-bar: “Eleven.
o Have the child create the numbers 11-13.Do a Three Period Lesson for 11-13.
o Then repeat for 14-16 and 17-19. Finish each Three Period Lesson with the
numbers in order.
Stage B
o Ask the child to make 12.
o Have the child verify by counting.
o Then have the child make 16 to the right of 12. Check by counting.
o Ask the child to make each teen number possible, one at a time. Keep 11 as the
last number created.
o Discuss with the child how many of the numbers have the word “teen” in them.
Review some of the numbers that have the word teen in it.
o Tell the child that the word “teen” means there is a ten in the number.
o Look at different examples such as seven-teen. “That means that there is a 7 and a
10.”
o After a few examples, look at 11 and say that this however doesn‟t have the word
teen in it.
o Have the child mix the bead bars and then create numbers 11-19 in order.
o Do a Three Period Lesson.
Purpose
Direct
The bead stair clearly distinguishes each number up to 9 as
separate entities of differing quantities. The bead bars hat compose it facilitate the
construction of the numbers from 11 to 19 and show respectively their relation to the
quantity of 10.
Control of Error
The child‟s own foolproof knowledge of the numerical order from 1 to 10 will be his
guide in forming the series. He needs only to become familiar with the new names and
their sequence.
Age
4 1/2 years onwards
Teens: Symbol
Materials
- Two boards each divided into five compartments. In nine of these compartments a large 10 is
printed in black.
- A set of cards, on which are printed the figures 1 – 9, which will slide into the boards, covering
the „0‟.
Presentation
Introduction
Have the child unroll a long mat.
Show the child the material and have him bring over the material. Sit at the mat so it is
vertically in front of you.
Place the two boards in a vertical line at the top of the mat.
Place all of the cards, in random order, to the right of the board.
Point to the first slot and ask what it is. (10)
Point to each until the child realizes that each has 10.
Slide the 1 card into the units spot in the top slot. Say, “This is eleven.”
Slide in the 2 card into the second slot and tell the child, “This is twelve.”
Repeat to create 13 under 12.
Do a Three Period Lesson for 11, 12, 13. For the 2nd Period, take out the cards and have
the child “create” 11, 12, 13.
Repeat, three numbers at a time until you have done 11-19.
Stage B
Have the child make the numbers 11-19 in random order directed by the directress.
Have the child take out the cards and have him create 11-19 in order.
Once the child is done, count all the numbers in order, and then backwards.
Purpose
Direct
To connect name and symbol.
Control of Error
The child‟s own knowledge.
Age
4 1/2 years onwards
Tens: Asscoiation of Quantity and Symbol, Boards, Cards and Beads
Materials
- Presentation 1:
Two boards similar to the teen boards but with the numbers 10 – 90 printed on them.
Nine bead bars of 10
- Presentation 2:
The ten boards
A set of loose cards from 1 – 9
Nine ten bars
Ten unit beads
Presentation 1: Terminology
1. Place all the beads at the top of the mat and then lay out the cards and boards in the
same way as in the Teens Presentation.
2. Read all of the numbers on the board with the child. (The child will probably say: 1
ten, 2 ten, 3 ten, etc.)
3. Give the correct names (ten, twenty, thirty, etc) three at a time in a Three Period
Lesson.
4. Once the child knows the names for all of the numbers, read through them forward
and then backward with the child.
5. Emphasize that most of them end in “ty”. Look with the child at the numbers that do
this: 20, 30, 40, 50, 60, 70, 80, 90. Tell the child that the “ty” tells us that there is a
ten in the number. “40 tells us that there are 4 tens.”
Presentation 2: Boards and Beads
Layout of the mat and
materials ready tobegin the
presentation:
1. Take out and place all of the beads onto the mat. Then place the 1 card to make 11 in
the top slot.
2. Place a ten-bar and a unit next to the cards. Have the child count and say how many
there are.
3. Ask if that is what the cards say. Yes.
4. Have the child add on unit. Have him count the beads. (12) Ask if that is how many
the cards say. No
5. Have the child change the cards to read 12.
6. Once you have made 14, show the child that we can simply point to the ten-bar and
automatically know there are ten.
7. Repeat until the child has formed 19.
8. When you reach 20 (made by a ten bar and ten unit beads), have the child take a ten
and exchange it for the ten unit beads bar to make 2 tens.
9. Ask if the cards say 20. No. Take the 9 card out of the slot and ask if there is a place
that says 20 (the second slot does).
10. Have the child bring the two ten-bars down next to the second slot.
11. Add a unit next to the two ten bars.
12. Have the child count: 10, 20, 21.
13. Ask if that is what the cards say. No. Have the child add the 1 card to the 20 to make
21.
Shows only half of the board
14. Repeat in this manner until 99.
Purpose
Presentation 1
To teach the names twenty, thirty, forty, etc…and to
show the child that twenty is two tens and so for the up to ninety.
Presentation 2
To teach sequence, the numbers from 11 to 99.
Control of Error
The child‟s own knowledge.
Age
4 1/2 years onwards
