Nota Hbmt1203.docx

Nota HBMT1203 1. 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 prenumber 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 2. TOPIC 1 NUMBERS 0 TO 10 2 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 3. TOPIC 1 NUMBERS 0 TO 10 3 (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. 4. TOPIC 1 NUMBERS 0 TO 10 4 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) 5. TOPIC 1 NUMBERS 0 TO 10 5 (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 6. TOPIC 1 NUMBERS 0 TO 10 6 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 7. TOPIC 1 NUMBERS 0 TO 10 7 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. 8. TOPIC 1 NUMBERS 0 TO 10 8 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. 9. TOPIC 1 NUMBERS 0 TO 10 9 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 10. TOPIC 1 NUMBERS 0 TO 10 10 (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. 11. TOPIC 1 NUMBERS 0 TO 10 11 Activity 2: Finding the Relationship between Two Sets of Objects Learning Outcomes: By the end of this activity, your pupils should be able to: (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). 12. TOPIC 1 NUMBERS 0 TO 10 12 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. 13. TOPIC 1 NUMBERS 0 TO 10 13 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 14. TOPIC 1 NUMBERS 0 TO 10 14 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?‰ 15. TOPIC 1 NUMBERS 0 TO 10 15 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: By the end of this activity, pupils should be able to: (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. 16. TOPIC 1 NUMBERS 0 TO 10 16 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.‰ 17. TOPIC 1 NUMBERS 0 TO 10 17 (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: By the end of this activity, pupils should be able to: (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. 18. TOPIC 1 NUMBERS 0 TO 10 18 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: By the end of this activity, pupils should be able to: (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. 19. TOPIC 1 NUMBERS 0 TO 10 19 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.: 20. TOPIC 1 NUMBERS 0 TO 10 20 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. 21. TOPIC 1 NUMBERS 0 TO 10 21 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 22. TOPIC 1 NUMBERS 0 TO 10 22 (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. 23. TOPIC 1 NUMBERS 0 TO 10 23 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. 24. TOPIC 1 NUMBERS 0 TO 10 24 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 25. TOPIC 1 NUMBERS 0 TO 10 25 WORKSHEET How many seeds are there in each apple? Count and write the numbers. 26. Topic 2 Addition within 10 and Place Value LEARNING OUTCOMES By the end of this topic, you should be able to: 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. 27. TOPIC 2 ADDITION WITHIN 10 AND PLACE VALUE 27 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. 28. TOPIC 2 ADDITION WITHIN 10 AND PLACE VALUE 28 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. TOPIC 2 ADDITION WITHIN 10 AND PLACE VALUE 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. TOPIC 2 ADDITION WITHIN 10 AND PLACE VALUE 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. TOPIC 2 ADDITION WITHIN 10 AND PLACE VALUE 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. TOPIC 2 ADDITION WITHIN 10 AND PLACE VALUE 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. TOPIC 2 ADDITION WITHIN 10 AND PLACE VALUE 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. TOPIC 2 ADDITION WITHIN 10 AND PLACE VALUE 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. TOPIC 2 ADDITION WITHIN 10 AND PLACE VALUE 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, icecream 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. TOPIC 2 ADDITION WITHIN 10 AND PLACE VALUE 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 softboard 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. TOPIC 2 ADDITION WITHIN 10 AND PLACE VALUE 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 placevalue method. Describe clearly how you will conduct the activities using suitable Âhands-onÊ teaching aids. SAMPLES OF TEACHING AND LEARNING 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 placevalue 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. TOPIC 2 ADDITION WITHIN 10 AND PLACE VALUE 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. TOPIC 2 ADDITION WITHIN 10 AND PLACE VALUE 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. TOPIC 2 ADDITION WITHIN 10 AND PLACE VALUE 40 Activity 2: Addition within the Highest Total of 10 Learning Outcomes: By the end of this activity, your pupils should be able to: (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. TOPIC 2 ADDITION WITHIN 10 AND PLACE VALUE 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. TOPIC 2 ADDITION WITHIN 10 AND PLACE VALUE 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: By the end of this activity, your pupils should be able to: (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. TOPIC 2 ADDITION WITHIN 10 AND PLACE VALUE 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. TOPIC 2 ADDITION WITHIN 10 AND PLACE VALUE 44 Activity 4: Place Value and Ordering Learning Outcomes: By the end of this activity, pupils should be able to: (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. TOPIC 2 ADDITION WITHIN 10 AND PLACE VALUE 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. TOPIC 2 ADDITION WITHIN 10 AND PLACE VALUE 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. TOPIC 2 ADDITION WITHIN 10 AND PLACE VALUE 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. TOPIC 2 ADDITION WITHIN 10 AND PLACE VALUE 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. TOPIC 2 ADDITION WITHIN 10 AND PLACE VALUE 49 (d) Match the following. (e) Match the following (Read and add).