Early Number 1-10

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TOPIC 1 NUMBERS UP TO 10

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Nor Hawan b. Misiran

INTRODUCTION

Beginning number concepts are much more complex than we realized. Just because children can say the words “one”, “two”, “three” and so on doesn’t mean they can count the numbers. We want children to think about what they are counting. Children can count numbers if they understand the word ‘how many’. As a teacher, we do not teach numerals in isolation with the quantity they present, because numeral symbols give’s have meaning for children only when they are introduced as labels of quantities.

In order to start teaching numbers, 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 numeration system, and the basic number concept such as meanings of numbers and numeral or digit. You will also learn about the stages of conceptual development for whole numbers such as pre numbers and early numbers. At this stage, children will learn to recognize and write numerals as they develop with beginning number concepts.

In the second part of this topic, you will learn more on strategies of teaching and learning numbers through some samples of teaching and learning activities given. You are also encouraged to have discussion with your tutor and classmates. Some suggested activities for discussion are also given.

OBJECTIVES

By the end of this topic, you should be able to:

1. recognize the major mathematical skills of whole numbers up to 10;

2. recognize the pedagogical content knowledge of pre numbers, early numbers and place value of numbers up to 10;

3. plan teaching and learning activities of pre numbers and early numbers up to 10; and

4. determine and master the strategies effectiveness of teaching and learning numbers in the way to perform an ‘active learning’ in classroom.

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TOPIC OVERVIEW

1.1 PEDAGOGICAL CONTENT KNOWLEDGE OF WHOLE NUMBERS

In this topic, we will focus on the major mathematical skills of pre-numbers and whole numbers as follow:

determine the concept of pre numbers recognize and name whole numbers up to 10

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count, read and write whole numbers up to 10 determine the base 10 place value for each digit up to 10 compare the values of whole numbers up to 10 arrange whole numbers in ascending and descending order up to 10

1.1.1 Pre Numbers

Pre numbers are about the development of number concepts for children in kindergarten and Year 1. Developing number concepts implies the development of number sense – the ability to deal meaningfully with whole number ideas as oppose to memorizing (Andria T. 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 about, discuss idea, ask and answer questions, draw pictures, write and build strategies. They begin to form and organize cognitive understanding. In short, children will learn the prerequisite skills needed as follows:

developing classification abilities (by their physical attributes) comparing the quantity of two sets of objects using one to one matching determining the quantitative relations such as many as, more than and less than

1.1.2 Early Numbers

Just to know your prior knowledge!

What is the difference between a number and a numeral, and a digit?

Jot down your answer here.

Mathematics began from 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. It depends on their numeration systems. A numeration system consists of a set of symbols and the rules for combining these symbols.

Early numerations system appear grown 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, ‘numbers’ are represented by ‘tally’ as shown below:

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e.g.:

1 2 3 4 5 6 7 8 9

Ancient Agypt

Babylon

. . . ... . .....Mayan . . . . . . . . . .

About 5000 years ago, people in places of ancient civilization began to use symbols to represent numbers for counting numbers. They had created their own number systems. In history, there are various types of numeration system found. For example, the Egyptian numeration system used picture symbols called hieroglyphics. This is a base 10 system which each symbol represents a power of ten. The Roman numeration, Greece numeration and Hindu-Arabic numeration are some of the famous system in history.

e.g. 1 2 3 4 5 6 7 8 9

Roman 200 B.C. I II III IV V VI VII VIII 1X

Greece 500 B.C. ƒ z

Hindu-Arabic 976 A.D. l 7 8 9

Along with the development of numbers, mathematics was further developed by the mathematicians. The numeration system used today is mostly 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 number, a numeral and a digit. The term of “numbers” and “numeral” are different. A number is an abstract idea that addresses the question, “how many”, means related to quantity. While numeral is a symbol used to represent a number. Thus, numerals are names for numbers.

Check back your answer in Section 1.1.2.

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1.2 SAMPLES OF TEACHING AND LEARNING ACTIVITIES

1.2.1 Teaching Pre Numbers

There are many pre number concepts that children must acquire to develop number sense. These are as followed:

compare and sort things in terms of properties (e.g. colour, shape, size, etc.) compare two sets and find whether one set has as many as, more than, or less than

the other set. learn the concepts of one more and one fewer

Activity 1: Classifying Things by Their Properties

Learning Outcomes

By the end of this activity, you will be able to:

classify things by their general property classify things by their specific property

Materials

sets of toy sets of pattern block (various shape, colour) plastic containers or boxes

Procedures

1. Classify Objects by Their General Property

Teacher asks children to work in group of five and distributes 4 types of toys (car, train, boat, and aeroplane) to each group.

Teacher: “Let’s work together, look at the toys”. “Which is the toys can fly? Which one can sail in the sea? Which vehicle is very long? Which is the smallest vehicle? Children respond.

In this activity, children should be asked why they chose an object and not the others Teacher should listen.

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2. Classify Objects by Their Specific Properties

Teacher distributes a set of pattern blocks with different shape and colour to each group.

Note: Circle : 2 blue, 1 orange Triangle : yellow, 1 green Rectangle : 1 yellow, 2 red Diamond : 1 brown, 2 purple

Teacher: “Firstly, classify these objects by their shape”. “Put the object into the box given according to their shape”. (round shape, long shape, have three sides, look as a kite).

A B C D

(round shape) (three sides) (long shape) (look as a kite)

Teacher : “Can you make another classification on your objects in Box A?”

Teacher guides the children to classify the objects in Box A by colours. Repeat this activity on Box B, Box C and Box D.

At this stage, children will recognize that shape is the first property to consider, followed by the colour as the second property. Children should be encouraged to find as many property as they can in classifying objects.

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You have to discuss this reinforcement activities:

(i) Making coloured tower city using unfix cubes

(ii) Duplicating a pattern such as robot, house, and building using unfix cubes

(iii) Extending pattern: Children are presented with a row of objects and asked to find the ones that come next.

?

(iv) Classifying objects by their texture (smooth, rough, fuzzy), by their size (big, small, short, long), etc.

Activity 2: Finding the Relation between Two Sets of Objects

Learning Outcomes

By the end of this activity, you will be able to

match items in one to one matching basis understand the concept of as many as, more than and less than compare the number of object among two sets

Materials

picture card A, picture card B, erasers, pencils, picture cards.

Procedures

1. One to One Matching

Children are presented with two sets consist of the same number of objects. Teacher demonstrates how to introduced ‘as many as’ relation using one to one matching as followed:

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Card A Card B

4 4

One to one matching

Teacher: “Are there as many moons as stars? Why?”

2. As Many As, More, and Less

Teacher takes out a star from Card B. “Are there as many moons as star? Why not? How can you tell?

4 3

?

Teacher guides the children to build the concept of ‘more’ and ‘less’.

e.g. Which card has more moons? Which card has less stars?

3. More Than, Less Than

The children are presented with two sets of object with different numbers, Card C and Card D. Teacher guides the children to compare the number of object among the two sets, and introduce the concept of more than and less than.

Teacher: “Can you match each marble in Card A one to one with a marble in Card B?” Why?

Teacher: “Children, we can say that Card A has more marbles than Card B, or, Card B has less marbles than Card A”.

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4. Group Activity

Teacher: “Sit together with your friends in a group”. “Everybody, show all your erasers and pencils you have to your friends”. “Can you compare and tell something to your friends using the words, more than or less than?”

Pupils should respond: ”I have more erasers than you but, I have less pencil than you”, “You have more erasers than me”, etc.

Teacher distributes a worksheet.

Activity 1.1

You have to produce

(i) a power point presentation as a reinforcement activity (ii) a sample of worksheet of the lesson

1.2.2 Teaching Early Numbers

Activity 3: Naming Numbers Name and Recognize Numerals 1 to 10

Learning Outcomes

By the end of this activity, pupils will be able to

naming numbers 1 to 5 recognize numerals 1 to 5

Materials

picture cards 0 to 5, number cards 0 to 5, power point slides.

Procedures

1. Claps and Count

Teacher claps and counts 1 to 5. Teacher and pupils clap and count a series of claps together. ‘Clap’, say “one”. ‘Clap’, ’Clap’, say “one”, “two”.

Do the same way until number 5. Repeat.

Teacher asks pupils to clap two times and count, four times etc. Pupils respond.

2. Slide Show

Teacher displays a series of power point slides one by one. The numerals come out after the objects.

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Teacher: “How many balls are there in this slide? Let us count together”.

Teacher points to the ball and count one by one in order. Then point to the numeral and say the number name. Pupils respond (eg. “There are a ball”, “There are two balls”, etc.). Repeat with different numbers and different objects/pictures.

3. Class Activity

Teacher shows a picture card and stick on the white board.

e.g.:

2 picture card number card

Teacher: “Look at the picture”. “How many clock are there?”

Pupils respond. Then teacher ask a pupil to choose the correct numeral card and stick on the picture.

Teacher repeats until the fifth card. At the end, teacher asks pupils to arrange the pictures in order (1 to 5). Ask them to count.

4. Group Activity

Pupils sit in group of five. Teacher distributes five picture cards of objects and five corresponding numeral cards (1 to 5).

Teacher: “Choose a pupil in your group”. “Put up number five on the left hand, and the correct picture card on the right hand”. “Help him/her to get the correct answer”. Asks the group to choose another pupil. Repeat all the numbers 1 to 5.

1 2

3 4 5

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Teacher distributes a worksheet.

Teacher: “Let’s sing a song about busy people together” (see Appendix 1).

Discuss with you classmate. (i) The concept of ‘zero’ or ‘nothing’ can be introduced by the

teacher in this lesson. Explain.

(ii) The strategy above can be used in teaching numbers, 6 to 10 and teaching number words, 1 to 10. Explain.

(iii) Jigsaw game. E.g.:

Activity 4: Read and Write Numbers, 1 to 10

Learning Outcomes

By the end of this lesson, pupils will be able to

read and write numbers from 1 to 10

Materials

Picture cards, cut out number cards

Procedures

1. Numbers 1 to 5

Teacher shows picture cards with numbers, 1 to 5 in sequence. Pupils count the picture, point the number and say the numbers name.

e.g.

1Teacher sticks the picture card on the writing board. Repeat this activity until the fifth card.

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2.. Technique of Writing Numbers

Teacher demonstrates in sequence the technique of writing numerals, 1 to 5. Firstly, teacher writes number ‘1’ on the writing board step by step as below:

e.g.:

1

Teacher writes number in the air followed by the pupils. Repeat until number 5.

1 1 1 1 3 3

22 2 2

Repeat until pupils able to write numbers in the correct way.

3. Teacher Distributes Some Plastecine

Teacher: “Let us build the numerals with plastecine, number 1 to 5”. “Arrange your numbers in sequence”.

4. Cut-out Number Card

Teacher gives pupils the cut-out number cards, 1 to 5. Then, ask them to trace the shape of each number on a piece of paper.

e.g.

cut-out number card

Teacher distributes worksheet 1 (see Appendix 2).

Note: This strategy can also be used in teaching number writing, 6 to 10.

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Can you write these numbers in the correct way?

Teacher are encouraged to use various technique in teaching numbers writing:

e.g.: (i) Write numbers at the back of pupil friends (ii) Write numbers on sand (iii) Write numbers using the fingers with water colour (iv) Write numbers following the dotted lines

Discuss in group.

Activity 5: The Concept of Zero

Learning Outcomes


understand the concept of ‘zero’ or ‘nothing’ determine, name and write number zero

Materials

picture cards, 3 boxes and 5 balls (each group)

Procedures

1. Teacher Shows Three Picture Cards

Cage A Cage B Cage C

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Teacher: “How many rabbits are there in Cage B?, Cage C?, Cage A?”.

Pupils respond: “There are a rabbit in Cage B, two rabbits in Cage C, and no rabbit in Cage A”. Teacher introduces the number ‘0’ to represents ‘no rabbit’ or ‘nothing’.

2. Teacher Distributes Some Balls into 3 Boxes

Box A Box B Box C

Teacher: "How many balls are there in Box A, Box C, and Box B respectively?”

Teacher guides pupils to determine the concept of ‘zero’ or ‘nothing’ according to the number of balls in Box B. Teacher reads and writes number ‘0” (zero) , followed by pupils.

Exercise 1.1

Plan a worksheet as a reinforcement activity for this lesson.

Activity 6: Count on and Count Back in Ones, 1 To 10

Learning Outcomes


count on in ones from 1 to 10 count back in ones from 10 to 1

Materials

number cards, picture cards, slides (power point)

Procedures

1. Flash Card

Teacher flashes picture cards in order, 1 to 10. Pupils count the objects in the picture and say the numbers. Teacher sticks the cards on the whiteboard in sequence.

e.g.

Count “one”, say “one aeroplane”.

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Count “one”, “two”, say “two aeroplanes”.

Count “one”, “two”, “three”, say “three aeroplanes”.

Continue until the 10 th picture card.

Pupils are asked to count on in ones from 1 to 10. Repeat.

2. Slide Show

Pupils are presented a series of slide show (power point presentation):

Say “one”

1 Stage 1

Teacher asks pupils to count and say the number name, “one”. Teacher clicks a button to show the second stage and asks pupils to count and say the number,

Stage 2 Say “two”

1 2 Stage 2

Continue until the 10 th stage. Repeat until the pupils are able to count on in ones from 1 to 10.

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Teacher presents another slide show: 10

Count on in ones 7

6

Count back in ones 4

4. Teacher Distributes a Worksheet

“Let's sing ‘Numbers Up And Down’ song together”. (see Appendix 1).

Activity 1.2

Do these activities in class as a microteaching exercise.

1. Arranging pupils in sequence

Teacher selects two groups of 10 pupils. Give them a set of number cards, 1 to 10 to each group. Teacher asks them to stand in front of the class in group. Teacher asks both groups to arrange themselves in order. Any group able to finish the first is the winner. The loser group is asked to count on and count back the numbers in ones. Repeat the game.

1 2 3 4 5 6 7 8 9 10

8

3

2

5

9

1

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2. Jump on the number blocks

Teacher asks pupils to sing ’Numbers Up and Down’ song while jumping on the number blocks around the pond. Counting on or counting back again and again!

Counting on Counting back

Start/Finish Start/Finish

3. Up and down stairs

Pupils are asked to count on in ones while go up stairs, and count back in ones while go down stairs.

SUMMARY

As a mathematics teacher, you have to generate as many as idea as possible about teaching and learning whole numbers. There is no one best way to teach whole numbers. As we know, the goals for children working in this chapter is to go beyond simply counting one to ten and recognizing numerals. The emphasis here is developing number sense, number relationships and developing facility with counting. The samples of teaching and learning activities in this chapter will help you to understand the basic number work from kindergarten and year 1. They need the ongoing experiences of these activities in order to develop consistency and accuracy with counting skills.

GLOSSARY

Ascending Order – Counting upwards in order.

Descending Order – Counting downwords in order.

Early Numbers – Stage that children concentrate on learning numbers 1 to 10 and zero.

Number – An abstract idea that addresses the question “how many”. means related to quantity.

2

1

3

4 5

6

7

8

9

10

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Number Sense – The ability to deal meaningfully with whole number ideas as oppose to memorizing.

Numeral – A symbol used to represent a number, names for numbers, digit.

One to One Matching – A one to one matching between two sets that is also an onto matching.

Pre Numbers – Stage that children learn the prerequisite skills to learn numbers.

Whole Numbers – A set of numbers denoted by W, consists of 0, 1.2,3, ......or W = {0, 1, 2, 3, ......}, a number which has no fraction attached.

http://teslj.org/Techniques/Klancar-Numbers.html

www.magicalchidhood.com/articles/numbers.html

www.yesican.gov/publications/teaching/numbers.html

TEST 1

1. Describe the chronological development of numbers from ancient civilization until now. Present your answer in a mind map.

2. Teaching number concepts using concrete materials can help pupils learn more effective. Explain.

TEST 2

1. Pupils might have difficulties to learn 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 number words in order, 1 to 9.

Suggest the best strategy that can be use in teaching and learning process according to the above learning outcomes.

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APPENDIX 1

Busy People One busy people sweeping the floor Two busy people closing the door

Three busy people washing baby’s shocks Four busy people are lifting the rocks Five busy people washing the bowls

Six busy people stirring ‘dodol’ 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 Songs4Teachers

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APPENDIX 2

Worksheet 1

How many seeds? Count and write the numbers.

Documents

Early Number 1-10