Topic 2 Addition within 10 and Place Value.pdf

8/10/2019 Topic 2 Addition within 10 and Place Value.pdf

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INTRODUCTION

Adding is a quick and efficient way of counting. Sometimes, we notice thatadding and counting are alike, but adding is faster than counting. You will alsosee that addition is more powerful than mere counting. It has its own specialvocabulary or words, and is easy to learn because only a few simple rules areused in the addition of whole numbers. When teaching addition to young pupils,it is important that you recognise the meaningful learning processes which can beacquired through real life experiences. The activities in this topic are designed as

an introduction to addition. It provides the kind of practice that most youngchildren need. What do children need to know in addition? Children do not gainunderstanding of addition just by working with symbols such as + and =.You have to present the concept of addition through real-world experiences

because symbols will only be meaningful when they are associated with theseexperiences. Young children must be able to see the connection between theprocess of addition and the world they live in. They need to learn that certainsymbols and words such as add, sum, total and equal are used as toolsin everyday life.

TTooppiicc

22 Addition

within 10 andPlace Value

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

1. Identify the major mathematical skills related to addition within 10and place value;

2. Determine the pedagogical content knowledge related to additionwithin 10 and place value; and

3. Plan teaching and learning activities for addition within 10 andintroduction to the place value concept.

LEARNING OUTCOMES


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TOPIC 2 ADDITION WITHIN 10 AND PLACE VALUE 27

This topic is divided into two main sections. The first section deals withpedagogical skills pertaining to addition within 10 and includes an introductionto the concept of place-value. The second section provides some samples of

teaching and learning activities for addition within 10. You will find that byreading the input in this topic, you will be able to teach addition to young pupilsmore effectively and meaningfully.

PEDAGOGICAL SKILLS OF ADDITIONWITHIN 10

In this section, we will discuss further the pedagogical skills of addition within10. This section will look into the concept of more than, teaching and learning

addition through addition stories, acting out stories to go with equations, numberbonds up to 10, reading and writing addition equations and finally reinforcementactivities.

2.1.1 The Concept of More Than

It is important for pupils to understand and use the vocabulary of comparing andarranging numbers or quantities before learning about addition. We can start bycomparing two numbers. For example, a teacher gives four oranges (or any otherconcrete object) each to two pupils. The teacher then gives another orange to oneof 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 more than, and one moreas well as addonemorefor additionby referring to the example above. The pupils are guidedto say the following sentences to reinforce their understanding of addition withrespect to the above concept.

e.g.: Five oranges are more thanfour oranges. Five is more thanfour.

Four and one moreis five.Four add one moreis five.

Teacher repeats with other numbers using different picture cards or counters andpupils practise using the sentence structures given above.

2.1


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TOPIC 2 ADDITION WITHIN 10 AND PLACE VALUE28

2.1.2 Teaching and Learning Addition ThroughAddition Stories

Initially, addition can be introduced through story problems that children can actout. Early story situations should be simple and straightforward. Here is anexample of a simple story problem for teaching addition with two addends:

At this stage, children have to make connections between the real world and theprocess of addition by interpreting the addition stories. Children must read andwrite the equations that describe the process they are working with. The conceptof addition should be introduced using real things or concrete objects. At thesame time, they have to read and write the equations using common words, suchas and, make, as well as equals 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 thestories. Based on the situations given, pupils can act out the stories in differentways as follows:

(a) Act out stories using real things as counters such as marbles, ice-creamsticks, 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 learningaddition.

Salmah has threeballs. Her mother bought two more balls for her. How manyballs does Salmah have altogether?


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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

plus and equal signs:

Figure 2.3:Flowchart for Acting out stories to go with equations


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After pupils are able to write equations according to teacher-directed stories, theycan begin writing equations independently using suitable materials (refer toFigure 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 goldfishyesterday. How many fish do I have altogether? See Figure 2.4.

2 clown fish nd 3 gold fish m ke 5 fish altogether.

2 + 3 = 5

Figure 2.4: Story problem

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 writesthe story problem and then begins a discussion with pupils on how to use thenumber line to answer the question as in the example shown in Figure 2.6:

Use the above example to show that 2 + 3 = 3 + 2 = 5.

ACTIVITY 2.1


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Four pupils and three pupils are seven pupilsFour 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 immersed in theactivities 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 avariety of addition strategies. The objective of these activities is to recognise theaddition 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 towerof four cubes and a tower of six cubes, (refer Figure 2.7) or any pairs of numbersadding 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 beforegetting them to produce all the possible pairs that add up to 10. Record eachaddition pair in a table as shown in Table 2.1:


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Table 2.1: Sample Table for Addition Activity: Addition Pairs Up to 10

Height of Tower Before

Breaking into Two Towers

Cubes)

After Breaking into Two Towers

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 bondsrepeatedly to facilitate instant and spontaneous recall in order to master the basicfacts of addition up to 10.

To develop the skill, the teacher should first break the tower of 10 cubes into twoparts. Show one part of the tower and hide the other. Then, ask pupils to state theheight of the hidden tower. To extend the skill, you may progressively ask thepupils to learn how to add other pairs of numbers, such as 9, 8, 7 and so on.

2.1.5 Reading and Writing Addition Equations

There are two common methods of writing the addition of numbers, eitherhorizontally or vertically, as shown below:

What is the commutative law in addition? How do you introduce thisconcept to your pupils? Explain clearly the strategy used for the teaching

and learning of the commutative law in addition.

ACTIVITY 2.2


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(a) Adding horizontally, in row form (i.e. Writing and counting numbers fromleft to right).

Example: 4+ 5 = 9

The activities discussed above are mostly based on this method, which aresuitable for adding two single numbers.

(b) Adding vertically, in column form (i.e. Writing and counting numbers fromtop to bottom).

Example: 3+ 4

7

This method is suitable for finding a sum of two or more large numbersbecause putting large numbers in columns makes the process of addingeasier compared to putting them in a row.

2.1.6 Reinforcement Activities

To be an effective mathematics teacher, you are encouraged to plan small groupor individual activities as reinforcement activities for addition within 10. Here aresome examples of learning activities that you can do with your pupils.

(a) Number ShapesHave 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 remainingspaces with counters of different colours. Finally, they describe the numbercombinations formed, as illustrated in Figure 2.8. Repeat with differentnumber shapes.

Numbers are most easily added by placing them in columns. Describehow you can create suitable teaching aids to enhance the addition of twoaddends using this method.

ACTIVITY 2.3


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Figure 2.8: Number shapes

(b) Number Trains

Let pupils fill their number-train outlines (e.g. 7, 8 or 9) with connectingcubes of two different colours. Ask them to describe the numbercombinations formed. See Figure 2.9.

Figure 2.9: Number train

In addition, pupils can also describe the number combination formed as three

plus threeplus twoequals eight, that is (3+ 3 + 2 = 8).

PLACE VALUE

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 sameactivities as for learning numbers up to 10 covered in Topic 1. Similar teachingaids and methods can be used. The only difference is that we should now havemore counters, say, at least 20. In this section, we will not be focusing on countingnumbers from 11 to 20 because it would just be repeating the process of countingnumbers from 1 to 10. You are, however, encouraged to have some references onthe strategies of teaching and learning numbers from 11 to 20.

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2.2.2 Teaching and Learning about Place Value

The concept of place value is not easily understood by pupils. Although they canread and write numbers up to 20 or beyond, it does not mean that they knowabout 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. Oncepupils have discovered the patterns in the number system, the task of writingtwo-digit numbers and beyond is simplified enormously. They will encounter thesame sequence of numerals, 0 to 9 over and over again. However, many pupilsdo not understand that numbers are constructed by organising quantities intogroups of tens and ones, and the numerals change in value depending on theirposition in a number.

In this section, you will be introduced to the concept of place value by formingand counting groups, recognising patterns in the number system and organisinggroups 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 countmanipulative 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 10placed 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) toyour 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 ina column or vertically as shown below. Here, you are encouraged to use theenquiry method to help pupils familiarise themselves with the place-value of tensand ones illustrated as follows:

Describe a strategy you would use for the teaching and learning ofcounting from 11 to 20.

ACTIVITY 2.4


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Example:Teacher asks: What number is 10 and one more? See Figure 2.11 (Pupils shouldrespond 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 boardsor 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 ofdifferent 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


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The repetition of the pattern for numbers 12 to 19 and 20 will make your pupilsunderstand 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 theaddition process. For example, 1 tens and 2 ones make 12, which means 10 andtwo more make 12.

SAMPLES OF TEACHING AND LEARNINGACTIVITIES

This section provides some samples of teaching and learning activities you cancarry out with your pupils to enhance their knowledge of addition within 10 andthe place-value concept.

Activity 1: Adding Using Patterns

Learning Outcomes:By the end of this activity, 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.

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In groups of four, create some reinforcement activities for teachingnumbers 11 to 20 using the place-value method. Describe clearly how youwill conduct the activities using suitable hands-on teaching aids.

ACTIVITY 2.5


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Procedure:

(a) Adding Using Patterns in Rows)

(i) Teacher divides the class into 5 groups of 6 pupils, and gives 10oranges to each group. Teacher then asks each group to count theoranges, see Figure 2.13.

Teacher says: Can you arrange the oranges so that you can countmore 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 offives 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 eggsare 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 alongone row first to get 4, and then add with another row of 4 to make 8eggs altogether?

Well done, if you have done so!

Let your pupils add using different patterns of different numbers of objectswith the help of PowerPoint slides. Guide your pupils to read and writeequations of addition of numbers in words, symbols and signs. (You maydiscuss how to write the story-board of your PowerPoint presentation.)


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(b) Adding Using Patterns in Columns)

(i) Teacher says: Let us look at the pictures and try to recognise thepatterns (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 dividedinto two parts, namely, the top and bottom parts as shown in Figure2.16:

Figure 2.16: Picture card: Addition using patterns (in columns)

(iii) This is a way of showing how to teach addition using columns by theinquiry-discovery method. As a conclusion, the teacher explains tothe pupils that arranging the objects in patterns will make it easier toadd them. Using columns to add also makes the addition of largenumbers easier and faster.

(c) Teacher distributes a worksheet on addition using patterns (in rows or incolumns).


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Activity 2: Addition within the Highest Total of 10

Learning Outcomes:

By the end of this activity, 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 ofworking out the addition of two groups of objects. See Figure 2.17.E.g.:

Figure 2.17: Finger addition


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(b) Addition of Two Groups of Objects

(i) Teacher puts three green apples on the right side of the tree andanother four red apples on the left side. Teacher asks pupils to countthe number of green apples and red apples respectively.

(ii) Teacher asks: How many green apples are there? How many redapples 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 asshown: Three apples and four apples make seven apples.

(v) Repeat with different numbers of apples or objects. Introduce theconcept 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 pupilsto 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 anumber sentence. Ask them to stick the correct number cards belowthe picture cards to form an addition equation as above. Repeat thisstep using different numbers.

(c) Problem Solving in Addition

(i) Teacher shows three balls in the box and asks pupils to put in somemore balls to make it 10 balls altogether.


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(ii) Teacher asks: How many balls do you need to make up 10? How didyou get the answer?

Let them discuss in groups using some counters. Ask them to explainhow 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.

(v) Teacher asks them to discuss the answer in groups. Encourage themto work with models or counters and let them come up with their ownideas 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.

Sarah has to read six story books this semester. If she has finished

reading four books, how many more story books has she got toread?


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Procedure:

(i) Teacher guides pupils to complete the addition table given. (Print out thetable in A4 size paper and laminate it). You can also use the table to explainthe 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 answerfrom the table.

(ii) Colour the numbers 10 in green (Table 2.2). List out all the pairs adding upto 10.

(iii) Colour the numbers totalling 9 in red. List out all pairs adding up to 9.(iv) Continue with other pairs of numbers using different colours for different

sums.


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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. Teacherdistributes some connecting cubes (say, at least 40 cubes) to eachgroup.

(ii) Teacher asks the following questions and pupils are required toanswer 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


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16 is one morethan 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 countbeginning 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 thenintroduces 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 representnumber 11 on the place-value block?

Teacher introduces the concept of tens and ones as follows. SeeFigure 2.20 (b):


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Figure 2.20 b): Representing numbers with place-value block and counters

(iii) Teacher asks pupils to put the correct number of counters into thecorrect column to represent the numbers 11, 12, etc until 20.

(iv) Teacher asks pupils to complete Table 2.3.

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 valuelearnt.

A teacher should know his or her pupils levels of proficiency when applyingstrategies to solve problems related to addition.

Problem solving related to addition depends on pupils ability to work basedon their counting skills.


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At an early stage, it is enough if they could work using counting all orcounting on.

However, you have to guide and encourage them to work by looking at therelationship or answer by mastering the number combinations or numberbonds.

Adding

Addition

Equation

Place value

Sum

Plus

1. An effective way to teach addition is to ask pupils to act out the stories inreal 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 zerousing real materials.

3. Counting numbers from 11 to 20 should be taught after pupils areintroduced to the concept of place value. Give your comments on this.

Based on the following learning outcome, By the end of the lesson, pupilsshould 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 processto achieve this learning outcome.


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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.


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(d) Match the following.

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

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Topic 2 Addition within 10 and Place Value.pdf