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M o d u l e 5 (Sample)
Mathematical Exercises (part 1)
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Chapter 2
Introducing
Numbers
0 to 10
“Rarely, however, can he count with certainty the fingers of one
hand, and when he does succeed in doing this, there is always the
difficulty of knowing why, … The extreme exactness and
correctness of a child’s mind needs clear and precise help. When
numerical rods are given to children, we see that even the smallest
take a lively interest in counting.”

Dr. Maria Montessori

The Number Rods

The Number Rods are ten wooden rods varying in length from 1 decimeter (10 centimeters) to 1 meter (100
centimeters). Each decimeter on every rod is colored alternately (and repeatedly) with red and blue. The first
decimeter length of each rod is always red. Thus, the first rod is entirely red. The second, which is two decimeters
long, is colored red and blue, and so on. These rods are equal in dimensions to the red rods (sensorial material).

1
8
Chapter 2 Introducing Numbers from 0 to 10

in order of length, just like the red rods, with red

Exercise 1 ends on the left, lined up evenly.
The Number Rods 7. Allow the child to take over at any stage.
Introductory Exercise
Exercise 2
MATERIAL
? The number rods The Number Rods
? A floor mat, preferably dark green (or any other Learning to count from 1 to 10
colour not matching with blue or red shades),
measuring about 4 feet by 3 feet. MATERIAL
Same as in Introductory Exercise.
AGE
4 years onwards PURPOSES
? Introduction to counting 1 – 10.
PURPOSES ? To understand the quantitative value/significance
To introduce the number rods to the children.
? of each number.
To establish the likeness between long rods and
? ? To learn the names "one" to "ten" and to associate
number rods. the names with the quantities.
To indirectly enable the children to visualize the
? ? Awareness of the sequence of numbers 1 to 10.
successive increase in quantity from 1 to 10 (in ? Awareness of the quantitative relationship
terms of length at every successive rod). between numbers, e.g. 2 is more than 1 and 3 is
more than 2, etc.
EXERCISE
EXERCISE
Note: Complete work cycle is to be observed
Note: Complete work cycle is to be observed
1. Set the mat on the floor.
2. Bring the rods on the workplace and place at 1. Set the mat on the floor at the place of work.
random horizontally with red ends on the left as 2. Take the first three rods i.e. rods of one, two and
shown in the picture on the previous page. three, and start Three Period Lesson.
3. Introduce the number rods e.g. by saying “These
are the number rods”. Further explain the analogy Period 1:
between the number rods and the long rods e.g. by Move the first rod close to the child.
?
saying, “Do you remember some material in the Point towards it and say “This is the rod of one”.
?
classroom, that you have used previously, which Name it several times. "One...one...this is one."
looks like the number rods?”

4. Wait for the response in terms of “red rods” from

the child, else, point to the red rods for him.
5. Tell the child that the number rods can also be
arranged in the same way as the long rods.
6. Beginning with the rod of one, arrange the rods

9
Chapter 2 Introducing Numbers from 0 to 10

Then, slide the second rod in front of the child and

? handover the rod of one. Then, say “Show me the
say, “This is the rod of two”. Then count the rod of two” and so on.
partitions touching the center of each segment with Extend the second period till you are sure the child
?
forefinger, being careful not to hide the rod with the is ready to move on to period 3.
hand, i.e. point to red side of the rod and say “one”,
and then point to the blue part and say “two”.
Repeat a few times.
?

Period 3:
? Point to any one rod and say 'What is this?” and
wait for the child to answer.
? At naming a rod correctly, also ask the child to
count the rod. For example, place the rod of three in
Then, take the rod of three and repeat the above
?
front of him and ask, "How much is this?” Or “What
steps. Name it several times like above.
is this?". If he says "Three", then she asks him to
"Three...three...this is three." Finally, count the
count it. He counts the segments, "One, two,
segments, "One...two...three", touching segments
three." This can be repeated several times with
of the rod.
each of the rods.
? On succeeding days, add one or more rods to
those already learned, until the child can count all
the rods. The rods are left on the shelf for the child
to count whenever he likes.

Period 2:
? Having introduced the first three rods, say “Show
me the rod of one”. The child will probably show or

10
Chapter 2 Introducing Numbers from 0 to 10

Exercise 3
Sandpaper Numbers
MATERIAL
Ten green wooden/acrylic cards with the numerals 0 to
9, cut out of the finest grade sandpaper, mounted on
each card. The format of the numerals must be similar
to the numeric writing pattern which the school follows.
(Numeral ‘0’ is skipped in this exercise and is
presented after working with the Spindle Boxes.)

Sensitizing Fingertips
Invite the child by telling him that before we can
work with the sandpaper numbers, we must clean
our hands and sensitize our fingertips.
PRESENTATION
? Take the child over to the sink.
? Wash your hands with soap.
PURPOSES ? Fill up a bowl with warm water.
? To learn to recognize the written symbol for ? Put your fingertips of the dominant hand into the
numbers 0 to 9. water.
? To associate numerals with their spoken name. ? Let them soak for a little while.
? Preparation for writing. ? Dry them by rubbing gently against the towel.
AGE ? Ask the child to sensitize his fingers in the same
4 years and older way.

EXERCISE

Note: Complete work cycle is to be observed.

1. Sensitize your and the child's fingers.

2. Move the material to a table (preferably).
3. Select the first two to three cards i.e. 1, 2 & 3 and
place them towards the top of the table. (Zero is
introduced after the child has worked with
spindle boxes).
4. Using a multisensory approach, involving the
child's sense of sight, touch and hearing, begin
Three Period Lesson as described on the next Suggest to the child to stimulate his fingertips in
?
page. the same way in the future.

11
Chapter 2 Introducing Numbers from 0 to 10

Period 1 Continue to repeat the name of the numeral each

?
Sit beside the child and take the first numerals i.e.
? time the child traces the number (if the child is not
1, leaving the other numerals to top side. saying the name himself). The child is not asked to
say the name at this point, but he may do so
spontaneously.
Make sure that the child traces the numeral in the
?
right direction of writing it, using his dominant hand.
Slide away the first numeral toward the top of the
?
table, and bring down the numeral 2 in the front.
Trace it lightly at least three times and say its name
?
in the same way as you did with numeral ‘1’. Invite
the child to try that.

Bring the numeral "1" card in front of you, and

?
holding it steady with your left-hand, gently trace
the numeral with the index and middle fingers of
your dominant hand in the right way of writing it.
Trace the numeral three times and each time say its
?
name like, "One...this is one...this is the way we
write… one."

Slide the numeral towards the child and say,

? Put away numeral 2 and repeat the above steps
?
“Would you like to try that?” with numeral 3.

1
92
Chapter 2 Introducing Numbers from 0 to 10

Period 3
? Place all numerals in front of the child.
? Point to a numeral and say, “What is this?”
? When the child tells you its name ask him to trace
that.
? Repeat for all the numerals.

Period 2
? Place all numerals in front of the child in the right
sequence 1, 2, 3 from left to right.
? Ask, “Can you show me one?”
? When the child shows you 1, ask him to trace it for
you once again.

Repeat the above question for numerals 2 and 3,

?
asking the child to trace the number each time on
showing correctly.
Change places of the numerals and ask the same
?
questions one by one again.
Repeat many times till you are sure that child can
?
make the association between all the numerals and
their names.
Extend ‘Period 2’ as per requirement.
?

5. Ask the child to put the material back, saying,

"Today we learned to write the numbers 1, 2 and
3".
6. Add more numbers in the already learned
numbers on subsequent days.
7. Leave the box in the shelf and tell the child that he
can work with sandpaper numbers anytime he
likes.

13
Chapter 2 Introducing Numbers from 0 to 10

3. Continue in the same way till all numerals and rods

Exercise 4 are associated.
Number Rods & Numerals
MATERIAL
? The Number Rods.
? One set of white wooden/acrylic cards with the
numerals 1 to 10 normally in black or red.
? Large felt mat for floor exercise.

PURPOSES
To relate
? the numerals 1 to 10 with the
corresponding quantities.
To see the numerals 1 to 10 in sequence.
?

AGE
4 years and older
EXERCISE 2
PRELIMINARY STEP 1. Place the rods and numeral cards at random on
As the child is, so far, familiar with numerals 1 to 9 only, the mat.
introduce number 10 by showing the 10 card. 2. Ask the child to find rod 1 and the numeral card 1,
and place the card next to the rod.
EXERCISE 1 3. Ask the child to continue placing the rest of the
numeral cards with the corresponding number
Note: Complete work cycle is to be observed. rods.
1. Place the rods and numeral cards at random on
the mat.

2. Point to a rod and ask the child to count it and then

find the corresponding numeral from the number EXERCISE 3
cards. For example, pointing to the rod of three, 1. Place the rods and numeral cards at random on
you ask him to count it. After the child has counted, the mat as in Presentation 1 and 2.
you ask him to find the number 3 from the cards 2. Invite the child to build the stairs.
and place it next to the rod (towards the right end of
the rod).

14
Chapter 2 Introducing Numbers from 0 to 10

3. Point to rod 1 and say, “This is the rod of 1”. To see the numerals 0 to 9 in sequence.
?
4. Then hold the number card of 1 and say, “This is To associate the corresponding loose quantities
?
how we write 1”. Place it next to the rod of 1. with the numerals.
5. Do the same for rod of 2 and 3 and then invite the
child to continue. AGE
6. Continue till all the cards are placed in correct 4 years and older
sequence from 1 to 10 along with the stairs made
up of rods. EXERCISE

Note: Complete work cycle is to be observed.

1. Bring the material to a table with the help of the

child.
2. Take all the spindles out of the box and lay them on
the table in front of the box with the help of the
child.
3. To make sure that the child can recognize
numbers till 9, point to the compartments one by
one and ask the child, “What number is this?”.

EXTENSION
Do the exercises some other day in reverse order by
showing numerals and asking children to find
corresponding rods to place them together.

Exercise 5
The Spindle Boxes
MATERIAL
? A wooden box with ten compartments. The
numerals 0 to 9 written at the back of the box.
? 45 wooden/plastic spindles.

4. Then, point to 1 and say, “One”.

CONTROL OF ERROR
There are exactly 45 spindles to be placed in all the
compartments, which is exactly the sum of all the
numbers 0 to 9. So, there is exactly the right number of
spindles to be placed in the compartments. If a
mistake is made, the child will be left with either more
than nine or less than nine spindles.

PURPOSES
? To introduce the concept of zero.

15
Chapter 2 Introducing Numbers from 0 to 10

5. Pick up one spindle with your right hand and put it

in the palm of the left hand counting one. Then, put
it in the compartment 1.

8. When this has been done, point to zero on the

6. Then point to number 2 on the spindle box and say back of the box and tell the child, "This is called
“two”. Pick up one spindle with your right hand and zero. This is the way we write zero. "Then say,
put it in the palm of the left hand saying one. Then, "you see this compartment is empty, that is
take the second spindle with your right hand and because zero means nothing, We do not put
put it in the palm of the left hand along with the anything in the zero compartment." At this
previous spindle and say 2. Put both the spindles stage show him the numeral ‘0’ from sandpaper
in compartment 2. numbers and ask him to trace that.
9. Once the child understands the exercise, he can
continue working independently and take the
spindle box and do the exercise as often as he
likes.

7. Continue in the same way till the right quantity of

spindles is placed in each of the compartments.

16
Chapter 2 Introducing Numbers from 0 to 10

10. Sometimes a child has trouble accepting that

“zero means nothing” and is tempted to put some
spindles in the zero compartment. If this happens,
give some extra help to the child.

Exercise 6
Number Cards & Counters
MATERIAL
? Cut-out numerals or number cards from 1 to 10 in
red on white cards.
? 55 counters all the same size and color.

6. Point to card 1 and say, “one”. Take one counter

and place it below the card 1 saying, “one”.

PURPOSES
? To give the concept of even and odd numbers
through a visual and concrete experience.
? To provide further practice in arranging the
numerals 1 to 10 in a sequence and associate
corresponding quantities with them.

AGE
4 years and older

EXERCISE

Note: Complete work cycle is to be observed.

1. Introduce the material to the child and bring to a

big table.
2. Take out all the cards and lay them on the table in
mixed order.
3. Find 1 and place it on the extreme left hand side of
the table.
4. Then, find 10 and place it on the extreme right hand
side of the table.
5. Ask the child to arrange the rest of the numeral
between 1 and 10.

17
Chapter 2 Introducing Numbers from 0 to 10

7. Point to card 2 and say, “two”. Then, place two 9. Continue to arrange the counters in pairs, with the
counters below card 2 horizontally while counting odd ones underneath in the same way till 10 as
the counters. (Place the first counter and say “1”. shown in the picture below.
Then place the second counter beside it leaving a
little space between the two in the middle and say
“2”.)

10. Allow the child to take over at any stage if he has

understood the arrangement pattern.

Period 1
? When the arrangement of counters is complete,
place your index finger at the base of each number
8. Then, point to card 3 and say, “three”. Place three card in the middle and slide down. If it is hit by a
counters below the card, while counting each counter say, “odd”, and if the finger passes through
counter, in such a way that 2 counters are in one without hitting any counter say, “even”.
row similar to the counters under card 2, while the
third counters is slightly below the two counters in
the middle.

18
Chapter 2 Introducing Numbers from 0 to 10

odd

odd

Period 2
? Ask the child if he can show you an odd number or
an even number one by one.
? “Can you show me an odd number?”

even

19
Chapter 2 Introducing Numbers from 0 to 10

“Can you show me an even number?

? CONTROL OF ERROR
“Can you show me another odd number?”
? There are 55 counters to be placed under the
And so on.
? numbers, which are exactly the sum of all the numbers
1 to 10. So, there is exactly the right number of
counters to be placed. If a mistake is made, the child
will be left with either more than ten or less than ten
counters at the last number.

Note
In this series of exercises for teaching the
understanding of the quantities and the numerals 1
to 10, each material serves a specific purpose, as
described below.

1. Number Rods - The quantities are fixed and the

numerals are loose. By building the rods into a
stair, from the shortest to the longest, and
placing the number cards on the end segment of
each rod, the child sees the numbers in correct
sequence.
2. Spindle Box - The quantities are loose and the
numerals are fixed in sequence along the top of
the box.
Period 3 3. Cards and Counters - Both numerals and
? Point to a number and ask what number is this. The quantities are loose. This is the first time we
child says its name e.g. 5. Then ask, “What is it… have asked the child to sequence number
even or odd?” without providing a control for the sequencing.
? Repeat for all the numbers.

Extension Exercise 1
Memory Game
MATERIAL
? 11 slips of folded paper placed in a container with
a number written on each… from 0 to 10.
? 11 sets of materials (with ten or more objects in
each set) e.g. paper clips, cubes of pink tower,
cylinders of knobless cylinders, pencils, ten
crayons, ten shapes of metal insets, ten spoons,
ten sandpaper letter etc.
? 11 trays

PURPOSES
? Reinforcement of numeric visual memory.
? To apply knowledge of numbers to everyday
objects.

AGE
4 years (usually at the end of Group 1)

EXERCISE
1. Invite 11 children and ask them to sit in a circle.
2. Give each child a tary.
3. Ask each child to take a folded paper strip from
the jar but not to look at what is written on it.

20
Chapter 2 Introducing Numbers from 0 to 10

4. Tell the children that you would come to each child “Fajar please knock at the door 5 times.”
?
one by one and ask to get a some objects from the “Abdullah please clap your hands 4 times.”
?
classroom. “Talha please jump ten times”.
?
5. Go to the first child and whisper in his ear what to 3. Ask other children to count along as a child
get e.g. pencils. Also tell the child to open his performs.
folded strip, read the number silently and bring that 4. Continue in the same way till the children are
many pencils. interested.
6. Go to the second child in the circle and tell him to
get something else e.g. crayons according to the
number on his folded slip. Extension Exercise 3
7. Continue in the same way by going to each child in Number Poems & Rhymes
the circle.
8. Once a child has collected what you asked for, he Poems and rhymes including numbers can be helpful
should sit back at his place in the circle. in illustrating and reinforcing number vocabulary and
9. Verify if each child has collected things according concepts especially when involves actions. Following
to the number written on the slip. are just a few examples;
10. Discuss why the child who got the slip of 0 has
brought nothing… because 0 means nothing. One two, buckle my shoe,
?
11. Collect the slips back and repeat the game if the Three four, shut the door,
children are interested, otherwise ask children to Five, six, pick up stick,
return the materials to the shelves. Seven, eight, lay them straight,
Nine, ten, a big fat hen.
Extension Exercise 2
Actions Game
MATERIAL
Non required

PURPOSE
To apply knowledge of numbers to everyday life.

AGE
4 years (usually at the end of Group 1)

EXERCISE
1. Invite a few children and make them stand in a
circle.
2. Ask children to perform certain actions a certain
number of times, For example,
? “Noor please stamp your feet 7 times.”

Nine juicy apples,

?
On my grandpa’s tree,
If you pick and eat one,
How many will there be?

Ten little monkeys jumping on the bed

?
One fell down and bumped his head
Mama called the doctor and the doctor said,
“No more monkeys jumping on the bed !”

21
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