HBMT 1203 Mathematic

Topic
1
Numbers
0 to 10
LEARNING OUTCOMES
By the end of this topic, you should be able to:
1. Recognise the major mathematical skills of whole numbers from 0 to
10;
2. Identify the pedagogical content knowledge of pre-number
concepts, early numbers and place value of numbers from 0 to 10;
3. Plan teaching and learning activities for pre-number concepts and
early numbers from 0 to 10; and
4. Determine and learn the strategies for teaching and learning
numbers in order to achieve Âactive learningÊ in the classroom.
INTRODUCTION
Beginning number concepts are much more complex than we realise. Just because
children can say the words ÂoneÊ, ÂtwoÊ, ÂthreeÊ and so on, does not mean that they
can count the numbers. We want children to think about what they are counting.
Children can count numbers if they understand the words Âhow manyÊ. As
teachers, we do not teach numerals in isolation with the quantity they represent
because numerals are symbols that have meaning for children only when they are
introduced as labels of quantities. In order to start teaching numbers effectively, it
is important for you to have an overview of the mathematical skills of whole
numbers. At the beginning of this topic, you will learn about the history of
various numeration systems and basic number concepts such as the meanings of
ÂnumberÊ, ÂnumeralÊ and ÂdigitÊ. You will also learn about the stages of conceptual
development for whole numbers including pre-number concepts and early
numbers. Children learn to recognise and write numerals as they learn to develop
early number concepts. In the second part of this topic, you will learn more about
the strategies for the teaching and learning of numbers through a few samples of

TOPIC 1 NUMBERS 0 TO 10
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teaching and learning activities. You are also encouraged to hold discussions
with your tutor and classmates. Some suggested activities for discussion are also
given.
PEDAGOGICAL CONTENT KNOWLEDGE OF
WHOLE NUMBERS: NUMBERS 0 TO 10
1.1
In this section, we will be focusing on the major mathematical skills for pre-number
concepts and whole numbers 0 to 10 as follows:
(a) Determine pre-number concepts;
(b) Compare the values of whole numbers 1 to 10;
(c) Recognise and name whole numbers 0 to 10;
(d) Count, read and write whole numbers 0 to 10;
(e) Determine the base-10 place value for each digit 0 to 10 ; and
(f) Arrange whole numbers 1 to 10 in ascending and descending order.
1.1.1 Pre-number Concepts
The development of number concepts for children in kindergarten begins with
pre-number concepts and emphasises on developing number sense the ability
to deal meaningfully with whole number ideas as opposed to memorising
(Troutman, 2003).
At this level, children are guided to interact with sets of things. As they interact,
they sort, compare, make observations, see connections, tell, discuss ideas, ask
and answer questions, draw pictures, write as well as build strategies. They begin
to form and organise cognitive understanding. In short, children will have to
learn the prerequisite skills needed as stated below:
(a) Develop classification abilities by their physical attributes;
(b) Compare the quantities of two sets of objects using one-to-one matching;
(c) Determine quantitative relationships including Âas many asÊ, Âmore thanÊ
and Âless thanÊ;
(d) Arrange objects into a sequence according to size (small to big), length
(short to long), height (short to tall) or width (thin to thick) and vice versa;
and

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(e) Recognise repeating patterns and create patterns by copying repeating
patterns using objects such as blocks, beads, etc.
1.1.2 Early Numbers
Mathematics starts with the counting of numbers. There are no historical records
of the first uses of numbers, their names and their symbols. Various symbols are
used to represent numbers based on their numeration systems. A numeration
system consists of a set of symbols and the rules for combining the symbols.
Different early numeration systems appeared to have originated from tallying.
Ancient people measured things by drawing on cave walls, bricks, pottery or
pieces of tree trunks to record their properties. At that time, ÂnumbersÊ were
represented by using simple Âtally marksÊ (/). Some numeration systems
including our present day system are shown in Table 1.1.
Table 1.1: Early Number Representations
Today 1 2 3 4 5 6 7 8 9
Ancient
Egypt
Babylon
Mayan . . . . . . . . . .
.
. .
. . .
. . . .
About 5000 years ago, people in places of ancient civilisations began to use
different symbols to represent numbers for counting. They created various
numeration systems. For example, the Egyptian numeration system used picture
symbols called hieroglyphics as illustrated in Figure 1.1.

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Figure 1.1: Egyptian hieroglyphics
This is a base-10 system where each symbol represents a power of 10.
What number is represented by the following illustration?
2(10 000) + 1000 + 3(100) + 4(10) + 6 = 21 346
Try writing the following numbers in hieroglyphics:
(a) 245
(b) 1 869 234
On the other hand, the Babylonians used a base-60 system consisting of only two
symbols as given below.
one ten
As such, the number 45 is represented as follows:
4(10) + 5 = 45
For numbers larger than 60, base-60 is used to represent numbers in the
Babylonian Numeration System.
Have fun computing the following illustrations:
(a)

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(b)
Apart from the nine symbols in Table 1.1, the Mayan Numeration System consists
of 20 symbols altogether and is a base-20 system, as shown in Figure 1.2.
Figure 1.2: Mayan numerals
The following illustration depicts clearly the unique vertical place value format of
the Mayan Numeration System, see Figure 1.3.
Figure 1.3: Mayan number chart
Source: Mayan number chart from http://en.wikipedia.org/wiki/Maya_numerals
What number is represented thus?
12 + 7(20) + 0(20.18) + 14(20.18.20)
= 12 + 140 + 0 + 100800 = 100952

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Simple addition can be carried out by combining two or more sets of symbols as
shown in the examples given below. Try computing these operations using
Hindu-Arabic numerals.
(a)
(b)
Solutions:
(a) 6 + 8 = 14
(b) {7 + 0(20) + 14(20.18) + 1(20.18.20)} + {14 + 0(20) + 3(20.18) + 2(20.18.20)} + {1
+ 1(20) + 17(20.18) + 3(20.18.20)}
= 7 + 0 + 5040 + 7200 + 14 + 0 + 1080 + 14400 + 1 + 20 + 6120 + 21600}
= 55482
The complexities of the above examples and illustrations of the various ancient
numeration systems discussed in this section should help you to realise why they
are no longer in use today. Table 1.2 shows some other famous historical
numeration systems used to this day including the Roman Numeration System,
Greek Numeration System and our Hindu-Arabic Numeration System.
Table 1.2: Famous Number Representations
Roman
200 B.C. I II III IV V VI VII VIII IX
Greek 500
B.C.
z
Hindu-
Arabic 500
A.D.
1 2 3 4 5 6 7 8 9
Hindu-
Arabic 976
A.D.
l

7 8 9

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Along with the development of numbers, mathematics was further developed by
famous mathematicians. The numeration system used today is based on the
Hindu-Arabic numeration system. Can you explain why the Hindu-Arabic
numeration system is being used today?
At this point, you should have a clearer picture about the difference between a
ÂnumberÊ, a ÂnumeralÊ and a ÂdigitÊ. The terms ÂnumberÊ, ÂnumeralÊ and ÂdigitÊ are
all different. A number is an abstract idea that addresses the question, Âhow
manyÊ and means Ârelated to quantityÊ, whereas a numeral is a symbol for
representing a number that we can see, write or touch. Thus, numerals are names
for numbers. A ÂdigitÊ refers to the type of numerals used in a numeration system.
For example, our present numeration system is made up of only 10 different
digits, that is, 0 to 9.
SAMPLES OF TEACHING AND LEARNING
ACTIVITIES
1.2
In this section, you will read about some samples of teaching and learning
activities that you can implement in your classroom.
1.2.1 Teaching Pre-number Concepts
There are many pre-number concepts that children must acquire in order to
develop good number sense. These are as follows:
(a) Classify and sort things in terms of properties (e.g. colour, shape, size, etc.);
(b) Compare two sets and find out whether one set has Âas many asÊ, Âmore
thanÊ, or Âless thanÊ the other set;
(c) Learn the concepts of Âone moreÊ and Âone lessÊ.
(d) Order sets of objects according to a sequence according to size, length,
height or width; and
(e) Recognise and copy repeating patterns using objects such as blocks, beads,
etc.
Now, let us look at some activities that you can do with your pupils.

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Activity 1: Classifying Things by Their Properties
Learning Outcomes:
By the end of this activity, your pupils should be able to:
(a) Classify things by their general and specific properties.
Materials:
Sets of toys;
Sets of pattern blocks (various shapes, colour, size, etc.); and
Plastic containers or boxes.
Procedure:
(a) Classify Objects by Their General Properties
Teacher asks children to work in groups of five and distributes four types of
toys (e.g. car, train, boat and aeroplane) to each group.
Teacher says: „LetÊs work together, look at the toys.‰
Teacher asks: „Which are the toys that can fly? Which one can sail in the
sea? Which is the longest vehicle? Which is the smallest vehicle? Which is
the fastest vehicle? Which is the slowest vehicle?‰
Children respond to questions asked.
In this activity, children should be asked why they chose that specific object
and not the others. Teacher listens to childrenÊs responses.
(b) Classify Objects by Their Specific Properties
Teacher distributes a set of pattern blocks with different shapes, sizes and
colours to each group, see Figure 1.4.

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Figure 1.4: Pattern blocks
(i) Teacher says: „Firstly, classify these objects by their shapes.‰
„Put the objects into the boxes: A, B, C and D according to their
shapes.‰ (e.g. circle, triangle, rectangle and rhombus, see Figure 1.5
(a).
Figure 1.5 (a): Pattern blocks and containers
(ii) Teacher says: „Secondly, classify these objects by their sizes.‰
„Put the objects into the boxes: A, B and C according to their sizes.‰
(e.g. small size in box A, medium size in box B and large size in box C
with respect to their shapes, see Figure 1.5 (b).
Figure 1.5 (b): Pattern blocks and containers

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(iii) Teacher says: „Lastly, classify these objects by their colours.‰
„Put the objects into the boxes: A, B, C, D, E and F according to their
colours‰. (e.g. orange, blue, yellow, red, green and purple, see Figure
1.5 (c).
Figure 1.5 (c): Pattern blocks and containers
At this stage, children will recognise that shape is the first property to consider,
followed by size and colour. Children should be encouraged to find as many
properties as they can when classifying objects.
You can also try some other activities with the children such as classifying objects
by their texture (smooth, rough and fuzzy) or by their size (short and long), etc.
to prepare them to learn about putting objects into a sequence, that is, the skill of
ordering or seriation, which is more difficult than comparing since it involves
making many decisions.
For example, when ordering three drinking straws of different lengths from short
to long, the middle one must be longer than the one before it, but shorter than the
one after it.
Next, in Activity 2, your pupils will be asked to find the relationship between two
sets of black and white objects. Let us now take a look at Activity 2.

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Activity 2: Finding the Relationship between Two Sets of Objects
Learning Outcomes:
(a) Match items on a one-to-one matching basis;
(b) Understand and master the concept of Âas many asÊ, Âmore thanÊ and Âless
thanÊ; and
(c) Compare the number of objects between two sets.
Materials:
Picture cards (A, B, C and D);
Erasers; and
Pencils, etc.
Procedure:
(i) One-to-One Matching Correspondence
Children are presented with two picture cards, (Card A and Card B)
consisting of the same number of objects.
Teacher demonstrates how the relationship of Âas many asÊ can be
introduced using a one-to-one matching basis as follows, see Figure 1.6 (a):
Figure 1.6 (a): One-to-one matching correspondence
Teacher asks: „Are there as many moons as stars? Why?‰
(ii) As Many As, More and Less
Teacher takes out a star from Card B and asks, „Are there as many moons
as stars now? Why? How can you tell? etc.‰ See example in Figure 1.6 (b).

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Figure 1.6 (b): One-to-one matching correspondence
Teacher guides the children to build the concept of ÂmoreÊ and ÂlessÊ. For
example, which card has more moons? Which card has fewer stars?
(iii) More Than, Less Than
The children are presented with another two picture cards (Card C and
Card D) with different numbers of objects. Teacher guides the children to
compare the number of objects between the two sets and introduces the
concept of Âmore thanÊ and Âless thanÊ.
Teacher says: „Can you match each marble in Card C one-to-one with a
marble in Card D? Why?‰
Teacher says: „Children, we can say that Card C has more marbles than
Card D, or, Card D has less marbles than Card C‰.
In addition, teacher can ask her pupils to do a group activity as follows:
Teacher says: „Sit together with your friends in a group‰. „Everybody, show all
the erasers and pencils you have to your friends‰. „Can you compare the number
of objects and tell your friends using the words, Âmore thanÊ or Âless thanÊ?‰
Pupils should be able to respond as such: „I have more erasers than you but, I
have fewer pencils than you‰, „You have more erasers than me‰, etc.
Do try and think of other appropriate activities you can plan and implement to
help children to acquire pre-number experience or concepts essential for
developing good number sense prior to learning whole numbers.
ACTIVITY 1.1
Which of the pupilsÊ learning activities do you like the most? Explain.

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1.2.2 Teaching Early Numbers
This section elaborates on the activities which you can implement with your
pupils to help them understand the concept of early numbers.
Activity 3: Name Numbers and Recognise Numerals 1 to 10
Learning Outcomes:
By the end of this activity, pupils should be able to:
(a) Name and recognise numerals 1 to 5.
Materials:
Picture cards (0 to 5);
Number cards (1 to 5); and
PowerPoint slides.
Procedure:
(a) Clap and Count
Teacher claps and counts 1 to 5. Teacher and pupils clap and count a series
of claps together. ÂClapÊ, say ÂoneÊ. ÂClapÊ, ÂClapÊ, say ÂoneÊ, ÂtwoÊ.
Teacher asks pupils to clap twice and count one, two; Clap four times and
count one, two, three, four, etc. Pupils respond accordingly. Do the same
until number 5 is done.
(b) Slide Show
Teacher displays a series of PowerPoint slides one by one as shown in
Figure 1.7. The numerals come out after the objects.
Figure 1.7: Picture numeral cards

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Teacher asks: „How many balls are there in this slide?‰ and says, „Let us
count together.‰
Teacher points to the balls and asks pupils to count one by one. Then, point
to the numeral and say the number name. Guide pupils to respond (e.g.
„There is one ball‰, „There are two balls‰, etc.). Repeat with different
numbers and different pictures of objects.
(c) Class Activity
(i) Teacher shows a picture card and asks pupils to stick the correct
number card beside it on the white board. e.g.:
Teacher says: „Look at the picture. How many clocks are there?‰
Pupils respond accordingly. Then teacher asks a pupil to choose the
correct number card and stick it beside the picture card on the white
board.
Teacher repeats the steps until the fifth picture card is used. At the
end, teacher asks pupils to arrange the picture cards in ascending
order (1 to 5) and then asks them to count accordingly.
(ii) Teacher shows a number card and asks the pupils to stick the correct
picture card beside it on the white board. e.g.:
Teacher says: „Look at the card. What is the number written on the
card?‰

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Pupils respond accordingly. Then teacher asks a pupil to choose the
correct picture card and stick it beside the number card on the white
board.
Teacher repeats the steps until the fifth numeral card is done. At the
end, teacher asks pupils to arrange the number cards in ascending or
descending order (e.g. 1 to 5 or 5 to 1) before asking them to count in
sequence and at random.
(d) Group Activity
Pupils sit in groups of five. Teacher distributes five picture cards of objects
and five corresponding numeral cards (1 to 5).
Teacher says: „Choose a pupil in your group. Put up the number five card
in his/her left hand and the correct picture card on his/her right hand.
Help him/her to get the correct answer.‰
Teacher asks the group to choose another pupil to do the same for the rest
of the cards. Repeat for all the numbers 1 to 5.
Teacher distributes a worksheet.
Teacher says: „LetÊs sing a song about busy people together.‰ (refer to
Appendix 1)
Activity 4: Read and Write Numbers, 1 to 10
Learning Outcomes:
(a) Read and write numbers from 1 to 10.
Materials:
Picture cards;
Cut-out number cards (1 5);
Number names (name cards, one to five); and
Plasticine.

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Procedure:
(i) Numbers 1 to 5
Teacher shows the picture cards with numbers, 1 to 5 in sequence. Pupils
count the objects in the picture card, point to the number and say the
number name out loud. e.g.:
Teacher sticks the picture card on the writing board. Repeat this activity for
all the picture and number cards, that is, until the fifth card is done.
(ii) Technique of Writing Numbers
Teacher demonstrates in sequence the technique of writing numerals, 1 to 5.
Firstly, teacher writes the number Â1Ê on the writing board step by step as
follows: e.g.:
1
Teacher writes the number in the air followed by the pupils. Repeat until
number 5 is done.
Repeat until the pupils are able to write numbers in the correct way.
(iii) Plasticine Numerals
Teacher distributes some plasticine to pupils and says: „Let us build the
numerals with plasticine for numbers 1 to 5. Arrange your numbers in
sequence.‰

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(iv) Cut-out Number Card
Teacher gives pupils the cut-out number cards, 1 to 5. Then, teacher asks
them to trace the shape of each number on a piece of paper. e.g.:
Teacher distributes Worksheet 1 (refer to Appendix 2).
Note: This strategy can also be used to teach the writing of numbers, from 6
to 10.
Can you write these numbers in the correct way?
Activity 5: The Concept of Zero
Learning Outcomes:
(a) Understand the concept of ÂzeroÊ or ÂnothingÊ; and
(b) Determine, name and write the number zero.
Materials:
Picture cards; and
Three boxes and five balls (Given to each group).
Procedure:
(i) Teacher shows three picture cards.

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Teacher asks: „How many rabbits are there in Cage A, B and C?‰
Pupils respond: „There is one rabbit in Cage B, two rabbits in Cage C and
no rabbits in Cage A.‰
Teacher introduces the number Â0Ê to represent Âno rabbitsÊ or ÂnothingÊ.
(ii) Teacher distributes some balls into three boxes.
Teacher asks: How many balls are there in Box A, Box B and Box C
respectively?‰
Teacher guides pupils to determine the concept of ÂzeroÊ or ÂnothingÊ
according to the number of balls in Box B.
Teacher reads and writes the digit Â0‰ (zero), followed by pupils.
Activity 6: Count On (Ascending) and Count Back (Descending) in Ones, from 1
to 10
Learning Outcomes:
(a) Count on in ones from 1 to 10;
(b) Count back in ones from 10 to 1; and
(c) Determine the base-10 place value for each digit from 1 to 10.
Materials:
Number cards (1 10);
Picture cards; and
PowerPoint slides.

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Procedure:
(a) Picture Cards
(i) Ascending Order
Teacher flashes picture cards and the corresponding number cards in
ascending order, (i.e. 1 to 10). Pupils count the objects in the picture
cards and say the numbers. Teacher sticks the cards on the whiteboard
in sequence. e.g.:
Continue until the 10th picture card is done.
Pupils are asked to count on in ones from 1 to 10. The activity is
repeated.
(ii) Descending Order
Teacher flashes picture cards and the corresponding number cards in
descending order, (i.e. 10 to 1). Pupils count the objects in the picture
cards and say the numbers. Teacher sticks the cards on the whiteboard
in sequence. e.g.:

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Continue until the first picture card is done.
Pupils are asked to count back in ones from 10 to 1. The activity is
repeated.
(b) Slide Show
(i) Ascending Order
Pupils are presented a series of slides (PowerPoint presentation):
Teacher asks pupils to count and say the number name, e.g. „one‰.
Teacher clicks a button to show the second stage and asks pupils to
count and say the number.

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Continue until the 10th stage. Repeat until the pupils are able to count
on in ones from 1 to 10.
(ii) Descending Order
Teacher repeats the process as above but in descending order (i.e. 10
to 1).
Teacher presents another slide show, see Figure 1.8:
Figure 1.8: Number ladder
(c) Teacher Distributes a Worksheet
(i) Jump on the Number Blocks
Teacher asks pupils to sing the ÂNumbers Up and DownÊ song while
jumping on the number blocks around the pond, that is, counting on
or counting back again and again!
„Let us sing the ÂNumbers Up and DownÊ song together‰ (see Figure
1.9).
Figure 1.9: Number blocks

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(ii) Arranging Pupils in Sequence
Teacher selects two groups of 10 pupils and gives each group a set of
number cards, 1 to 10, see Figure 1.10. Teacher asks them to stand in
front of the class in groups. Teacher asks both groups to arrange
themselves in order. The group that finishes first is the winner. The
losing group is asked to count on and count back the numbers in ones.
Repeat the game.
Figure 1.10: Number cards
(iii) Going Up and Down the Stairs
Pupils are asked to count on in ones while going up the stairs and
count back in ones while going down the stairs.
As a mathematics teacher, you have to generate as many ideas as possible
about the teaching and learning of whole numbers. There is no „one best
way‰ to teach whole numbers.
As we know, the goal for children working on this topic is to go beyond
simply counting from one to 10 and recognising numerals. The emphasis here
is developing number sense, number relationships and the facility with
counting.
The samples of teaching and learning activities in this topic will help you to
understand basic number skills associated with childrenÊs early learning of
mathematics.
They need to acquire ongoing experiences resulting from these activities in
order to develop consistency and accuracy with counting skills.

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Ascending order
Descending order
Digit
Early numbers
Number
Numeral
One-to-one matching correspondence
Pre-number Concepts
Seriation
Whole numbers
1. Describe the chronological development of numbers from ancient civilisation
until now. Present your answer in a mind map.
2. Teaching number concepts using concrete materials can help pupils learn
more effectively. Explain.
1. Pupils might have difficulties in understanding the meaning of 0 and 10
compared to the numbers 1 to 9. Explain.
2. Learning outcomes: At the end of the lesson, pupils will be able to count
numbers in ascending order (1 to 9) and descending order (9 to 1) either
through:
(a) Picture cards first and number cards later; or
(b) Number cards first and picture cards later.
Suggest the best strategy that can be used in the teaching and learning
process of numbers according to the above learning outcomes.

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APPENDIX
Busy People
One busy person sweeping the floor
Two busy people closing the door
Three busy people washing babyÊs socks
Four busy people lifting the rocks
Five busy people washing the bowls
Six busy people stirring ÂdodolÊ
Seven busy people chasing the mouse
Eight busy people painting the house
Nine busy people sewing clothes
Resource: Pusat Perkembangan Kurikulum
Numbers Up and Down
I'm learning how to count,
From zero up to ten.
I start from zero every time
And I count back down again.
Zero, one, two, three,
Four and five, I say.
Six, seven, eight and nine,
Now I'm at ten ~ Hooray!
But, I'm not finished, no not yet,
I got right up to ten.
Now I must count from ten back down,
To get to zero again!
Ten, nine, eight, seven,
Six and five, I say.
Four, three, two, one,
I'm back at zero ~ Hooray!
Resource: Mary Flynn's Songs 4 Teachers

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WORKSHEET
How many seeds are there in each apple?
Count and write the numbers.

Topic
2
Addition
within 10 and
Place Value
LEARNING OUTCOMES
1. Identify the major mathematical skills related to addition within 10
and place value;
2. Recognise the pedagogical content knowledge related to addition
within 10 and place value; and
3. Plan teaching and learning activities for addition within 10 and
introduction to the place value concept.
INTRODUCTION
Adding is a quick and efficient way of counting. Sometimes we notice that
adding and counting are alike, but adding is faster than counting. You will also
see that addition is more powerful than mere counting. It has its own special
vocabulary or words, and is easy to learn because only a few simple rules are
used in the addition of whole numbers. When teaching addition to young pupils,
it is important that you recognise the meaningful learning processes which can be
acquired through real life experiences. The activities in this topic are designed as
an introduction to addition. It provides the kind of practice that most young
children need. What do children need to know in addition? Children do not gain
understanding of addition just by working with symbols such as Â+Ê and Â=Ê. You
have to present the concept of addition through real-world experiences because
symbols will only be meaningful when they are associated with these
experiences. Young children must be able to see the connection between the
process of addition and the world they live in. They need to learn that certain
symbols and words such as ÂaddÊ, ÂsumÊ, ÂtotalÊ and ÂequalÊ are used as tools in
everyday life.

TOPIC 2 ADDITION WITHIN 10 AND PLACE VALUE
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This topic is divided into two main sections. The first section deals with
pedagogical skills pertaining to addition within 10 and includes an introduction
to the concept of place-value. The second section provides some samples of
teaching and learning activities for addition within 10. You will find that by
reading the input in this topic, you will be able to teach addition to young pupils
more effectively and meaningfully.
PEDAGOGICAL SKILLS OF ADDITION
WITHIN 10
2.1
In this section, we will discuss further the pedagogical skills of addition within
10. This section will look into the concept of 'more than', teaching and learning
addition through addition stories, acting out stories to go with equations, number
bonds up to 10, reading and writing addition equations and finally reinforcement
activities.
2.1.1 The Concept of ‘More Than’
It is important for pupils to understand and use the vocabulary of comparing and
arranging numbers or quantities before learning about addition. We can start by
comparing two numbers. For example, a teacher gives four oranges (or any other
concrete object) each to two pupils. The teacher then gives another orange to one
of the pupils and asks them to count the number of oranges each of them has.
Teacher: How many oranges do you have? Who has more oranges?
Teacher introduces the concept of Âmore thanÊ, Âand one moreÊ as well as Âadd one
moreÊ for addition by referring to the example above. The pupils are guided to
say the following sentences to reinforce their understanding of addition with
respect to the above concept.
e.g.: Five oranges are more than four oranges. Five is more than four.
Four and one more is five.
Four add one more is five.
Teacher repeats with other numbers using different picture cards or counters and
pupils practise using the sentence structures given above.

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2.1.2 Teaching and Learning Addition Through
Addition Stories
Initially, addition can be introduced through story problems that children can act
out. Early story situations should be simple and straightforward. Here is an
example of a simple story problem for teaching addition with two addends:
Salmah has three balls. Her mother bought two more balls for her. How many
balls does Salmah have altogether?
At this stage, children have to make connections between the real world and the
process of addition by interpreting the addition stories. Children must read and
write the equations that describe the process they are working with. The concept
of ÂadditionÊ should be introduced using real things or concrete objects. At the
same time, they have to read and write the equations using common words, such
as ÂandÊ, ÂmakeÊ, as well as ÂequalsÊ as shown in Figure 2.1:
Figure 2.1: Acting out addition stories
However, you have to study effective ways in which your pupils can act out the
stories. Based on the situations given, pupils can act out the stories in different
ways as follows:
(a) Act out stories using real things as counters such as marbles, ice-cream
sticks, top-up cards, etc.;
(b) Act out stories using counters and counting boards (e.g. trees, oceans.
roads, beaches, etc.);
(c) Act out stories using models such as counting blocks; and
(d) Act out stories using imagination (without real things).
Figure 2.2 shows some appropriate teaching aids for teaching and learning
addition.

29
Figure 2.2: Acting out addition stories using appropriate teaching aids
2.1.3 Acting Out Stories to go with Equations
Figure 2.3 suggests a way for acting out stories to go with equations using the
ÂplusÊ and ÂequalÊ signs:
Figure 2.3: Flowchart for ÂActing out stories to go with equationsÊ

30
After pupils are able to write equations according to teacher-directed stories, they
can begin writing equations independently using suitable materials (refer to
Figure 2.2). Here are some examples of how to use the materials.
Example 1: Counting Board (e.g. Aquarium)
I have two clown fish in my aquarium. My mother bought three goldfish
yesterday. How many fish do I have altogether? See Figure 2.4.
2 clown fish and 3 gold fish make 5 fish altogether.
2 + 3 = 5
Figure 2.4: Story problem
ACTIVITY 2.1
Use the above example to show that 2 + 3 = 3 + 2 = 5.
2.1.4 Number Bonds Up to 10
Activity 1: Count On and Count Back in Ones, from 1 to 10
There are three boys playing football. Then another
boy joins them. How many boys are playing football
altogether? See Figure 2.5.
3 + 1 = 4
Figure 2.5: Count on: Using an Abacus
Teachers can also use number cards as a number line. The teacher reads or writes
the story problem and then begins a discussion with pupils on how to use the
number line to answer the question as in the example shown in Figure 2.6:

31
„Four pupils and three pupils are seven pupils‰
„Four plus three equals seven‰
4 + 3 = 7
Figure 2.6: Count on: Aligning number cards to form a number line
Teachers are encouraged to teach the addition of two addends within 5 first,
followed by addition within 6 until 10. Pupils need to be ÂimmersedÊ in the
activities and go through the experience several times. By repeating the tasks,
pupils will learn the different number combinations for bonds up to 10 efficiently.
Activity 2: Count On and Count Back in Ones, from 1 to 10
The activities on number bonds provide opportunities for teachers to apply a
variety of addition strategies. The objective of these activities is to recognise the
addition of pairs of numbers up to 10. You can start by asking your pupils to
build a tower of 10 cubes and then break it into two towers, for example, a tower
of four cubes and a tower of six cubes, (refer Figure 2.7) or any pairs of numbers
adding up to 10.
Example:
Figure 2.7: Number towers
Guide pupils to produce addition pairs up to 10, e.g. 4 + 6 = 10 or 6 + 4 = 10.
Repeat with other pairs of numbers. Ask pupils what patterns they can see before
getting them to produce all the possible pairs that add up to 10. Record each
addition pair in a table as shown in Table 2.1:

32
Table 2.1: Sample Table for ÂAddition ActivityÊ: Addition Pairs Up to 10
After Breaking Height of Tower Before into Two Towers
Breaking into Two Towers
(Cubes)
Height of First
Tower (Cubes)
Height of Second
Tower (Cubes)
10 0 10
10 1 9
10 2 8
10 3
10 4
10 5
10 6
10 7
10 8
10 9
10 10
Discuss the results with pupils and ask them to practise saying the number bonds
repeatedly to facilitate instant and spontaneous recall in order to master the basic
facts of addition up to 10.
To develop the skill, the teacher should first break the tower of 10 cubes into two
parts. Show one part of the tower and hide the other. Then, ask pupils to state the
height of the hidden tower. To extend the skill, you may progressively ask the
pupils to learn how to add other pairs of numbers, such as 9, 8, 7 and so on.
ACTIVITY 2.2
What is the Âcommutative law in additionÊ? How do you introduce this
concept to your pupils? Explain clearly the strategy used for the teaching
and learning of the commutative law in addition.
2.1.5 Reading and Writing Addition Equations
As we know, there are two common methods of writing the addition of numbers,
either horizontally or vertically, as shown below:

33
(a) Adding horizontally, in row form (i.e. Writing and counting numbers from
left to right).
Example: 4 + 5 = 9
The activities discussed above are mostly based on this method, which are
suitable for adding two single numbers.
(b) Adding vertically, in column form (i.e. Writing and counting numbers from
top to bottom).
Example: 3
+ 4
7
This method is suitable for finding a sum of two or more large numbers
because putting large numbers in columns makes the process of adding
easier compared to putting them in a row.
ACTIVITY 2.3
Numbers are most easily added by placing them in columns. Describe
how you can create suitable teaching aids to enhance the addition of two
addends using this method.
2.1.6 Reinforcement Activities
To be an effective mathematics teacher, you are encouraged to plan small group
or individual activities as reinforcement activities for addition within 10. Here are
some examples of learning activities that you can do with your pupils.
(a) Number Shapes
Have pupils take turns rolling a number cube to see how many counters
they have to place on their number shapes. Then they fill in the remaining
spaces with counters of different colours. Finally, they describe the number
combinations formed, as illustrated in Figure 2.8. Repeat with different
number shapes.

34
Figure 2.8: Number shapes
(b) Number Trains
Let pupils fill their number-train outlines (e.g. 7, 8 or 9) with connecting
cubes of two different colours. Ask them to describe the number
combinations formed. See Figure 2.9.
Figure 2.9: Number train
In addition, pupils can also describe the number combination formed as Âthree
plus three plus two equals eightÊ, that is (3 + 3 + 2 = 8).
PLACE VALUE
2.2
This section teaches you how to introduce the place-value concept to your pupils.
2.2.1 Counting from 11 to 20
Pupils will be able to read, write and count numbers up to 20 through the same
activities as for learning numbers up to 10 covered in Topic 1. Similar teaching
aids and methods can be used. The only difference is that we should now have
more counters, say, at least 20. In this section, we will not be focusing on counting
numbers from 11 to 20 because it would just be repeating the process of counting
numbers from 1 to 10. You are, however, encouraged to have some references on
the strategies of teaching and learning numbers from 11 to 20.

35
ACTIVITY 2.4
Describe a strategy you would use for the teaching and learning of
ÂCounting from 11 to 20Ê.
2.2.2 Teaching and Learning about Place Value
The concept of place value is not easily understood by pupils. Although they can
read and write numbers up to 20 or beyond, it does not mean that they know
about the different values for each numeral in two-digit numbers. We are lucky
because our number system requires us to learn only 10 different numerals.
Pupils can easily learn how to write any number, no matter how large it is. Once
pupils have discovered the patterns in the number system, the task of writing
two-digit numbers and beyond is simplified enormously. They will encounter the
same sequence of numerals, 0 to 9 over and over again. However, many pupils
do not understand that numbers are constructed by organising quantities into
groups of tens and ones, and the numerals change in value depending on their
position in a number.
In this section, you will be introduced to the concept of place value by forming
and counting groups, recognising patterns in the number system and organising
groups into tens and ones. The place-value concept can be taught in kindergarten
in order to help pupils count large numbers in a meaningful way.
You can start teaching place value by asking pupils to form and count
manipulative materials, such as counting cubes, ice-cream sticks, beans and cups,
etc. For example, ask pupils to count and group the connected cubes from 1 to 10
placed either in a row or horizontally as shown in Figure 2.10.
Figure 2.10: Connected cubes placed horizontally
You can now introduce the concept of place value of ones and tens (10 ones) to
your pupils. The following steps can be used to demonstrate the relationship
between the numbers (11 to 19), tens and ones. The cubes can also be arranged in
a column or vertically as shown below. Here, you are encouraged to use the
enquiry method to help pupils familiarise themselves with the place-value of tens
and ones illustrated as follows:

36
Example:
Teacher asks: What number is 10 and one more? See Figure 2.11 (Pupils should
respond with 11).
Can you show me using the connecting cubes?
The above step is repeated for numbers 12, 13, , 20.
Figure 2.11: Connected cubes placed vertically
In order to make your lesson more effective, you should use place-value boards
or charts to help pupils organise their counters into tens and ones. A place-value
board is a piece of thick paper or soft-board that is divided into two parts of
different colours. The size of the board depends on the size of the counters used.
An example of the place-value board is given in Figure 2.12:
Figure 2.12: Place value board

37
The repetition of the pattern for numbers 12 to 19 and 20 will make your pupils
understand better and be more familiar with the concept of place value. They will
be able to learn about counting numbers from 11 to 20 or beyond more
meaningfully. At the same time, you can also relate the place-value concept to the
addition process. For example, 1 tens and 2 ones make 12, which means 10 and
two more make 12.
ACTIVITY 2.5
In groups of four, create some reinforcement activities for teaching
numbers 11 to 20 using the place-value method. Describe clearly how you
will conduct the activities using suitable Âhands-onÊ teaching aids.
ACTIVITIES
2.3
This section provides some samples of teaching and learning activities you can
carry out with your pupils to enhance their knowledge of addition within 10 and
the place-value concept.
Activity 1: Adding Using Patterns
Learning Outcomes:
At the end of this activity, your pupils should be able to:
(a) Add two numbers up to 10 using patterns;
(b) Read and write equations for addition of numbers using common words;
and
(c) Read and write equations for addition of numbers using symbols and signs.
Materials:
Picture cards; and
PowerPoint slides.

38
Procedure:
(a) Adding Using Patterns (in Rows)
(i) Teacher divides the class into 5 groups of 6 pupils, and gives 10
oranges to each group. Teacher then asks each group to count the
oranges, see Figure 2.13.
Teacher says: „Can you arrange the oranges so that you can count
more easily?‰ Discuss with your friends.
Teacher says: „Now, take a look at this picture card.‰
Figure 2.13: Picture card: Addition using patterns
(ii) Teacher says: „Can you see the pattern? Let us count in groups of
fives instead of counting on in ones.‰
For example: Five and five equals ten, or 5 + 5 = 10
(iii) Teacher says: „Now, let us look at another pattern. How many eggs
are there in the picture given below (see Figure 2.14)?‰
Figure 2.14: Picture card: Addition using patterns (in rows)
(iv) Teacher says: „Did you count every egg to find out how many there
are altogether? Or did you manage to see the pattern and count along
one row first to get 4, and then add with another row of 4 to make 8
eggs altogether?‰
„Well done, if you have done so!‰
Let your pupils add using different patterns of different numbers of objects
with the help of PowerPoint slides. Guide your pupils to read and write
equations of addition of numbers in words, symbols and signs (You may
discuss how to write the story-board of your PowerPoint presentation).

39
(b) Adding Using Patterns (in Columns)
(i) Teacher says: „Let us look at the pictures and try to recognise the
patterns (see Figure 2.15). Discuss with your friends.‰
Figure 2.15: Picture cards
(ii) Teacher discusses the patterns with pupils. For example, teacher
shows the third picture [Picture (c)] and tells that it can be divided
into two parts, namely, the top and bottom parts as shown in Figure
2.16:
Figure 2.16: Picture card: Addition using patterns (in columns)
(iii) This is a way of showing how to teach addition using columns by the
inquiry-discovery method. As a conclusion, the teacher explains to
the pupils that arranging the objects in patterns will make it easier to
add them. Using columns to add also makes the addition of large
numbers easier and faster.
(c) Teacher distributes a worksheet on addition using patterns (in rows or in
columns).

40
Activity 2: Addition within the Highest Total of 10
Learning Outcomes:
(a) Add using fingers;
(b) Add by combining two groups of objects; and
(c) Solve simple problems involving addition within 10.
Materials:
Fingers;
Counting board (tree);
Picture cards;
Number cards;
Counters;
Storybooks;
Apples; and
Other concrete objects, etc.
Procedure:
(a) Addition Using Fingers
(i) Initially, use fingers to practise adding two numbers as a method of
working out the addition of two groups of objects, see Figure 2.17.
e.g.:
Figure 2.17: Finger addition

41
(b) Addition of Two Groups of Objects
(i) Teacher puts three green apples on the right side of the tree and
another four red apples on the left side. Teacher asks pupils to count
the number of green apples and red apples respectively.
(ii) Teacher asks: „How many green apples are there? How many red
apples are there?‰
(iii) Teacher tells and asks: „Put all the apples at the centre of the tree.
Count on in ones together. How many apples are there altogether?‰
(iv) Teacher guides them to say and write the mathematical sentence as
shown: „Three apples and four apples make seven apples‰.
(v) Repeat with different numbers of apples or objects. Introduce the
concept of plus and equals in a mathematical sentence.
e.g. „There are two green apples and three red apples in Box A.‰
„There are five apples altogether.‰
„Two plus three equals five.‰
(vi) Teacher sticks the picture cards on the whiteboard. Encourage pupils
to add by counting on in ones (e.g. 4 ... 5, 6 ,7) and guide them to say
that „Four plus three equals seven‰ (see Figure 2.18).
Figure 2.18: Picture card: Addition of two groups of objects
(vii) Introduce the symbols for representing „plus‰ and „equals‰ in a
number sentence. Ask them to stick the correct number cards below
the picture cards to form an addition equation as above. Repeat this
step using different numbers.
(c) Problem Solving in Addition
(i) Teacher shows three balls in the box and asks pupils to put in some
more balls to make it 10 balls altogether.

42
(ii) Teacher asks: „How many balls do you need to make up 10? How did
you get the answer?‰
Let them discuss in groups using some counters. Ask them to explain
how they came up with their answers.
(iii) Repeat the above steps with different pairs of numbers.
(iv) Teacher discusses the following problem with the pupils.
Sarah has to read six story books this semester. If she has finished
reading four books, how many more story books has she got to
read?
(v) Teacher asks them to discuss the answer in groups. Encourage them
to work with models or counters and let them come up with their own
ideas for solving the problem. For example:
(Note: They can also use mental calculation to solve the problem.)
Activity 3: Reinforcement Activity (Game)
Learning Outcomes:
(a) Complete the addition table given; and
(b) Add two numbers shown at the toss of two dices up to a highest total of 10.
Materials:
Laminated Chart (Addition Table Table 1.2);
Two dices for each group; and
Crayons or colour pencils.

43
Procedure:
(i) Teacher guides pupils to complete the addition table given. (Print out the
table in A4 size paper and laminate it). You can also use the table to explain
the additive identity (i.e. A + 0 = 0 + A = A).
Table 2.2: Adding Squares
+ 0 1 2 3 4 5 6 7 8 9
0
1
2
3
4
5
6
7
8
9
Instructions for Game:
(i) Toss two dices at one go. Add the numbers obtained and check your answer
from the table.
(ii) Colour the numbers 10 in green (Table 2.2). List down all the pairs adding
up to 10.
(iii) Colour the numbers totalling 9 in red. List down all pairs adding up to 9.
(iv) Continue with other pairs of numbers using different colours for different
sums.

44
Activity 4: Place Value and Ordering
Learning Outcomes:
(a) Read and write numerals from 0 to 20;
(b) Explain the value represented by each digit in a two-digit number; and
(c) Use vocabulary for comparing and ordering numbers up to 20.
Materials:
Connecting cubes;
Counting board;
Place-value block/frame; and
Counters.
Procedure:
(a) Groups of Tens
(i) Teacher divides the class into 6 groups of 5 pupils each. Teacher
distributes some connecting cubes (say, at least 40 cubes) to each
group.
(ii) Teacher asks the following questions and pupils are required to
answer them using the connecting cubes:
What number is one more than 6?, 8?, and 9? 11?, 17? and 19?
What number comes after 5?, 7?, and 9? 12?, 16? and 19?
Which number is more, 7 or 9?, 3 or 7?, 14 or 11? etc.
e.g.: 14 is more than 11 as shown in Figure 2.19.
Figure 2.19: Representing numbers using connecting cubes

45
16 is one more than a number. What is that number?
Repeat the above steps with different numbers.
(b) Place Value and Ordering
(i) Teacher introduces a place-value block and asks pupils to count
beginning with number 1 by putting a counter into the first column
(see Figure 2.20 (a). Teacher asks them to put one more counter on the
board in that order. Repeat until number 9 is obtained. Teacher then
introduces the concept of „ones‰.
1 ones represents 1
2 ones represent 2, ..., 9 ones represent 9
Figure 2.20 (a): Representing numbers with place-value block and counters
(ii) Teacher asks: „What is the number after 10? How do you represent
number 11 on the place-value block?‰
Teacher introduces the concept of „tens‰ and „ones‰ as follows, see
Figure 2.20 (b):

46
Figure 2.20 (b): Representing numbers with place-value block and counters
(iii) Teacher asks pupils to put the correct number of counters into the
correct column to represent the numbers 11, 12, etc. until 20.
(iv) Teacher asks pupils to complete Table 1.3.
Table 2.3: Place Value
Number Tens Ones Number Tens Ones
11 1 3
12 9
13 17
16 14 4
19 1 8
20
15 1
(v) Teacher distributes a worksheet to reinforce the concept of place value
learnt.
A teacher should know his/her pupilsÊ levels of proficiency when applying
strategies to solve problems related to addition.
Problem solving related to addition depends on pupilsÊ ability to work based
on their counting skills.

47
At an early stage, it is enough if they could work using counting all or
counting on.
However, you have to guide and encourage them to work by seeing the
relationship or answer by knowing and mastering the number combinations
or number bonds.
Adding
Addition
Equation
Place Value
Sum
Plus
1. An effective way to teach addition is to ask pupils to act out the stories in
real life using their imagination (without real things) and their own ideas.
Elaborate using one example.
2. Describe clearly how you would teach addition up to 10 involving zero
using real materials.
3. Counting numbers from 11 to 20 should be taught after pupils are
introduced to the concept of place value. Give your comments on this.
Based on the following learning outcome, „At the end of the lesson, pupils will be
able to count numbers from 11 to 20 using place-value blocks‰, suggest the best
strategy or method that can be used in the teaching and learning process to
achieve this learning outcome.

48
APPENDIX
WORKSHEET
(a) Count and add.
(i)
(ii)
(b) Count and add.
(c) Draw the correct number of fish on each plate and complete the equation.

49
(d) Match the following.
(e) Match the following (Read and add).

Topic
3
Subtraction
within 10
LEARNING OUTCOMES
1. Recognise the major mathematical skills pertaining to subtraction
within 10;
2. Identify the pedagogical content knowledge pertaining to subtraction
within 10; and
3. Plan teaching and learning activities for subtraction within 10.
INTRODUCTION
This topic will provide you with the instruction and practice you need to
understand about subtraction. Beginning with the comprehension of basic skills
in subtraction, this topic will cover various strategies for teaching and learning
subtraction. The step-by-step approach used in this topic will make it easy for
you to understand the ideas about teaching and learning subtraction especially at
kindergarten level. As in all other topics, some examples of teaching-learning
activities are also given. They include several classroom activities incorporating
the use of concrete materials and a variety of methods such as inquiry-discovery,
demonstration, simulation, etc. The inquiry-discovery method comprises
activities such as planning, investigating, analysing and discovering. It is very
important that pupils take an active part in the teaching-learning activities
because by doing mathematics, they will learn more meaningfully and
effectively.

TOPIC 3 SUBTRACTION WITHIN 10
51
PEDAGOGICAL SKILLS OF SUBTRACTION
WITHIN 10
3.1
Subtraction in simple words means taking away. When you take objects away
from a group, the mathematical term for this process is known as ÂsubtractionÊ or
ÂsubtractingÊ. It is all about separating a large group of things into smaller groups
of things. Besides taking away, some other common terms or vocabulary that
also indicate subtraction are ÂremainderÊ or Âwhat is leftÊ, Âcounting backÊ and
Âfinding the differenceÊ. Subtraction is also involved when phrases or questions
such as ÂHow many more?Ê, ÂWhat is the amount to be added?Ê, as well as ÂHow
many remain?Ê etc., are used.
There are at least three ways to illustrate the meaning of subtraction as listed
below:
(a) Subtraction as counting back;
(b) Subtraction as taking away; and
(c) Subtraction as the difference.
You will be shown how to teach subtraction contextually according to each of the
meanings of subtraction mentioned above. In addition, you also have to know
about other important parts related to the teaching and learning of subtraction
such as teaching materials, the relationship of subtraction with addition and
pairs of basic subtraction facts.
3.1.1 Subtraction as Counting Back
Subtraction is the reverse of addition. Counting on in ones is simply counting by
ones or moving forward between numbers one at a time. As counting on is a
reliable but slow way of adding, counting back is the reverse and is thus a slow
but reliable way of subtracting. Initially, subtraction within 10 as counting back
can be introduced by counting backwards either from 5 to 0 or from 10 to 0, that
is 5, 4, 3, 2, 1, 0 or 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0.
Take a look at Figure 3.1. For example, a teacher can give out number cards of 0
to 5 to six pupils and ask them to come out to the front and hold up their cards.
Get the pupils to arrange themselves in ascending order and ask who should
come first if the numbers are to be counted backwards from 5 to 0.

52
Figure 3.1: Count on and count back using number cards
Ask pupils to count backwards from 5 to 0. Repeat with counting backwards,
starting with any other number less than 5, for example starting from 4 or 3, etc.
Next, ask pupils to try doing the same thing without using number cards.
Then, guide the pupils to compare the difference between counting onwards and
counting backwards. At this stage, do not introduce the words subtract or minus
yet. Just use common words such as Âone lessÊ and ÂbeforeÊ as shown below:
„In the sequence of numbers between 0 to 5, what is the number before 5?,
before 4?‰ and so on.
„4 is one less than 5‰, „3 is one less than 4‰, „2 is one less than 3‰, etc.
Let them try to count backwards from 10 to 0, 9 to 0 and so on. At this stage,
pupils should also be able to arrange the numbers in descending order from 10 to
0.
Subtraction can also be done by counting back using a ruler as a number line.
Here is an example of how to count back using a ruler in order to solve the
subtraction problem given:
Sally has 7 sweets. She wants to give 3 to her friend. How many can she keep
for herself (see Figure 3.2)?
Answer: The result is 4. So Sally can keep 4 sweets for herself.

53
Figure 3.2: Counting back using a ruler
Suggest a teaching and learning activity to demonstrate subtraction as the
process of counting back using a calendar.
3.1.2 Subtraction as Taking Away
Subtraction facts are the numbers we get when we take one or more objects from
a group of objects, or the answer we get when we take one number from another.
First, let us look at the following steps for finding the six basic subtraction facts
illustrated in Figure 3.3 (a), (b) and (c).
For example, we start off with a group of six oranges.
(a) Put the oranges in a row, to make it easier to see what we are doing (see
Figure 3.3 (a).
Figure 3.3 (a): One group of six oranges
(b) Separate them into two groups, see Figure 3.3 (b): (Separating, in actual fact,
is a way of subtracting).
Figure 3.3 (b): Two groups of oranges
ACTIVITY 3.1

54
The numbers in the boxes tell us how many members are in each group. We
can describe the ÂsubtractionÊ process using common words like below:
Six take away one leaves five, or
Taking one from six leaves five.
(c) Repeat by working with groups of two and four oranges, as illustrated in
Figure 3.3 (c):
Figure 3.3 (c): Another two groups of oranges
Six take away two leaves four, or
Taking two from six leaves four.
(d) Repeat with other possible combinations of two groups of oranges, i.e. three
and three, four and two, as well as five and one in that order. At this stage,
you may also introduce subtracting terms, such as, minus, in order to teach
pupils to read and write the subtraction equations or mathematical
sentences given below:
Six take away one leaves five.
Six minus one equals five.
6 – 1 = 5
Six take away two leaves four.
Six minus two equals four.
6 2 = 4
3.1.3 Subtraction as the Difference
Sometimes you need to count on to find the difference between two numbers. For
example, if you have to answer 10 questions as practice but you have just
finished six only, you can find the number of remaining questions to be
answered in this way:
„I have finished six questions. To find out how many more questions I need to
answer in order to finish all the 10 questions, I can count on in ones starting from
7‰.
„7 + 1 = 8, 8 + 1 = 9, and 9 + 1 = 10‰, meaning 7 + 1 + 1 + 1 = 10

55
By using a ruler as a number line, you can find that the difference between 10
and 6 is 4 by counting on in ones as illustrated in Figure 3.4:
Figure 3.4: Number line
The difference is thus 4 questions. This means that you need to do 4 more
questions to finish off. It is now obvious that by counting on from seven to 10, six
plus four gives 10. Pupils can be guided to state that the difference between 10
and six is four, i.e.
Â6 + 4 = 10Ê is the same as Â10 6 = 4Ê.
This may be the case with your pupils because they were probably right to think
that counting on was much easier than subtracting. However, this was only
because the numbers were small. A real-life example is counting change. For
example if we gave RM1 (or ten 10 sen) to the cashier at the shop counter, and
the price of the things that you bought was only 60 sen, usually, the cashier will
give you back 40 sen as your change by counting on in 10 sen. The cashier will
normally say: „70 sen, 80 sen, 90 sen, RM 1. Here is the change, 40 sen.‰
What do you think of this way of doing subtraction? Is this a correct way to do
subtraction? Do you have other ideas?
3.1.4 Pairs of Subtraction Facts
We usually get two subtraction facts from each addition fact. Pupils have learnt
that adding two numbers together in any order gives the same result. However,
you have to encourage them to find out the results when they do subtraction.
Here is a way in which they can discover related subtraction facts. Pupils are
asked to work in groups.
(a) Give out seven rings to each group. Ask them to arrange the rings in a row
and separate them into two groups, i.e. a group of 3 rings and a group of 4
rings respectively, as illustrated below:

56
Let them read and write the addition fact depicted in the diagram above:
3 + 4 = 7
(b) Using the above addition fact, guide them to work out the subtraction facts
below:
(i) First subtraction fact:
7 3 = 4
(ii) Second subtraction fact:
7 4 = 3
Note: The order of the numbers to be subtracted is important!
ACTIVITY 3.2
Try listing out other fact families such as for the addition fact, 3 + 5 = 8.
3.1.5 Subtraction Using Models
Another way to do subtraction is to use any type of counters or teaching
materials as models to set up the problem.

57
Here are some examples:
(a) Subtract 3 from 8 using Counters
(i) Set up 8 counters as 8 units like below.
(ii) Subtract 3 units by crossing out three counters as shown.
(iii) Then, count the units that are left. The answer is 5 units. Ask pupils
to write down the subtraction equation as follows:
8 3 = 5
(iv) You are also encouraged to use another model such as illustrated
below:
Say: 8 take away 3 leaves 5
(b) Subtract 2 from 7 using Counting Board and Counters
(i) Story problem:
There are seven apples on a tree. Two of them fall down to the
ground. How many apples are left on the tree? (See Figure 3.5)

58
Figure 3.5: Story problem that can be used in teaching subtraction
(ii) First, ask them to stick on seven green counters on the tree. Then
colour two of them in red and pull them down from the tree. Put
them on the ground.
(You may like to make your counters from either soft paper or manila
card. Explain your choice.)
(iii) Write down the subtraction equation and find the answer:
7 2 = 5
Say: Taking away two from seven leaves five.
Answer: There are five mangosteens left on the tree.
(c) Subtract 4 from 9 using an Abacus and Counting Chips
Figure 3.6: Sample subtraction of 4 from 9

59
(i) Ask pupils to put on 9 counting chips in the first column of the
abacus. Then pull out 4 chips (either one by one or all at once), refer
to Figure 3.6.
(ii) Ask pupils to count and say how many chips are left.
(iii) Guide your pupils to write and read the subtraction equation as
follows:
Taking four from nine leaves five
9 4 = 5
(iv) Repeat the activity with different numbers of chips.
3.1.6 Number Sentences for Subtraction
We can write subtraction equations in rows or columns. Most of the examples in
this topic thus far have focused on writing equation in rows. Subtraction in a
column requires us to put the number we are subtracting from at the top and the
number we are going to subtract at the bottom. Make sure the numbers are lined
up exactly below each other in the column. Take a look at the following example
in Figure 3.7:
Figure 3.7: Number sentences for subtraction
ACTIVITY 3.3
What happens to the signs: Â-Ê and Â=Ê when you write down the ÂrowÊ
equation into a ÂcolumnÊ equation? Explain the process that occurs.

60
ACTIVITIES
Some samples of teaching-learning activities that you can implement to help
guide young children to understand and build the concept of subtraction in order
to acquire the skill are included in this section.
Activity 1: Working Out ÂOne Less ThanÊ
Learning Outcomes:
(a) Use Âone less thanÊ to compare two numbers within 10; and
(b) Count back in ones from 10 to 0.
Materials:
10 balloons;
11 number cards (0 10);
String; and
Worksheet 1.
Procedure:
(a) Get 10 balloons and hang them in a row or horizontal line. Initially, stack
the 11 number cards, numbered 0 - 10 in sequence, with the card numbered
10 at the top followed by the card numbered 9 below and so on, with the
card numbered 0 at the bottom of the pile. Hook the stack of number cards
on the extreme right as shown in Figure 3.8.
Figure 3.8: Ten balloons in a row
(i) Get one pupil to count the balloons and say the number out loud.
(ii) Ask another pupil to pick and burst any one of the balloons, count
the remaining balloons and say „9‰. Then, take out the card
numbered 10 to show the card numbered 9 underneath.
3.2

61
(iii) Teacher asks the pupils:
„How many balloons are left?‰ (9)
„Are there more or less balloons now compared to before?‰ (less)
„How many less?‰ (1 less)
(iv) Teacher explains that 9 is Âone less thanÊ 10.
(v) Continue doing the activity until the last balloon is pricked.
(b) Ask pupils to count back in ones, starting with any number up to 10 e.g.
You can start with number 8 or 7 and so on.
(c) Get the 11 number cards and ask pupils to arrange the cards in sequence
again. Practise using the phrase Âone less thanÊ to compare two numbers
within 10 e.g. Start from number 10 and say. Â9 is one less than 10Ê, 8 is one
less than 9, etc.
(d) Teacher distributes Worksheet 1 (refer to Appendix).
Activity 2: Subtracting Sums by Finding the Difference
Learning Outcomes:
(a) Use Âless thanÊ and Âmore thanÊ to compare two numbers; and
(b) Find the difference of two numbers.
Materials:
Table (worksheet);
Balls;
PowerPoint slides; and
Plain paper.
Procedure:
(a) Start with a story problem (PowerPoint slides).
1st Slide:
Salleh has 5 balls, while Salmah has 3 balls. Who has more balls?
What is the difference?

62
2nd Slide:
Show the following illustration, see Figure 3.9 (a).
Figure 3.9 (a): Finding the difference
Teacher asks: „Who has more balls?‰
„How many are there?‰
„Which one is more, 3 or 5?‰
„Which one is less, 3 or 5?‰
(At this stage, the teacher just wants to introduce the concept of Âone-to-one
matchingÊ and it is not necessary for pupils to answer the questions yet if
they are unable to do so).
(b) Teacher asks them to show how they arrived at the answer using the
materials given.
(i) Step 1:
Distribute some counters and a piece of plain paper to each group.
(ii) Step 2:
Guide them to work out the Âone-to-one matchingÊ correspondence
using the materials given as shown in Figure 3.9 (b).

63
Figure 3.9 (b): One-to-one matching correspondence
(iii) Step 3:
„How many balls have no match?‰
Teacher now introduces the concept of difference and relates this to
the words, more and less.
e.g. 5 is more than 3.
3 is less than 5.
The difference between 5 and 3 is 2.
(iv) Step 4:
Teacher guides pupils to compare two numbers by using the words
more and less before finding the difference using Table 3.1 given.
e.g. Compare the numbers 4 and 6.
Which is more?
Which is less?
What is the difference?
Teacher then asks pupils to write the numbers in the correct space in
the table before finding the difference.
For example, write 6 in the ÂmoreÊ column, 4 in the ÂlessÊ column and
2 as the difference in the space provided (see Table 3.1).

64
Table 3.1: Sample of a Table that can be Used for
Recording the Difference between Two Numbers
(v) Step 5:
Teacher gets pupils to do the same for the other numbers in Table 3.1
above and asks them to record the answers in the table given.
(c) Group activity:
Give a set of number cards numbering 1 to 10 to each group. Ask them to
play the game as follows:
(i) Step 1: Teacher gives the instructions on how to play the game.
(ii) Step 2: Teacher says: „Listen, choose two numbers with a difference
of 1. Whoever gets the correct answer first is the winner. Check your
answers together.‰
(iii) Step 3: Repeat the game using other numbers with differences of 2, 3,
etc.

65
(iv) Step 4: Teacher asks them to find out all possible pairs of numbers in
their groups using the number cards and record the results in Table
3.2.
Table 3.2: Subtraction Pairs
Difference List Down All Possible Pairs
1 e.g.
10 - 9
2 10 - 8 9 - 7
3 10 - 7 9 - 6
4
5
6
7
8
9
10
(v) Step 5: Check all the answers together.
(d) Closure: (You may teach subtraction involving zero in the next lesson!).
Teacher: „What is the answer of 5 0? 4 4? 7 0?‰
ACTIVITY 3.4
Suggest two suitable teaching and learning activities for this statement:
„Subtracting zero from a number does not change the value of the number‰.
Activity 3: Subtracting by Taking Away
Learning Outcomes:
(a) Subtract by taking away; and
(b) Use subtraction to solve word problems.

66
Materials:
Counting boards;
Counters; and
Plasticine.
Procedure:
(i) Initially, use fingers to practise taking away as a method for working out
the subtraction process, see Figure 3.10. e.g.:
Figure 3.10: Subtracting with fingers
(ii) Teacher shows a story problem on a question card.
Aida has 8 apples. She gives 3 of them to Sharifah.
How many apples are left?
Get two pupils to come in front and act out the story. They will act as Aida
and Sharifah, respectively. The others are asked to solve the problem by
observing the action shown.
(iii) Teacher shows the subtraction process using a counting board and some
counters, see Figure 3.11.

67
Figure 3.11: Subtraction using a counting board and counters
(iv) Teacher shows another story problem with a different context.
There are 6 players on the field. 2 of them take a rest.
How many players are left on the field?
Ask pupils to act out the story using a counting board and some plasticine
or encourage them to role play in the class, see Figure 3.12.
Figure 3.12: Sample subtraction of 4 from 9
(v) Teacher asks them to solve the story problem in groups.
„Write the subtraction equations on the card given. Present your answers
in front of the class‰.
(vi) Do a quick mental-recall of the activity in the class. This will help pupils to
work fast and accurately.
e.g. 8 take away 4?
10 take away 5? Take away 4? Take away 6?
What take away 5 leaves 3? Leaves 2? Leaves 5?
(vii) Distribute Worksheet 2 (refer to Appendix).
Can you think of another suitable activity like the above?

68
Activity 4: Predicting the Missing Part
Learning Outcomes:
(a) Predict the missing part in a subtraction problem; and
(b) Relate the subtraction problem to the addition process.
Materials:
Connecting cubes;
Number lines;
Beads; and
Cups.
Procedure:
(a) Teacher puts several connecting cubes (or counters) on a number line.
e.g. 8 connecting cubes.
(b) Teacher then keeps any 3 of the cubes behind her/him, while the pupils
predict how many cubes are hidden.
(c) Teacher guides the pupils to get the answer as follows:
(i) How many connecting cubes are there at first? (8)
(ii) How many connecting cubes are there left now? (5)
(iii) How many connecting cubes are hidden?
Let pupils brainstorm to get some suggestions from them.

69
(d) Teacher shows a way to solve the problem as shown below:
(i) „We have 5 cubes left. How many more cubes do we need to make 8
cubes?‰
(ii) Teacher adds 3 red cubes one by one on the number line and asks
pupils to count on in-ones from 5 to 8. „Start at 5, then 6, 7 and 8‰.
(iii) „We have added 3 red cubes which represents the number of cubes
hidden‰. „We thus write the subtraction equation as 8 3 = 5‰.
(iv) „We can also write down the addition equation as 5 + ? = 8, to find
the number of cubes hidden‰.
(e) Ask them to work out the game in groups. You are encouraged to let them
work out another game, e.g. Âbeads and cupÊ.
(i) First, count the number of beads given to pupils.
(ii) Put some of the beads into the cup. Take out 3 beads and ask pupils
to predict the number of beads (hidden) under the cup.
(f) Let pupils do other examples to reinforce the skill learnt.
ACTIVITY 3.5
Create another game as an enrichment activity for the subtraction process.

70
You need to pay attention when teaching the meanings of subtraction
because conceptual understanding of this operation will help students learn
the topic more efficiently.
The concrete materials used can help pupils master the subtraction algorithms
better.
The samples of teaching and learning activities for subtraction provided in
this topic are to motivate you to collect a set of good teaching-learning
activities for subtraction.
The more activities you know of, the more creative and innovative you will
be when planning your mathematics lessons.
Counting back
Difference
Fact family
Subtraction
Subtraction fact
Taking away
1. Define the term ÂfactÊ.
2. Subtraction can be defined as Âtake awayÊ. Explain this meaning of
subtraction with the help of a suitable teaching and learning activity using
concrete materials.
3. Addition is the reverse of the subtraction process. Explain addition as the
reverse of the Âtake awayÊ process with the help of a suitable teaching and
learning activity using concrete materials.

71
Explain the statements below with the help of a suitable teaching and learning
activity using concrete materials:
(a) ÂThe differenceÊ.
(b) The order of the numbers in a subtraction problem is important.
(c) You can subtract only one number at a time, but you can add more than
one number at one go.
APPENDICES
WORKSHEET 1
Answer all questions.
1. Write the number which is one less than the one given in the space
provided.
2. Colour the number which is less.
3.

72
4. Fill in the blanks starting with the biggest number for each row of numbers.
WORKSHEET 2
1. 6 take away 4 leaves
8 take away 4 leaves
2. Complete the subtraction sentences below:
3. Circle the objects which have to be taken away. Write down the subtraction
sentences.

73
4. 4 3 = ________ 7 1 = ________
6 3 = ________ 9 7 = ________
10 3 = _______ 10 2 = _______
5. Colour two pairs of numbers that give the same answer.
6. Circle the correct answers.
(a)
(g)
(b)
(h)
(c)
(i)
(d)
(i)
(e)
(k)
(f)
(l)

Topic
4
Numbers to
100 and Place
Value
LEARNING OUTCOMES
1. Explain how to say, count, read and write numbers to 100;
2. Demonstrate how to count in tens and ones;
3. Describe how to arrange numbers to 100 count on and count back;
and
4. Explain the concept of place value of numbers to 100.
INTRODUCTION
You need to recall what was discussed in Topic 1 in order to understand this
topic better. After mastering numbers 1 to 10, children should now learn how to
say numbers up to 100 progressively. For example, you have to teach them to
understand, count and write numbers from 10 to 20 before getting them to count
in tens and ones until 100. To ensure that your pupils know how to say numbers
to 100 either in words or in symbols correctly, it is essential to stress on the
correct pronunciation of the names of numbers up to 100. The next step is to teach
pupils to read and write numbers to 100 in words as well as in symbols neatly
and correctly. Then, let pupils arrange numbers to 100 in sequence either by
counting on (in ascending order), or counting back (in descending order), using
various methods. Last but not least, teach pupils to recognise place value, first
discussed in Topic 2. The place-value concept of tens and ones is introduced for
counting numbers up to 100, especially when larger numbers are involved. Pupils
can do regrouping with numbers from 10 onwards e.g. ten ones is the same as
one tens and zero ones; eleven ones can be regrouped as one tens and one ones,
and so on and so forth. In conclusion, the most important thing to remember
when teaching kindergarten and elementary Mathematics is to make the teaching

TOPIC 4 NUMBERS TO 100 AND PLACE VALUE
75
and learning process as interesting and as fun as possible. The samples given in
the following section will help you to teach Mathematics more effectively and
meaningfully to the young ones.
SAY AND COUNT NUMBERS TO 100
4.1
This section will further discuss how to say and count numbers to 100.
4.1.1 Say Numbers to 100
In general, parents or guardians normally feel so proud or are thrilled when they
hear their children say numbers written in words or symbols flawlessly for the
first time. With this in mind, it is thus the responsibility of parents or guardians
and teachers especially, to guide them to pronounce the names of numbers up to
100 correctly.
There are a lot of ways to encourage pupils to practise saying the numbers. One
effective way is by using picture-number cards that have numbers in words
and/or symbols on them, or number charts. For example, you can easily use
number charts in the form of 10 X 10 grids made from manila cards (or other
suitable material) like the one in Table 4.1:
Table 4.1: Number Chart (Numbers 1 to 100)
1 2 3 4 5 6 7 8 9 10
11 12 13 14 15 16 17 18 19 20
21 22 23 24 25 26 27 28 29 30
31 32 33 34 35 36 37 38 39 40
41 42 43 44 45 46 47 48 49 50
51 52 53 54 55 56 57 58 59 60
61 62 63 64 65 66 67 68 69 70
71 72 73 74 75 76 77 78 79 80
81 82 83 84 85 86 87 88 89 90
91 92 93 94 95 96 97 98 99 100
Using the 10 X 10 grid shown above, cover some numbers and let the pupils say
the numbers occupying the covered spots. Alternatively, you may also jumble up
the sequence of the numbers by putting the numbers at the wrong places and

76
then ask the pupils to rearrange them in order before getting them to say the
numbers.
Some sample teaching-learning activities to reinforce the skill of counting
numbers up to 100 are discussed here.
Activity 1: Say the Number Names
Learning Outcome:
By the end of this activity, the pupils should be able to:
(a) Pronounce the names of numbers up to 100 correctly.
Materials:
10 pieces of manila cards (size 15 cm by 20cm) per group;
Colour pencils; and
Books or magazines with page numbers.
Procedure:
In general, there are five steps, which are:
(i) Divide pupils into two groups. Ask them to make five picture number
cards with numbers written in symbols by drawing some pictures/objects
for different numerals (numbers up to 100) allocated to each group and
another five drawings for cards with numbers written in words. Ask them
to give the finished products to you to be checked for accuracy before
giving them back the respective cards.
(ii) Once they are ready, you can start the activity of „Saying number names‰.
Tell them to make sure that all the drawings can only be revealed one by
one by their own group members. The first group (Group 1) will show one
of their picture numeral cards, for example, the card with the numeral „99‰
written on it. The other group (Group 2) will have to say the number
Âninety-nineÊ out loudly and clearly. Award two points if the second group
can say it correctly.
(iii) Next, the second group takes turns to show a picture number card with the
number written in words e.g. Âsixty-fourÊ and ask the other group to say the
number on the card loudly and clearly. Award two points to Group 1 if
they can say the number name correctly. Continue doing this until all the
drawings have been shown.

77
(iv) Another way to let your pupils practise saying numbers to 100 is by
showing them the page numbers from various kinds of books or
magazines. Just randomly flip through one page at a time and then ask the
pupils to say what number is on the next page. This activity can be carried
out in pairs or groups.
(v) Finally, distribute Worksheet 1 to your pupils to reinforce the skill of saying
numbers to 100.
4.1.2 Count Numbers to 100
It is natural for pupils to use their fingers when they first start counting and if
that is not enough, some will even continue to count using their toes which can
be rather awkward. However, when counting larger numbers such as numbers
more than 20, other more suitable manipulatives (e.g. counters) are required.
The fun way to teach pupils to count is by using counting objects such as beads,
beans, nuts, marbles, etc. Fill up a jar with beads, beans, nuts or marbles and pour
them out onto a mat or table cloth. Then, ask the pupils to count them in different
ways other than in ones. For example, get the pupils to group the beads into
groups of ÂfivesÊ or ÂtensÊ. Counting in tens means adding ten to the previous
number in the sequence each time, for instance, 10, 20, 30, 40, 50, 60, 70, 80, 90 and
100.
Finally, help the pupils make some conclusions. When counting on in tens, the
numbers create a pattern. All the numbers end with zero and the first digits are
the same as when you count from 1 to 9, that is, (1, 2, 3, 4, 5, etc.).
Once the pupils have discovered the patterns in the number system, the task of
writing numerals of two digits and beyond is simplified enormously. They will
encounter the same sequence of numerals, 0 to 9 over and over again. However,
at this stage, many pupils do not know yet that numbers are constructed by
organising quantities into groups of tens and ones, and that the digits in
numerals change value depending on their positions in a number, thereby giving
rise to the concept of place value in our number system.
Activity 2: Count Numbers to 100
Learning Outcome:
(a) Count numbers to 100.

78
Materials:
Picture cards of bicycles, aeroplanes, flowers, motorcycles, etc.;
Manila cards with pictures;
Colour pencils; and
Objects (Beads or beans or nuts or marbles, etc.).
Procedure:
In general, there are three steps, which are:
(i) Show pupils the pictures of bicycles, aeroplanes, flowers, motorcycles, etc.
Ask them to count the number of objects on the cards.
(ii) Ask them to colour the pictures on the manila cards and then count how
many objects there are on each card.
(iii) Distribute Worksheet 2 to the pupils.
READ AND WRITE NUMBERS TO 100
This section will guide you through some relevant activities on reading and
writing numbers to 100. It is useful to revise the correct techniques of writing 0 to
9 taught in Topic 1 earlier.
4.2.1 Read and Write Numbers to 100
First of all, you need to revise or teach the pupils the correct way of writing the
numbers as shown in Figure 4.1.
Figure 4.1: Correct way for writing numbers
4.2

79
Write down the numbers randomly on a piece of manila card or on a sheet of
paper. Ask the pupils to read the numerals. Next, do the reverse, that is, get them
to write down the numbers, in words, randomly on the manila card or on the
sheet of paper. Then, ask the pupils to read the numbers in word form.
Activity 3: Read and Write Numbers to 100
Learning Outcome:
(a) Read and write numbers to 100 correctly.
Materials:
Manila card or a sheet of paper; and
Pencils.
Procedure:
(i) Ask the pupils to fill in the empty boxes in Table 4.2:
Table 4.2: Drawing and Writing numbers
Read Draw and Write the Numerals Write the Numbers in Words
20
55 Fifty-five
67
77 Seventy-seven
18
29
98 Ninety-eight
(ii) Distribute Worksheet 3 to your pupils.

80
ARRANGE NUMBERS TO 100 IN ORDER
(ASCENDING OR DESCENDING ORDER)
4.3
This section will focus on „arranging the numbers to 100‰ in ascending or
descending order.
4.3.1 Arrange Numbers to 100 in Order
In general, there are two ways in arranging numbers to 100 in order, which are:
(a) Arrange Numbers to 100 in Ascending Order (Count On)
ÂCount onÊ order means arranging the numbers in ascending order. You can
start at any number as long as the sequence of the numbers is in order. The
same thing goes with the gap or the difference in value between the
numbers. You can have any value for the difference as long as it is the same
throughout the whole number sequence.
(b) Arrange Numbers to 100 in Descending Order (Count Back)
ÂCount backÊ order means arranging the numbers in descending order. You
can again start at any number as long as the sequence of the numbers is in
order. The same thing goes with the gap or the difference in value between
the numbers. You can have any value for the differences as long as it is the
same throughout the whole number sequence.
Activity 4: Count On and Count Back in Ones using a Number Ladder or
Number Chart Up to 100 (Snakes and Ladders Game)
Learning Outcome:
(a) Count on and count back in ones to 100.
Materials:
Dice;
Markers; and
Number ladder game (Snakes and Ladders Game).

81
Procedure:
In general, there are five steps, which are:
(i) Several pupils can participate in this game at the same time. Each of them
will be given a marker. Players take turns to roll the dice.
(ii) After taking turns to throw the dice, the players have to move their markers
according to the number rolled. For example, if the first player rolls a 5, he
will have to move his marker along five squares until it reaches the fifth
square. If it happens that at the fifth square there is a ladder pointing to
square number 23, then the player will have to climb up the ladder to end
on the square number 23.
(iii) On the other hand, if the marker lands on a square with a snake slithering
down, the player will have to follow suit and slide down the snake to
wherever it should be. e.g. If the marker reaches, say, square number 46
showing a snake slithering down to square number 14, the player must
follow the snake and place his/her marker on square number 14.
(iv) The winner is the first player to reach the number 100.
(v) Distribute Worksheet 4 to your pupils.
PLACE VALUE OF NUMBERS TO 100
4.4
When objects are placed in order, we use ordinal numbers to tell their position.
Ordinal numbers are similar to the numbers that you have learned before. The
pupils need to understand the ordinality of numbers to enable them to position
items in a set. If 10 pupils ran a race, we would say that the pupil who ran the
fastest was in first place, the next pupil was in second place, and so on until the
last runner. Here, we are actually arranging the winners in order. In short, the
first 10 ordinal numbers are listed as: first, second, third, fourth, fifth, sixth,
seventh, eighth, ninth and tenth.
4.4.1 Place Value of Numbers to 100
Place value is used within number systems to allow a digit to carry a different
value based on its position, that is, the place it occupies has a value. The concept
of place value is very important when applied to basic mathematical operations.
The skill of regrouping numbers in tens and ones is very important to help
develop the concept of place value at the early stage for numbers to 100.

82
In our present number system, place value works in the same way for all whole
numbers no matter how big the number is. Numbers, such as Â84Ê, have two
digits. Each digit is at a different place value. For instance, the left digit, Â8Ê is at
the tens place. It tells you that there are 8 tens in this number. The last digit on the
right is in the ones place, that is, 4 ones in this example. Therefore, there are 8
tens plus 4 ones in the number 84, as illustrated below:
Activity 5: Ordinal Numbers and Place Value of Tens and Ones
Learning Outcomes:
(a) Label pupils in a row from left to right using ordinal numbers such as, first,
second, third, etc; and
(b) Identify the place value of tens and ones for two-digit numbers up to 100.
Materials:
Word cards (Ordinal numbers: first, second, ... tenth);
Ten pupils;
Number cards (two-digit numbers up to 100); and
Place value chart/mat.
Procedure:
The four steps in this procedure are:
(i) Ask 10 pupils to line up from left to right in front of the class. Then ask
another pupil to determine which pupil is in third position from the left
side? Label the pupilÊs position using the correct ordinal card. Do the same
with other positions, e.g. the sixth from pupilsÊ left, etc.
(ii) Repeat the activity by asking pupils to label various positions of the pupils
from the right side using the appropriate ordinal number cards.

83
(iii) Show pupils how to identify the place value for each digit in a two-digit
number. Ask pupils to fill in the place value for numbers up to 100 given in
the place-value chart or place value mat below:
Place Value
Number
Tens Ones
98 9 8
29 2 9
64 ? ?
75
13
60
(iv) Distribute Worksheet 5.
Familiarise yourself with numerals and numbers in words by saying them
loud and clear.
Know how to read and write numbers in words and in symbols
spontaneously.
Know how to arrange the numbers to 100 in ascending or descending order.
The skill of regrouping by tens and ones is an important process to understand
the concept of counting and place value.
Ascending
Count back
Count on
Descending
Ordinal Numbers

84
What other concrete objects can you use as base-10 materials in teaching the
concept of place value? How would you use the materials to show ones, tens and
hundreds?
Consider the following scenario:
LetÊs say one of your pupils knows how to count using concrete materials and
can clearly count out loud e.g.„one, two and three, etc.‰. When you ask her:
„How many objects are there?‰, she immediately starts to count them all over
again.
Discuss based on the above scenario.
What do you know about her understanding of counting? What do you think is
the next step in her learning? How might you enable her to achieve this?
APPENDICES
WORKSHEET 1
1. (a) Say the numbers given on the door of each house.
44 34 66 70 98
22 10 33 50 79

85
(b) Say the numbers written on the manila cards.
Fifty-eight Ninety-six
Sixty-one
Eighty-two
One
hundred
Twenty-seven
WORKSHEET 2
1. Count the heart-shaped beads. Write the numerals in the boxes provided.
(a)
(b)

86
(c)
(d)
2. Fill in the boxes with the correct numbers.
(a)
(b)

87
(c)
(d)
(e)
(f)

88
WORKSHEET 3
1. Write the missing numerals or words.
(a) thirty-four =
(k) =
(b) sixty-nine =
(l) =
(c) thirteen =
(m) =
(d) forty =
(n) =
(e) ninetythree =
(o) =
(f) thirtyeight =
(p) =
(g) forty-four =
(q) =
(h) thirty-seven =
(r) =
(i) thirty =
(s) =
(j) sixteen =
(t) =
99
87
77
70
61
35
11
79
80
36

89
WORKSHEET 4
1. Fill in the missing numbers in the boxes/spaces below. (Count on/count
back).
Number Patterns
(a) (i)
(ii)
(b) (i) 21, 31, 41, __, __, 71, __, __
(ii) 80, 70, 60, 50, __, __, 20, __
(c) (i)
(ii)
(iii)
(iv)
(d) Now try to write your own number patterns.
(i) __, __, __, __, __, __, __, __, __, __,
(ii) __, __, __, __, __, __, __, __, __, __
(e) (i) Between 51, _____, 53
(ii) Just after 1, 2, _____
(iii) Just before _____, 5, 6

90
(iv) Just before and after _____, 74, _____
(v) In the middle of 98, _____, 96
(f) Order each group of numbers from smallest to largest.
(i) 37, 11, 90 _____, _____, _____
(ii) 26, 12, 82 _____, _____, _____
(iii) 83, 59, 95 _____, _____, _____
(iv) 97, 0, 15 _____, _____, _____
(g) Order each group of numbers from largest to smallest.
(i) 74, 42, 47 _____, _____, _____
(ii) 39, 74, 91 _____, _____, _____
(iii) 28, 82, 49 _____, _____, _____
(iv) 27, 1, 80 _____, _____, _____
WORKSHEET 5
(a) What is the position of the yellow car from the right?
(b) What is the position of the yellow car from the left?
(c) What is the position of the red car from the right?
(d) What is the position of the red car from the left?
(e) Which car is in the first position from the left?
(f) Which car is in the last position from the left?
(g) Which cars are in the first three positions from the right?
(h) Which cars are in the last two positions from the right?
(i) Which car is in the middle?
(j) What is the position of the purple car from the left?

91
(k) What is the position of the purple car from the right?
(l) Which car is in the fifth position from the right?
(m) Which car is in the second position from the right?

Topic
5
Addition
within 18
LEARNING OUTCOMES
1. Describe how to add one more, two more and beyond to a number
for addition within 18;
2. Explain how to add numbers by combining two groups of objects for
addition within 18;
3. Explain how to add numbers by counting on for addition within 18;
and
4. Demonstrate how to write number bonds for addition within 18.
INTRODUCTION
Previously, in Topic 2, addition within 10 was introduced whereby pupils
learned the concept of Âone moreÊ either by counting all or counting on. Number
bonds up to 10 were also highlighted. Here, the discussion is further extended to
include addition within 18 and covers number bonds up to 18. A sound
knowledge of number bonds, or basic facts of addition, is a must to enable pupils
to apply them when adding bigger numbers to go beyond totals of 18. The
process of addition is usually taught with the help of suitable teaching aids and
concrete manipulatives such as counters, number lines, picture cards, etc. As in
other chapters, some samples of teaching and learning activities for addition
within 18 are provided to show how pupils can be helped to acquire this basic
concept effectively.

TOPIC 5 ADDITION WITHIN 18
93
ADDING ‘ONE MORE’ TO A NUMBER
In this section, we will discuss further the concept of adding 'one more' to a number.
5.1.1 The Concept of ‘One More’
In order to approach the concept of addition as Âone moreÊ than a number, a
variety of methods can be used. For instance, if you want the pupils to learn what
is one more than 16, you can try the ones suggested below.
(a) Use suitable counters such as beads, beans, nuts or marbles, etc. to add one
more to a number. Ask pupils to first count how many beads are in a jar
and then ask them how many beads will there be if one more bead is
added. For example, if there are 16 beads in the jar initially, how many
beads will there be if one more bead is added?
Encourage them to first say ÂOne more than 16 is 17Ê or Â17 is one more than
16Ê and then show them how to write the mathematical sentence for the
addition operation as in Figure 5.1:
Figure 5.1: Adding one more to a number using counters
(b) Next, you can also use a number line. Addition on a number line
corresponds to moving to the right along the markings on a number line.
The number line below is marked with ticks at equal distance intervals of 1
unit. To add one more to 16, first move 16 units from 0 and then move 1
more unit to finally end up at 17. The sum of 16 + 1 which is equal to 17 is
shown in Figure 5.2. The addition operation that corresponds to the
situation acted out on the number line is represented as 16 + 1 = 17.
Figure 5.2: Adding one more to a number using a number line
5.1

TOPIC 5 ADDITION WITHIN 18
94
(c) Another way is to use number cards, see Figure 5.3. For example, first show
the number card 16 to the pupils.
Then, ask the pupils what number card is supposed to come out next if you
add one more to the number 16.
Get them to write the mathematical sentence for this operation, that is, 16
add one equals 17.
Figure 5.3: Adding one more to a number using number card
(d) The concept of addition can be modelled using other concrete and
manipulative materials. Addition can be done by counting on or by counting
all as shown in Figure 5.4.
(i) Finding one more than a number.
e.g. 1 more than 10 is ___. (Ask pupils to get the answer by counting
on).
(ii) Finding the total by counting all the objects.
e.g. ____ is 1 more than 13. (Ask pupils to get the answer by counting
all the objects).
Figure 5.4: Adding one more to a number using concrete materials
Activity 1: Adding One More to a Number
Learning Outcomes:
(a) Add one more to numbers up to 18; and
(b) Write the mathematical sentence for addition within 18.

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