Module Year 2

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PREFACE

This Module is produced to enable teachers to have a better understanding of the

requirements and teaching strategies for the Abacus and Mental Arithmetic Course for

Year Two and to ensure an effective teaching and learning process.

1. Contents

The Abacus and Mental Arithmetic Course for Year Two includes the following:

(1) Addition and subtraction of numbers up to 100;

(2) Addition and subtraction of numbers up to 1 000;

(3) Multiplication within basic facts;(4) Division within times-tables;

(5) Revision.

2. Teaching Objectives

The objectives for the teaching and learning of Abacus and Mental Arithmetic for Year

Two are as follows:

(1) To understand the concept of multiplication and division;

(2) To know and understand the relationship between multiplication and division;

(3) To memorize multiplication facts within 1 to 5 times-tables;

(4) To get the quotient from division using multiplication within basic facts;

(5) To master the formation of static bead image of numbers up to 1 000;

(6) To accurately and promptly perform addition and subtraction of numbers

involving up to four 2-digit numbers in Listen Abacus Calculation, Rea Abacus

Calculation, Listen Mental Calculation and Read Mental Calculation;

(7) To accurately and promptly perform addition and subtraction of numbers

involving up to three 3-digit numbers in Listen Abacus Calculation, Read

Abacus Calculation and two 3-digit numbers in Listen Mental Calculation

and Read Mental Calculation.

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3. Analysis of Course Material

The course contents for Year Two requires a firm foundation in Abacus and Mental

Arithmetic skills covered in Year 1. One of the objectives of this course is to enable the

students to understand multiplication and division within times-tables.

This is very important as it is the foundation of multi-digit multiplication and division.

The ability of students to master multiplication and division within times-tables will affect

their speed and accuracy in multi-digit multiplication and division.

Multiplication and division within times-tables are basic skills the students must learn.

The abacus is a good instrument to strengthen these basic skills. Adding the samenumber repeatedly on the abacus helps the students to understand the meaning of

multiplication. In the same way, by subtracting the same number repeatedly from a

given number helps to introduce the concept of division. The teacher can further help

students to understand the concept of division by demonstrating the various modals,

using hands-on aids. A lot of practice is necessary to enable students to master the

tables and give the answers spontaneously.

This course also enables the students to add and subtract up to four 2-digit numbers

and three 3-digit numbers up to 1 000 quickly and accurately. Just as in Year One,

students perform addition and subtraction on the abacus as well as mentally. It is

important to master addition and subtraction as this will affect the students ability to

multiply and divide. Thus, this course puts a lot of emphasis on addition and

subtraction.

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CONTENTS AND TEACHING SUGGESTIONS

UNIT 1

Addition and Subtraction of Numbers Up To 100

1.1 Objectives

1. To be able to recognize, read and move the beads promptly and accurately for

numbers from 21 to 100;

2. To be able to visualize the beads for any number up to 50 in the mind;

3. To master the bead movement of pool-five addition with carrying and break-fivesubtraction with removing;

4. To master the basic operations of addition and subtraction in Abacus Calculation;

5. To be able to perform addition and subtraction of up to five 1-digit numbers in

Listen Mental Calculation and Read Mental Calculation, and up to three 2-digit

numbers in Listen Mental Calculation.

1.2 Explanation on Teaching Material

This unit consists of the following contents:

Part I: Recognizing the bead images of numbers up to 100.

Part II: Addition and subtraction of numbers up to 50.

(i) Addition without carrying of numbers up to 50.

(ii) Subtraction without removing of numbers up to 50.

(iii) Addition with carrying of numbers up to 50.

(iv) Subtraction with removing of numbers up to 50.

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Part III: Addition and subtraction of numbers up to 100.





Part I: Recognizing the bead images of Numbers Up To 100.

There are two examples:

[Example 1] Count on in tens. How many is 5 times of ten?


Recognizing the bead images of numbers from 21 to 100 is the same as recognizing

the bead images of numbers within 20. As in numbers up to 20, teachers need to

explain the place values of Ones, Tens and Hundreds. The teaching material will

enable the students to build up their understanding of numbers from concrete to

abstract. Exercises such as Let us practice and Let us think are included at the end

of each part so as to strengthen the skills of the students.

Part II: Addition And Subtraction Of Numbers Up To 50.


There are 3 examples:

[Example 3] Abacus Calculation. 3 + 36 = 39

[Example 4] Abacus Calculation. 23 + 13 = 36

[Example 5] Listen Mental Calculation. 13 + 32 = 45



[Example 6] Abacus Calculation. 37 25 = 12

[Example 7] Mental Calculation. 47 23 = 24

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[Example 8] Abacus Calculation. 38 26 + 13 = 25

[Example 9] Mental Calculation. 17 + 21 26 = 12

Points To Note:

Teachers need to emphasize that in abacus calculation of addition and

subtraction, all numbers are calculated from left to right (from the higher place

value).

Students need to master the basic skills in addition with carrying and subtraction

with removing before proceeding to calculation involving multi-digit numbers.



[Example 10] Abacus Calculation: 14 + 27 = 41

[Example 11] Move up 49, move up 1

[Example 12] Abacus Calculation: 17 + 15 + 18 = 50

[Example 13] Listen Mental Calculation: 17 + 29 = 46



[Example 14] Abacus Calculation. 32 17 = 15

[Example 15] Move up 50, move down 1.

[Example 16] Abacus Calculation. 50 3 18 = 29

[Example 17] Listen Mental Calculation. 42 16 = 26



Point To Note:

(iii) and (iv) involve pool-five addition and break-five subtraction besides addition

with carrying and subtraction with removing.

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Part III: Addition And Subtraction Of Numbers Up To 100.



[Example 20] Abacus Calculation. 21 + 12 + 50 = 83

[Example 21] Mental Calculation. 46 + 20 + 12 = 78




[Example 23] Mental Calculation. 75 34 + 26 = 67

Point To Note:

Teachers need to guide the students and ensure that by now the students are

able to form a clear bead image in the mind.



[Example 24] Move up 26, move up 27.

[Example 25] Abacus Calculation. 15 + 36 + 28 = 79

[Example 26] Mental Calculation. 18 + 24 + 19 = 61





[Example 29] Mental Calculation. 92 14 29 = 49



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Point To Note:

(iii) and (iv) form the basics for more operations of addition and subtraction as

well as for exercises in multiplication and division.

1.3 Teaching Suggestions

1.3.1 Recognizing the bead images of Numbers Up To 100


ExplanationReview the representation of numbers from 11 to 20 and the place values of Ones and

Tens. The students can then try the preparatory exercise on Page 1 of the textbook:

Count on in ones. What is 10 ones? Subsequently, discuss Example 1 on Page 1 of

the textbook with the students: Count on in tens. How many is 5 times of 10? Use

pictures of objects and the abacus to explain.

The students practice with numbers up to 50 using activities such as:

Listen to the numbers and move the beads;

Look at the numbers and move the beads;

Look at the beads and read the numbers;

Look at the beads and write the numbers.

Ensure that the students master the above skills.

Point To Note:

The number on Tens is equivalent to the value in Tens. Example: 5 on Tens

means 50.

The following instructions may be given to guide the students.

(1) Count the squares in tens.

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(2) Move the beads on the abacus: move up 10, move up 10 again, move up 10

again, (until a total of 50).


Explanation

Revise the place values of Ones and Tens and the representation of numbers up to 50.

By now the students should have no problems in recognizing numbers up to 50. Use a

hundred grid board for explaining [Example 2]. Explain with the help of strips of tens.

Each strip contains 10 squares. Each strip shows 10 Ones is equivalent to ten. Each

strip also shows that 1 Tens is equivalent to 10. Arrange the strips to show 10, then 20,

then 30, and so on until we come to the tenth strip. Explain to the students that the tenstrips total up to 100. This means that 10 Tens is equivalent to 100.

Subsequently, by referring to the diagram on Page 2 of the text book and by moving the

beads on the abacus, show the place values of Ones, Tens and Hundreds. Explain that

10 Ones means 10 (or 1 at Tens), and 10 Tens means 100 (or 1 at Hundreds).

Emphasis in this example is moving up 1, when there is already 9 on a rod. Remember,

if there is 9 at Ones, one more bead (up 1) will require the students to move down 9 at

Ones and carry 1 at Tens. In the same way, when there are already 9 at Tens, one

more bead at Tens (up 10) will require the student to move down 9 at Tens and carry 1

at Hundreds.

Exercises such as Let us practice, Let us think and Let us try will strengthen the

skills in:


Look at the numbers and move the beads;

Listen to the numbers and visualize the beads;

Look at the number and visualize the beads;

Look at the beads and read the numbers;

Look at the beads and write the numbers.

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Point To Note:

Show 48 on the abacus. Then move up 1 at Ones to show 49. Direct the

students to move up 1 again. This time, the bead movement will be: move down

9 at Ones and carry 1 at Tens. (This involves pool-five addition). This part

strengthens the skill and speed of students in bead movement.

The following instructions and explanation may be given to guide the students:

(1) Count the squares in tens.

(2) Move the beads on the abacus: move up 10, move up 1 again (there is 20 now),move up 10 again, until a total of 100.

(3) The first rod on the right represents the place value Ones; the second rod

Represents Tens and the third rod represents Hundreds. Each lower bead at

Hundreds represents 100.

1.3.2 Addition Without Carrying of Numbers up to 50


Explanation

This example is taught based on the skill learnt in addition of 1-digit numbers. The

focus here is on the addition of numbers with digits in the same place values.

The students can try the preparatory exercises on Page 4 of the text book:

(1) 5 + 7 + 4 =

(2) 9 + 8 + 2 =

Give the question 12 + 4 for the students to try. At the same time, guide them by

asking: On which rod do we move the beads when adding 4? Why? Then give the

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question the other way round: 4 + 12 and ask: How many digits does 12 have? How

many beads are there at Tens and at Ones? Emphasize that calculation is done only

on numbers with digits in the same place value, that is add 2 to 4 at Ones (rod).

The same procedure applies when explaining Example 3 - Abacus Calculation:

3 + 36 = 39.So, regardless of how many Tens is to be added to Ones, or how many

Ones is to be added to Tens, the same procedure applies.

Points To Note:

Arrange the numbers according to the place values and add accordingly.

In abacus calculation, all numbers are calculated from the higher place value to

the lower place value.


(1) 3 + 36. How do we calculate it?

(2) Ready;

(3) First, move up 3.

(4) Plus 36, move up 3 at Tens and move up 6 at Ones.

(5) Equals to 39.


Explanation

The skill in [Example 3] should be mastered first before explaining [Example 4].

Instruct the students to try the following questions before teaching [Example 4]:

(1) 23 + 3 =

(2) 20 + 10 =

(3) 23 + 10 =

Ask the students: When adding 10, what do we do? On which rod do we move up 1?

Why?

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Explain that [Example 4] Abacus Calculation: 23 + 13, follows the same procedure.

Again stress on the need to add numbers with digits in the same place values.



(2) Ready;



(5) Equals to 36.


Explanation

First review the following:

Listen to the numbers and memorize the numbers.

Addition and subtraction involving up to five 1-digit numbers in Listen Mental

Calculation.

As this is the first time addition of 2-digit numbers in mental calculation is taught, the

focus is on memorizing the bead images. Discuss [Example 5] on Page 6 of the

textbook. Instruct the students to move up 13, move up 32, on the visualized abacus.

Thus, by using the same procedure,[ Example 5 ] Listen Mental Calculation: 13 + 32 =

45 is calculated on the visualized abacus.



(2) Ready; put your head down and close your eyes.

(3) Use your fingers to move the visualized beads. First, move up 13.


(5) Equals to 45.

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1.3.3 Subtraction Without Removing Of Numbers Up To 50

[Example 6] Abacus Calculation: 37 25 = 12

Explanation

Apply the same skill taught in subtraction of 1-digit numbers. Stress on the need to

subtract numbers with digits in the same place values.

The students practise the preparatory exercises on Page 8 of the textbook beforeteaching [Example 6].

(1) 13 4 =

(2) 15 9 =

(3) 9 + 9 - 8 =

(4) 8 + 6 3 =

Instruct the students to try 37 5. Ask: When subtracting 5, on which rod do we move

down 5? Why? The students then calculate 30 20. Ask: Which rod is used to move

down the 2 when subtracting 20?

Explain that [Example 6] Abacus Calculation: 37 25 = 12 follows the same

procedure.

Points to Note:

Arrange the numbers according to the place values and subtract accordingly.

In abacus calculation, all numbers are calculated from the higher place value to the

lower place value.


(1) 37 25. How do we calculate it?

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(2) Ready;


(4) Minus 25, move down 2 at Tens and move down 5 at Ones.

(5) Equals to 12.

[Example 7] Mental Calculation: 47 23 = 24

Explanation

First review the following:


Addition and subtraction involving up to five 1-digit numbers in Listen Mental

Calculation and Read Mental Calculation.

Addition of two 2-digit numbers in Listen Mental Calculation.

As this is the first time subtraction of 2-digit numbers in mental calculation is taught, the

focus is on memorizing the bead images. Refer to [Example 7] on Page 9 of the

textbook. Instruct the students to move up 47, move down 23, on the visualized

abacus. Thus, using the same procedure, calculate [Example 7] Mental Calculation:

47 23 = 24 on the visualized abacus.


(1) 47 - 23. How do we calculate it?

(2) Ready, put your head down and close your eyes.



(5) Equals to 24.

[Example 8] Abacus Calculation: 38 26 + 13 = 25

Explanation

This example is to be taught based on the skills learnt in [Example 4] Abacus

Calculation: 23 + 13 and [Example 6] Abacus Calculation: 37 25. It is a combination

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of addition without carrying and subtraction without removing in abacus calculation. The

focus here is addition and subtraction of numbers with digits in the same place values.

First, review addition without carrying of 2-digit numbers and subtraction without

removing of 2-digit numbers in abacus calculation. By referring to [Example 8] on Page

11 of the textbook, instruct the students to calculate 38 26 and then 12 + 13 on the

abacus. After that, instruct them to try [Example 8] Abacus Calculation: 38 26 + 13

= 25. Emphasize the need to add and subtract numbers with digits in the same place

values.


(1) 38 26 + 13. How do we calculate it ?(2) Ready;



(5) Plus 13 move up 1 at Tens and move up 3 at Ones.

(6) Equals to 25.

[Example 9] Mental Calculation: 17 + 21 26 = 12

Explanation

This example is to be taught based on the skills learnt in [Example 5] Listen Mental

Calculation: 13 + 32 and [Example 7] Mental Calculation: 47 23. It is a combination

of addition without carrying and subtraction without removing in Mental Calculation. The

focus here is memorizing the beads representing 2-digit numbers.

First, review the following:


Addition without carrying of 2-digit numbers in Mental Calculation.

Subtraction without removing of 2-digit numbers in mental calculation.

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Then, by referring to[Example 9] on Page 12 of the textbook, instruct the students to try

17 + 21 and 38 26 in Mental Calculation. After that, instruct them to try [Example 9 ]

Mental Calculation : 17 + 21 26 = 12.

Note :

The example can be written in the vertical form:

17

21

26

First, (by covering 26 with a piece of paper) calculate 17 + 21

in Read Mental Calculation :17

21

Then with the bead image of 38, calculate 38 26 in Read

Mental Calculation to get 12.


(1) 17 + 21 26. How do we calculate it ?



(4) Plus 21 move up 2 at Tens and move up 1 at Ones.


(6) Equals to 12.

1.3.4 Addition With Carrying Of Numbers Up To 50


Explanation

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This example is to be taught based on the skill learnt in addition without carrying of 2-

digit numbers in Abacus Calculation. The focus here is addition of numbers with digits

in the same place values and carrying 1 at Tens.

First, instruct the students to practise the preparatory exercise on Page 14 of the

textbook.

(1) 32 + 6 =

(2) 24 + 13 =

(3) 43 + 5 =

(4) 15 + 20 =

After that, instruct the students to try 34 + 7. Ask: When adding 7, on which rod do wemove up 7? What do we do when there are not enough beads at Ones? Refer to

Example 10 on Page 14 of the textbook. Instruct the students to calculate 14 + 27 on

the abacus. Explain that all numbers are calculated from the higher place value to the

lower place value (Tens first, then Ones). Also remind the students to carry 1 at Tens

when there are not enough beads at Ones.


(1) 14 + 27. How do we calculate it ?

(2) Ready;


(4) Plus 27, up 2 at Tens and up 7 at Ones,

but there are not enough beads at Ones;

so down 3 and carry 1.

(5) Equals to 41.


Explanation

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This example involves pool-five addition. The focus here is on the Tens rod. When

there are not enough beads at Ones, we carry 1 at Tens which will require pool-five

addition as there is already 4 at Tens.

First, instruct the students to try the preparatory exercise on Page 15 of the textbook:

(1) Move up 9, move up 1.




Then, by referring to [Example 11] on Page 15 of the textbook: move up 49, move up 1,

ask the students: On which rod do we move up 1? What do we do when there are notenough beads at Ones? Then when we carry 1 at Tens and there is already 4 at Tens,

what do we do? Explain that when we carry 1 at Tens and there is already 4 at Tens,

we need to apply pool-five addition at Tens.

The students then try the following:





Point To Note:

This example forms the basics for addition of multi-digit numbers.


(1) Move up 49, move up 1. How do we do it?

(2) Ready;


(4) Then move up 1, but there are not enough beads at Ones; so down 9 and carry 1.

There are not enough lower beads at Tens; what do we do?

Think! Who is the little friend of 1? (It is 4).

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So, up 5 and down 4.


Explanation

This example is to be taught based on the skill learnt in [Example 11]. The focus here is

on the Tens rod. When there are not enough beads at Ones, we carry 1 at Tens which

will require pool-five addition as there is already 4 at Tens.

First, instruct the students to calculate 17 + 15. Then instruct them to calculate 32 + 18.

Explain that when adding 18, first add the digits at Tens followed by the digits at Ones

(calculate from the higher place value). When there are not enough beads at Ones,

carry 1 at Tens and as there is already 4 at Tens, apply pool-five addition.

After that, the students try[ Example 12] on Page 16 of the textbook.

Point To Note:

At this stage, speed and accuracy will be affected if the students need to think

before moving the beads. Ensure that the students master these skills before

trying [Example 12].


(1) 17 + 15 + 18. How do we calculate it ?

(2) Ready;


(4) Plus 15, up 1 at Tens and up 5 at Ones, but there are not enough beads at

Ones;


(5) Plus 18, up 1 at Tens and up 8 at Ones, but there are not enough beads at

Ones;

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(6) Equals to 50.


Explanation

This example is to be taught based on the skills learnt in addition without carrying of 2-

digit numbers in Mental Calculation and addition with carrying of 2-digit numbers inAbacus Calculation.

First, instruct the students to try the preparatory exercise on Page 18 of the textbook:

(1) 4 + 3 + 6 + 2 7 =

(2) 8 + 7 4 + 6 + 2 =

(3) 5 + 9 + 3 8 + 4 =

(4) 6 + 8 + 2 9 + 5 =

Then, instruct the students to try 37 + 9 in Mental Calculation. Guide them by asking:

When adding 9, what do we do when there are not enough beads at Ones?

At the same time, the students can refer to[Example 13] on Page 18 of the textbook.

Instruct the students to try 17 + 20 and then 17 + 29 in Mental Calculation. Explain that

when adding 29, first add the digits at Tens followed by the digits at Ones (calculate

from the higher place value). When there are not enough beads at Ones, carry 1 at

Tens.

Point To Note:

Ensure that by now the students are good at:

addition of numbers with digits in the same place values; and

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carrying 1 at Tens when there are not enough beads at Ones.





(4) Plus 29, up 2 at Tens and up 9 at Ones, but there are not enough beads at Ones;


(5) Equals to 46.

1.3.5 Subtraction With Removing Of Numbers Up To 50


Explanation

This example is to be taught based on the skill mastered in subtraction without

removing of 2-digit numbers in Abacus Calculation. The focus here is subtraction of

numbers with digits in the same place values and removing 1 at Tens when there are

not enough beads at Ones.

Instruct the students to first try 32 10 and then try 22 7. Guide them by asking:

When subtracting 7, what do we do when there are not enough beads at Ones?

At the same time, the students refer to [Example 14] on Page 20 of the textbook.

Explain that in the example, when subtracting 17, first subtract the digits at Tens and

then subtract the digits at Ones (calculate from the higher place value). Explain also

that when there are not enough beads at Ones, remove 1 at Tens.



(2) Ready;

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(4) Minus 17, down 1 at Tens and down 7 at Ones, but there

are not enough beads at Ones; so remove 1 and up 3.

(5) Equals to 15.


Explanation

This example involves break-five subtraction. The focus here is on the Tens rod. When

there are not enough beads at Ones, remove 1 at Tens which will require break-fivesubtraction as there is no lower bead at Tens.

Instruct the students to try the preparatory exercise on Page 21 of the textbook:

(1) Move up 10, move down 1.




Then, by referring to[ Example 15] on Page 21 of the textbook: move up 50, move down

1, ask the students: On which rod do we move down 1? What do we do when there

are not enough beads at Ones? Then when we remove 1 at Tens and there is only 5 at

Tens, what do we do? Explain that when we remove 1 at Tens and there is only 5 at

Tens, we need to apply break-five subtraction at Tens.

Point To Note:

This example forms the basics for subtraction of multi-digit numbers.


(1) Move up 50, move down 1. How do we move it?

(2) Ready;

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(4) Then move down 1, but there are not enough beads at Ones; what do we

do ?

so remove 1 and up 9.

It is 5 at Tens; what do we do?

Up 4 and down 5.

[Example 16] Abacus Calculation: 50 3 18 = 29

Explanation

This example is to be taught based on the skill learnt in[Example 15]. The focus here ison the Tens rod.

First, instruct the students to calculate 50 3. Ask: When subtracting 3, what do we do

when there are not enough beads at Ones? Then when we remove 1 at Tens and there

is only 5 at Tens, what do we do? After that, instruct the students to calculate 47 18.

Remind the students that when subtracting 18, first subtract the digits at Tens followed

by the digits at Ones (calculate from the higher place value). When there are not

enough beads at Ones, remove 1 at Tens.

The students then refer to [Example 16] on Page 22 of the textbook and calculate on

the abacus.


(1) 50 3 18. How do we calculate it ?

(2) Ready;


(4) Minus 3, down 3, but there are not enough beads at Ones;


(5) Minus 18, down 1 at Tens and down 8 at Ones,


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(6) Equals to 29.

[Example 17] Listen Mental Calculation: 42 16 = 26

Explanation

This example is to be taught based on the skill learnt in subtraction with removing of 2-

digit numbers in Abacus Calculation and subtraction with removing of 2-digit numbers in

Mental Calculation. The focus here is memorizing the bead images of 2-digit numbers

and the process in which the bead images change when there are not enough beads at

Ones.

Before proceeding, review the following:

Subtraction without removing of 2-digit numbers in Mental Calculation.

Subtraction without removing of 2-digit numbers in Abacus Calculation.

Then, instruct the students to try 42 10 and 32 6 in Mental Calculation. Guide them

by asking: When there are not enough beads at Ones in 32 6, what do we do?

By referring to the illustration on Mental Calculation in [Example 17] on Page 24 of the

textbook, the students try to visualize the procedure of the bead movements in 42 16.

This will be more difficult as it is a longer process. Explain that when subtracting 16,

subtract the digits at Tens first followed by the digits at Ones. When there are not

enough beads at Ones, remove 1 at Tens.

Point To Note:

Remind the students to pay attention to the whole process which also includes

pool-five addition.




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(5) Equals to 26.


ExplanationThis example is to be taught based on the skills learnt in subtraction with removing of 2-

digit numbers and addition with carrying of 2-digit numbers in Abacus Calculation. It is

a combination of addition with carrying and subtraction with removing in Abacus

Calculation. The focus here is addition and subtraction of numbers with digits in the

same place values involving carrying 1 at Tens and removing 1 at Tens when there are

not enough beads at Ones.

First of all, the students need to practise addition with carrying and subtraction with

removing of 2-digit numbers in Abacus Calculation. Then instruct them to calculate 48

19 and 29 + 13.

By referring to[ Example 18] on Page 26 of the textbook, instruct the students to

calculate 48 19 + 13.


(1) 48 19 + 13. How do we calculate it ?

(2) Ready;



but there are not enough beads at Ones; so remove 1 and up 1.

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but there are not enough beads at Ones; so down 7 and carry 1.

(6) Equals to 42.


ExplanationThis example is to be taught based on the skill learnt in addition with carrying and

subtraction with removing of 2-digit numbers in Mental Calculation. The focus here is

memorizing the bead images of 2-digit numbers and the process in which the bead

images change when there are not enough beads at Ones.

Before proceeding, the students need to practise addition of two 2-digit numbers and

subtraction of two 2-digit numbers in Mental Calculation. Then, instruct the students to

try 28 + 15 and 43 26 in Mental Calculation. Guide them by asking: What do we do

when there are not enough beads at Ones?

After that, instruct the students to try 28 + 15 26 in Mental Calculation based on

[Example 19] on Page 27 of the textbook.

Point To Note:

By now, the skill in Mental Calculation should be well mastered. Ensure that the

students are able to visualize and memorize the process in which the bead

images change when there are not enough beads at Ones. Teaching here

should focus on developing the Mental Arithmetic skill through Abacus

Calculation and enrichment exercises in Mental Arithmetic.

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(1) 28 + 15 26. How do we calculate it?









(6) Equals to 17.

1.3.6 Addition Without Carrying Of Numbers Up To 100


Explanation

This example is to be taught based on the skill mastered in addition of numbers up to 50

in Abacus Calculation.

First, review addition without carrying of numbers up to 50.

Then guide the students to try [Example 20] on Page 31 of the textbook. This example

will further strengthen the students skill in addition in Abacus Calculation.


(1) 21 + 12 + 50. How do we calculate it?

(2) Ready;


(4) Plus 12, up 1 at Tens and up 2 at Ones.

(5) Plus 50, up 5 at Tens.

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(6) Equals to 83.

[Example 21] Mental Calculation: 46 + 20 + 12 = 78

Explanation

This example is to be taught based on the skill learnt in addition of numbers up to 50 in

Mental Calculation. The focus here is memorizing the bead images of numbers more

than 50.

First, review the following:

Addition of numbers up to 50 in Mental Calculation. Listen to the numbers and visualize the beads.

Look at the numbers and visualize the beads.

Then, instruct the students to try 46 + 20 and 66 + 12. After that, by referring to

[Example 21] on Page 32 of the textbook, guide the students to calculate 46 + 20 + 12 =

78 in Listen Mental Calculation and also in Read Mental Calculation

Point To Note:

Ensure that the students are able to memorize the bead images of 66 and 70.





(4) Plus 20, up 2 at Tens.


(6) Equals to 78.

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1.3.7 Subtraction Without Removing Of Numbers Up To 100


Explanation

This example is to be taught based on the foundation built in subtraction of numbers up

to 50 in Abacus Calculation.

First review the skills learnt in subtraction without removing of numbers up to 50.

Then, by referring to[Example 22] on Page 34 of the textbook, guide the students to try

98 21 14 = 63 in Abacus Calculation.

Point To Note

This example will further strengthen the students skill in subtraction using

Abacus Calculation.


(1) 98 21 14. How do we calculate it?

(2) Ready;


(4) Minus 21, down 2 at Tens and down 1 at Ones.


(6) Equals to 63.

[Example 23] Mental Calculation: 75 34 + 26 = 67

Explanation

This example is to be taught based on the skill learnt in subtraction of numbers up to 50

in Mental Arithmetic. The focus here is memorizing the bead images of numbers up to

50. First, review addition without carrying and subtraction without removing of numbers

up to 50 using Mental Arithmetic.

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Then, guide them to calculate 75 34, and then 41 + 26 on the visualized abacus.

After that, by referring to the illustration for [Example 23] on Page 35 of the textbook,

instruct the students to move up 75, then move down 34 and move up 26 on the

visualized abacus.

Point To Note

Ensure that the students are able to visualize the process in the changes of the

bead images.


(1) 75 34 + 26. How do we calculate it?(2) Ready; put your head down and close your eyes.




(6) Equals to 67.

1.3.8 Addition With Carrying Of Numbers Up To 100


Explanation

This example forms the basics for learning pool-five addition with carrying. Both the

skills (pool-five addition and addition with carrying) are applied in one operation of

addition.

First, review the bead movement in Move up 49, move up 1, which involves both pool-

five addition and addition with carrying.

Then the students try the preparatory exercise given on Page 37 of the textbook:


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After that the students try to move up 26, move up 20; followed by move up 46, move

up 7. Ask: On which rod do we move up 7? What do we do when there are not

enough beads at Ones? Then what do we do when there is already 4 at Tens?

The students then can try [Example 24] on Page 37 of the text book. Emphasize that

when there are not enough beads at Ones, we need to carry 1 at Tens.

The following instructions may be given to guide the students.(1) Move up 26, move up 27. How do we do it?

(2) Ready;


(4) Move up 27; up 2 at Tens and up 7 at Ones,

but there are not enough beads at Ones.

So down 3 and carry 1.


Explanation

This example is to be taught based on the skill learnt in[ Example 24]. The focus here is

carrying 1 at Tens when there are not enough beads at Ones.

Review [Example 24] first before instructing the students to calculate 15 + 36. Discuss

and explain that when adding 36, calculate from the higher place value, which is from

Tens to Ones. Explain also that when there are not enough beads at Ones, we need to

carry 1 at Tens.

The students then try [Example 25] found on Page 38 of the textbook.

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Point To Note:

The section on How do we move the beads? stresses on the process of bead

movement when adding 6 in 15 + 36.



(2) Ready;

(3) First, up 15.



(6) Equals to 79.


Explanation

This example is to be taught based on the skill learnt in addition without carrying of

numbers up to 100 in Mental Arithmetic.


Addition of numbers up to 50 in Mental Arithmetic;

Addition without carrying of numbers up to 100 in Mental Arithmetic.

Then, by referring to the illustration for [Example 26] on Page 39 of the textbook,

instruct students to move up 18, move up 24 and move up 19 on the visualized abacus

in Listen Mental Arithmetic and also Read Mental Arithmetic.

Point To Note:

Remind students on the need to calculate from the higher place values and to

carry 1 at Tens when there are not enough beads at Ones.


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(6) Equals to 61.

1.3.8 Subtraction With Removing Of Numbers Up To 100


ExplanationThis example forms the basics for learning break-five subtraction with removing. Both

the skills (break-five subtraction and subtraction with removing) are applied in one

operation of subtraction.

First, review the bead movements in Move up 50, move down 1, which involves both

break-five subtraction and subtraction with removing. Then the students try the

preparatory exercise on Page 41 of the textbook.





After that, the students try to move up 63, move down 10; followed by move up 53,

move down 8. Ask: On which rod do we move down 8? What do we do when there

are only 3 at Ones?

The students can then try [Example 2] found on Page 41 of the textbook. Move up 63,

move down 18. Explain that, to move down 18, first move down 1 at Tens and then

move down 8 at Ones. Remind students that when there are not enough beads at

Ones, we need to remove 1 at Tens.

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(1) Move up 63, move down 18. How do we do it?

(2) Ready;


(4) Move down 18; down 1 at Tens and down 8 at Ones,


So remove 1 and up 2.


Explanation

This example is to be taught based on the skill learnt in [Example 27].

Before proceeding, review [Example 27]. Then instruct the students to calculate 62

10 and 52 6 on the abacus. Ask: What do we do when there are not enough beads

at Ones in 52 6?

Then the students try [Example 28] on Page 42 of the text book: 62 16 24. First,

calculate 62 16. When subtracting 16, subtract the digits at Tens first, followed by the

digits at Ones. Remove 1 at Tens when there are not enough beads at Ones. As there

is only 5 at Tens, apply break-five subtraction. After that, calculate 46 24.



(2) Ready;


(4) Minus 16, down 1 at Tens and down 6 at Ones;



(5) Minus 24, down 2 at Tens and down 4 at Ones;

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(6) Equals to 22.

[Example 29] Mental Calculation: 92 14 29 = 49

Explanation

This example is to be taught based on the skill learnt in subtraction of numbers up to 50

in Mental Calculation.

Before proceeding, review subtraction of 2-digit numbers in Mental Calculation.

Questions such as 47 28 and 76 21, can be given.

Then students try to calculate 92 14 and 78 29. When subtracting 29, subtract the

digits at Tens first, followed by the digits at Ones. Remove 1 at Tens when there are

not enough beads at Ones. When there is only 5 at Tens, apply break-five subtraction.

After that, it will be easier for the students to calculate [Example 29]: 92 14 29. This

example, with repeated operation in subtraction, will further strengthen the students

ability in Mental Calculation.







(6) Equals to 49.


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Explanation

This example is to be taught based on the skills learnt in pool-five addition with carrying

and break-five subtraction with removing.


Pool-five addition with carrying of 2-digit numbers (such as 26 + 28).

Break-five subtraction with removing of 2-digit numbers (such as 76 27).

By referring to [Example 30] on Page 45 of the textbook, guide the students and explain

that when subtracting 28 in 73 28, subtract the digits at Tens first, followed by the

digits at Ones. Remove 1 at Tens when there are not enough beads at Ones. When

there is only 5 at Tens, apply break-five subtraction. Then explain that when adding 17

in 45 + 17, add the digits at Tens first followed by the digits at Ones. Carry 1 at Tens

when there are not enough beads at Ones.

Point To Note:

This example can further enhance the calculation skills of the students in addition

and subtraction.


(1) 73 28 + 17. How do we calculate it?

(2) Ready;




(6) Equals to 62.


Explanation

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This example is to be taught based on the skills learnt in:

i. Pool-five addition with carrying of 2-digit numbers in Mental Arithmetic;

ii. Break-five subtraction with removing of 2-digit numbers in Mental Calculation.

This is also the last example for Unit 1.


i. Addition of 2-digit numbers in Mental Calculation;

ii. Subtraction of 2-digit numbers in Mental Calculation.

By referring to [Example 31] on Page 47 of the text book, guide the students to

calculate 32 + 59. When adding 59, add the digits at Tens first, followed by the digits at

Ones. Carry 1 at Tens when there are not enough beads at Ones. Similarly, whensubtracting 14, subtract the digits at Tens first, followed by the digits at Ones. Remove

1 at Tens when there are not enough beads at Ones.

Point To Note:

Addition and subtraction of 2-digit numbers will further strengthen the students

ability to calculate and hence form a firm foundation for calculation in addition

and subtraction, as well as multiplication and division of multi-digit numbers.


(1) 32 + 59 14. How do we calculate it?





So down 1 and carry 1.




(6) Equals to 77.

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UNIT 2Addition And Subtraction Of Numbers Up To 1 000

2.1 Objectives

1. To be able to recognize, read, write and move the beads promptly and accurately

For numbers up to 1 000;

2. To be able to visualize the beads for any number up to 1 000 in the mind;

3. To be able to perform addition and subtraction involving up to three 3-digit numbers

using Listen Abacus Calculation and Read Abacus Calculation.

4. To be able to perform addition and subtraction involving up to three 2-digit numbers

using Listen Mental Arithmetic and Read Mental Arithmetic.

2.2 Explanation Of Teaching Material

This unit consists of the following contents:

Part I: Recognizing numbers up to 1 000.

Part II: Addition and subtraction of numbers up to 500.

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(ii) Addition and subtraction of numbers up to 500.


[Example 11] Abacus Calculation: 128 + 89 72 58 = 87

[Example 12] Mental Calculation: 17 + 86 21 + 24 = 106


[Example 14] Abacus Calculation: 363 65 + 23 26 = 295

[Example 15] Mental Calculation: 59 + 83 + 94 38 = 198


[Example 17] Abacus Calculation: 384 56 + 172 8 = 492

[Example 18] Mental Calculation: 487 194 = 293

Point To Note: The above skills need to be mastered as they form the foundation for multi-digit

addition and subtraction; and later, multiplication and division involving multi-digit

numbers.

Part III : Addition and subtraction of numbers up to 1 000.

(i) Addition of numbers up to 1 000.



[Example 20] Abacus Calculation: 364 + 219 + 417 = 1 000

[Example 21] Mental Calculation: 367 + 529 = 896


(ii) Addition and subtraction of numbers up to 1 000.



[Example 24] Abacus Calculation: 129 + 871 5 = 995



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2.3 Teaching Suggestions

2.3.1 Recognizing Numbers Up To 1 000

[Example 1] Count on in hundreds. How many is 5 times of one hundred?

Explanation

Revise the representation of numbers up to 100 and the place values of Ones, Tens

and Hundreds. The students can then try the preparatory question: Count on in tens.

What is 10 tens? Now that the students know that 10 tens is the same as 100, guide

them to move the beads 100 at a time, on the abacus.

The following instructions and questions may be given to guide the students.

i. Move up 100, move up 100 again. How many do we have?

ii. Move up 100 again. How many do we have?

When the students have 400 on the abacus,

i. Move up 100 again. What do we do? How many do we have?

Point To Note:

The number on Hundreds (rod) is equivalent to the value in Hundreds; example:

5 on Hundreds (rod) means 500.

The following instructions may be given to help the students master the above skills:

Move up 100, move down 100.

Move up 200, move down 200; until

Move up 500, move down 500.

Ensure that the students master the above skills.

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[Example 2] Count on in hundreds. How many is 10 times of onehundred?

Explanation

This example is taught based on the method used in Example 1. Guide the students to

move the beads, 100 at a time, using the instructions given in Example 1. When the

students have 900 on the abacus, give the following instruction and question:

Move up 100 again. What do we do?

The teacher can then go on to explain that 10 times of 100 is equal to 1 000. The

exercises given under Let us think and Let us practice will enable the students tomaster the required skills of moving the beads and recognizing numbers up to 1 000. In

addition to that, it is also important for the students to have the following practice:

Listen to the numbers and memorize the numbers;


Read the numbers and move the beads.

This type of practice will enable the students to improve the speed of bead movement.

2.3.2 Addition Of Numbers Up To 500

[Example 3] Abacus Calculation: 24 + 45 + 56 + 93 = 218

Explanation

This example is taught based on the skills learnt in addition of numbers up to 100 and

recognizing numbers up to 1 000. The focus here is on the Tens rod. When the result

of addition at Tens is more than 10, (in other words, there are not enough beads at

Tens), then, regrouping will require carrying 1 at Hundreds.

Before teaching [Example 3], the following exercise can be given.

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(1) 27 + 45 =

(2) 38 + 17 =

(3) 16 + 49 + 17 =

(4) 32 + 18 + 14 =

Explain that in[ Example 3]: 24 + 45 + 56 + 93, the first step, 24 + 46 is equal to 69.

24 + 45 + 56 + 93

= 69 + 56 + 93

The next step involves adding 5 to 6 at Tens and adding 6 to 9 at Ones. Since there

are not enough beads at Tens to move up 5, regrouping requires carrying 1 at

Hundreds. Similarly, as there are not enough beads at Ones to move up 6, carrying 1 isagain required at Tens.

24 + 45 + 56 + 93

= 69 + 56 + 93

= 125 + 93

The third step, 125 + 93 involves adding 9 to 2 at Tens and adding 3 to 5 at Ones.

Again, since there are not enough beads at Tens to move up 9, carrying at Hundreds is

required.


(1) 24 + 45 + 56 + 93. How do we calculate it?



(4) Plus 56, first move up 5 at Tens, but there are not enough beads at Tens.

Down 5 at Tens and carry 1 at Hundreds. Next, move up 6 at Ones, but there

are not enough beads at Ones.

Down 4 at Ones and carry 1 at Tens.

(5) Plus 93, first up 9 at Tens; down 2 at Ones and carry 1 at Hundreds.

Next, up 3 at Ones.

(6) Equals to 218.

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Explanation

This example is taught based on the skills already mastered in mental addition and

subtraction of numbers up to 100.

The difficulty faced in this example is the bead image of numbers more than 100.

Before teaching [Example 4], get the students to calculate the following sums mentally.(1) 46 + 30 =

(2) 37 + 58 =

(3) 29 + 43 + 19 =

(4) 17 + 36 + 28 =

Refer to the illustration on Page 55 of the textbook. The focus here is on memorizing

the beads especially the beads at Hundreds.



(2) Ready, put your head down and close your eyes.

(3) Use your fingers to move the visualized beads. 72, up 72.

(4) Plus 54, first up 5 at Tens; down 5 at Tens, carry 1 at Hundreds; up 4 at Ones.

(5) Plus 31, up 3 at Tens, then up 1 at Ones.

(6) Equals to 157.


Explanation

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This example demonstrates the bead movement for addition of numbers with carrying.

When the addition of numbers at Ones is 10 or more than 10, carry one at Tens. In the

same way, when the addition of numbers at Tens is 10 or more than 10, carry 1 at

Hundreds. This example demonstrates the difficulties students face when doing bead

movement involving successive carrying.

Before teaching [Example 5], let the students do the following exercise on Page 57 of

the textbook.





Then, let the students perform the following bead movement involving carrying.





An illustration of the bead movement for Example 5 is on Page 57 of the textbook.

The following instructions can be used to guide the students.

(1) Move up 146, move up 57. How do we move the beads?

(2) Ready. First up 146.

(3) Move up 57; first up 5 at Tens;

Then up 7 at Ones; the sum is more than 10, so carry 1 at Tens;

But, there are already 9 at Tens, so carry 1 at Hundreds.

[Example 6] Abacus Calculation: 54 + 13 + 38 + 96 = 201

Explanation

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This example is taught based on the skills learnt in [Example 5] where the bead

movement requires successive carrying. As in [Example 5], the difficulty is carrying 1 at

Tens when the number at Tens is already 9. This requires another carrying at

Hundreds. Before teaching [Example 6], let the students do the following exercise.





Refer to the illustration for [Example 6] on Page 58 of the textbook. Then guide the

students to calculate [Example 6] - Abacus Calculation: 54 + 13 + 38 + 96.

The first step: 54 + 13 = 67.The second step: 67 + 38. Here, adding 8 to 7 at Ones requires carrying at Tens; but

there are already 9 at Tens, so carry 1 at Hundreds. We get 105.

The third step: 105 + 96. Here, adding 6 to 5 at Ones requires carrying at Tens; but

there are already 9 at Tens, so carry 1 at Hundreds. We get 201.

Point To Note:

The students should pay special attention to the following: 10 or more than 10 at

Ones, carry 1 at Tens; 10 or more than 10 at Tens, carry 1 at Hundreds.



(2) 54, up 54.

(3) Plus 13, up 1 at Tens, up 3 at Ones.

(4) Plus 38, up 3 at Tens, then up 8 at Ones;

but there are 9 at Tens, so carry 1 at Hundreds.

(5) Plus 96, first up 9 at Tens, then up 6 at Ones.

(6) Equals to 201.

Point To Note:

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The instructions should be given slowly and clearly so that students have time to

reflect on the successive carrying from Ones to Tens and from Tens to Hundreds.

[Example 7] Mental Calculation: 52 + 83 + 70 + 24 = 229.

Explanation

This example is taught based on the skills learnt in [Examples 3 and 4], and the addition

and subtraction of numbers up to 100 using the abacus. Again, the difficulty is

memorizing the bead image of numbers more than 100.

Before teaching[ Example 7], let the students revise the following:

i. Mental Calculation: Addition with carrying of numbers up to 100ii. Mental Calculation: Addition of three 2-digit numbers up to 500.

Refer to the illustration for [Example 7] on Page 59 of the textbook. Then guide the

students to calculate[ Example 7].

The first step: 52 + 83. First add the numbers at Tens. As the sum is more than 10,

carry 1 at Hundreds. Ask the students to specially memorize the bead image of 1 at

Hundreds.

The second step: plus 70. Again, adding 7 at Tens involves carrying 1 at Hundreds.

Now, the students have to memorize the bead image of 2 at Hundreds.

The third step: plus 24, up 24.



(2) Ready.

(3) 52, use your fingers to move up 52.

(4) Plus 83, first move up 8 at Tens, then move up 3 at Ones.

(5) Plus 70, move up 7 at Tens.


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(7) Equals to 229.


Explanation

This example involves the addition of 3-digit numbers on the abacus. Before teaching

[Example 8], refer to the illustration for [Example 8] on Page 61 of the textbook. Guide

the students to calculate on the abacus. Discuss the steps to be taken. Add the

Hundreds first, then the Tens and lastly the Ones. The students have to be reminded to

add only numbers in the same place values.



(2) First, up 172.

(3) Plus 294; up 2 at Hundreds, 9 at Tens (carry 1 at Hundreds), then up 4 at

Ones.

(4) Equals to 466.

Let the students calculate on the abacus. Ask them to do another question: 294 + 172.

Compare the answer with the answer obtained for [Example 8]. Other pairs of

questions can be found on Page 61 of the textbook.

Point To Note:

It is good practice for the students to check their answers. When doing addition,

the students just change the position of the numbers to be added.


Explanation

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This example is taught based on the skills learnt in [Example 8]. Refer to the illustration

for Example 9 on Page 55 of the textbook. In [Example 9], the first step is 136 + 28

which is equal to 164. Therefore, the second step would be 164 + 336; first add the

Hundreds, then the Tens and finally the Ones. Remind the students to carry 1 at Tens if

the there are 10 or more than 10 Ones, and carry 1 at Hundreds if there are 10 or more

than 10 Tens. In this example, there are already 9 Tens. Carrying 1 more at Tens

would involve successive carrying of 1 at Hundreds.



(2) First, up 136.

(3) Plus 28, up 2 at Tens, then up 8 at Ones. (Carry 1 at Tens.)(4) Plus 336, up 3 at Hundreds, then up 3 at Tens and 6 at Ones. (Carry 1 at

Tens.

As there are already 9 at Tens, then carry 1 at Hundreds.)

(5) Equals to 500.

[Example 10] Mental Calculation: 264 + 152 = 416

Explanation

This example involves the addition of two 3-digit numbers mentally. It is taught based

on the skills learnt in [Example 8] and [Example 9]. As in previous examples of Mental

Calculation, the difficulty that the students face lies in visualizing the bead image at

Hundreds.

To improve the students memory abilities, let the students revise the following before

doing the above example.

i. Listen to the numbers and memorize the numbers.

ii. Read the numbers and memorize the numbers.

iii. Listen to the numbers and visualize the bead images.

iv. Read the numbers and visualize the bead images.

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Refer to the illustration for [Example 10] on Page 63 of the textbook. As this is the first

time students are attempting mental addition of two 3-digit numbers, remind them to add

first at Hundreds, then Tens and then Ones. Remind them also to memorize the bead

image at Hundreds.



(2) Ready, lower your head and close your eyes.

(3) Use you fingers to move the visualized beads.

(4) 164, up 264

(5) Plus 152, up 1 at Hundreds, up 5 at Tens (carry 1 at Hundreds), then up 2 at Ones.(6) Equals to 416.

2.3.3 Addition And Subtraction Of Numbers Up To 500

[Example 11] Abacus Calculation: 128 + 89 72 58 = 87

Explanation

This is the first example involving both addition and subtraction of numbers up to 500.

The students are already familiar with removing 1 from Tens when there are not enough

beads at Ones to subtract. In the same way, explain to the students that if there are not

enough beads at Tens for subtraction, they should remove 1 at Hundreds.

Before doing [Example 1]1, revise subtraction with removing of numbers up to 100:

(1) 61 38 =

(2) 74 15 =

(3) 82 24 =

(4) 53 46 =

(5) 86 39 =

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Refer to the illustration for[Example 11] on Page 65 of the textbook. The first step is

128 + 89. By now, the students should have mastered addition involving 3-digit

numbers.

128 + 89 72 58

= 217 72 58

The second step is 217 72. First, minus at Tens; as there are not enough beads at

Tens, remove 1 at Hundreds. Then minus at Ones; again as there are not enough

beads at Ones, remove 1 from Tens.

128 + 89 72 58

= 217 72 58

= 145 58

Stress on the following: When there is not enough at Tens to minus, remove 1 at

Hundreds. When there is not enough at Ones to minus, remove 1 at Tens.


(1) 128 + 89 72 58. How do we calculate it?

(2) First up 128.

(3) Plus 89, up 8 at Tens (carry 1 at Hundreds);

up 9 at Ones (carry 1 at Tens).

(4) Minus 72, down 7 at Tens (not enough to minus, remove 1 at Hundreds);

then down 2 at Ones.

(5) Minus 58, down 5 at Tens (remove 1 at Hundreds);

down 8 at Ones (remove 1 at Tens).

(6) Equals to 87.

[Example 12] Mental Calculation: 17 + 86 21 + 24 = 106

Explanation

This example involves the mental addition and subtraction of four 2-digit numbers.

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Before doing this example, go through the following exercise using Mental Calculation.

(1) 12 + 34 + 45 =

(2) 30 + 13 + 28 =

(3) 24 16 + 79 =

(4) 95 48 + 17 =

(5) 23 + 18 + 78 + 92 =

(6) 65 + 74 + 13 + 88 =

(7) 315 + 128 =

(8) 179 + 246 =

Refer to the illustration for[ Example 12] on Page 66 of the text book. As in previous

examples involving mental addition and subtraction of numbers up to 500, the difficultyis visualizing and memorizing the bead image at Hundreds. The first step is 17 + 86.

This involves successive carrying from Ones to Tens and from Tens to Hundreds.

17 + 86 = 103. The second step is 103 21. This involves removing 1 at Hundreds.

The answer so far is 82. The third step is 82 + 24. This step requires carrying 1 at

Hundreds. The answer is 106. Remind the students to pay special attention to

memorizing the bead image at Hundreds.

The following instructions may be used to guide the students.

(1) 17 + 86 21 + 24. How do we calculate it?



(carry 1 at Tens, then carry 1 at Hundreds).

(4) Minus 21, down 2 at Tens (remove 1 at Hundreds),

then down 1 at Ones.

(5) Plus 24, up 2 at Tens (carry 1 at Hundreds),

then up 4 at Ones.

(6) Equals to 106.

[Example 13] Move up 214, Move down 18.

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Explanation

This example is the bead movement of repeated subtraction with removing up to 500. It

based on the foundation build in subtraction with removing up to 100.

Before proceeding to teaching, let pupils review on the practice of subtraction with removing

up to 100 on page 68 of the textbook.

(1) Move up 10, move down 1;




Through these practice, let pupils understand: remove 1 at Tens if there is insufficient at

Ones.

Before proceeding to teaching the [Example 13] let pupils look at the Abacus Calculation

demonstration figures for [Example 13] on page 68 of the textbook. Then with the

instruction from teacher, perform the example 13.

i. The first step is move up 214;

ii. The second step is move down 18, first move down 1 at Tens. Then movedown 8 at Ones, not enough beads at ones, so remove 1 at Tens; There is

zero at Tens, how to do it? Remove 1 at Hundreds.

Then the teacher draws a conclusion of repeated subtraction with removing:

If there are not enough beads at Ones, remove 1 at Tens;

If there is zero at Tens, remove 1 at Hundreds.

Then ask pupils to think : move up 500, move down 6, how to move?


1) Move up 214, move down 18, how to move/

2) First move up 214;

3) Move down 18, first move down 1 at Tens;

Then move down 8 at Ones, not enough beads at Ones, remove 1 at Tens;

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There is zero at Tens, remove 1 at Hundreds.

[Example 14] Abacus Calculation 363-65+23-26=295

Explanation

This example is based on[Example 13]. Focus and difficulty in the teaching is : If there are

not enough beads at Ones for subtraction, remove 1 at Tens, if there is zero at Tens,

remove 1 at Hundreds.

Before teaching this example, let pupils review on bead movement of repeated subtraction

with removing up to 500. For example:

1) Move up 316, move down 19;



4) Move up 282, move down 186.

Through the practice above, let pupils understand: If there are not enough beads at Ones

for subtraction, remove 1 at Tens, if there is zero at Tens, remove 1 at Hundreds.


demonstration figures for [Example 14] on page 69 of the textbook. Then with the

instruction from teacher, perform the [Example 14].

i. The first step is363 - 65, first subtract numbers at Tens. Then add numbers

at Ones. If there are not enough beads at Ones for subtraction, remove 1 at

Tens, if there is zero at Tens, remove 1 at Hundreds. Equals to 298.

ii. The second step is 298 + 23, first add numbers at Tens. Then add numbersat Ones. Equals to 321.

iii. The third step is 321-26, first subtract numbers at Tens. Then subtract

numbers at Ones, not enough beads at Ones, remove 1 at Tens, there is

zero at Tens, how to do it? Remove 1 at Hundreds. Equals to 295.

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During the teaching, remind pupils to focus on the memorization of bead images at

Hundreds.

The teacher should mention the this regulation again.

If there are not enough beads at Ones, remove 1 at Tens;If there is zero at Tens, remove 1 at Hundreds.


1) 363 65 + 23 - 26, how to do it?

2) First up 363;

3) Minus 65, first down 6 at Tens

Then down 5 at Ones, not enough beads at Ones, so remove 1 at Tens,

there is zero at Tens, remove 1 at Hundreds

4) Plus 23, first up 2 at Tens, not enough beads at Tens, so down 8 at Tens carry 1 at

Hundreds; Then up 3 at Ones, not enough beads at Ones, so down 7 at Ones carry 1 at

Tens.

5) Minus 26, first down 2 at Tens,

Then down 6 at Ones, not enough beads at Ones, remove 1 at Tens, there is

zero at Tens, remove 1 at Hundreds.

6) Equals to 295.

[Example 15] Mental Calculation 59+83+94-38=198

Explanation

This example is to be taught based on mental calculation up to 100, mental addition up to

500 and abacus addition and subtraction up to 500 . Focal and difficult point is the

memorization of beads for numbers with 3 unit-place number, especially the memorization

of bead image at Hundreds.

Before proceeding to the teaching, teacher may let the pupils do some revision:

1) Mental addition and subtraction up to 100;

2) Mental addition up to 500;

3) Abacus addition and subtraction up to 500;

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When explaining this example, let pupils look at the Mental Calculation demonstration

figures for [Example 15] on page 70 of the textbook. Then with the instruction from

teacher, perform the mental calculation for [Example 15].

i. The first step is 59 + 83, first add numbers at Tens. Then add numbers

at Ones. Equals to 142.ii. The second step is 142 + 94, first add numbers at Tens. Carry 1 at

Hundreds when there are 10 in Units. Then add numbers at Ones.

Equals to 236.

iii. The third step is 236 - 38, first subtract numbers at Tens. Carry 1 at

Hundreds when there are 10 in Units. Then subtract numbers at Ones,

not enough bead so remove 1 at Tens, there is zero at Tens, remove 1

at Hundreds. Equals to 198.

During the teaching, remind pupils to focus on the memorization of bead images at

Hundreds. Let the pupils manage this regulating of repeated subtraction with removing : If

there are not enough beads at Ones, remove 1 at Tens; If there is zero at Tens, remove 1 at

Hundreds.


1) 59 + 83 + 94 - 38, how to do it?

2) First up 59;

3) Plus 83, first up 8 at Tens, not enough beads Tens, so down 2 atTens and carry 1 at Hundreds;

Then up 3 at Ones, not enough beads at Ones, so down 7 at Ones and

carry 1 at Tens.

4) Plus 94, first up 9 at Tens, not enough beads at Tens, so down 1 at Tens

carry 1 at Hundreds;

Then up 4 at Ones, not enough beads at Ones, so down 6 at Ones carry 1 at Tens.

5) Minus 38, first down 3 at Tens,

Then down 8 at Ones, not enough beads at Ones, remove 1 at Tens, there is

zero at Tens, remove 1 at Hundreds.

6) Equals to 198.

[Example 16] Abacus Calculation 437-162=275

Explanation

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This example is teaching of 3 unit-places number subtract 3 unit-places number up to 500

and checking computations.

Focal and difficult point of the teaching is: subtraction on numbers in the same place value

and the checking computation of subtraction.


demonstration figures for [Example 16]on page 72 of the textbook.

When explaining this example, ask pupils: how to calculate? What is the first step? What is

the second? What is the last step? Then with the instruction from teacher, perform the

abacus calculation for [Example 16].

Firstly, subtract numbers at Hundreds. Then subtract numbers at Tens, remove 1 at

Hundreds if there are not enough beads at Tens. Then subtract numbers at Ones. Finally,

the teacher draws the conclusion of the rule of 3 unit-places number subtract 3 unit-places

number: subtract numbers at Hundreds, subtract numbers at Tens, subtract numbers at

Ones. Briefly written as subtraction on numbers in the same place value.


1) 437 - 162, how to do it?2) First up 437;

3) Minus 162, first down 1 at Hundreds. Then down 6 at Tens, not enough

beads at Tens, remove 1 at Hundred. Then down 2 at Ones

4) Equals to 275.

Then ask pupil to have a try : abacus calculation 275 + 162. They will find the answer is

437. It is the same as the minuend of the question 437 - 162.

Then ask pupils do Make a try on page 72 of the textbook: abacus calculation, lets check if

the sum of difference and subtrahend equal to minuend?

(1) 428 179 =

249 + 179 =

(2) 307 162 =

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145 + 162 =

(3) 394 - 138 =

256 + 138 =

(4) 412 - 116 =

296 + 116 =

After calculating, we will find the sums of differences and subtrahends equal to minuends.

Finally, the teacher draws a conclusion of the method of checking computation: subtraction

checking computation is adding difference and subtrahend.

[Example 17 ]abacus calculation 384-56+172-8=492

Explanation

This example is the comprehensive calculation of repeated addition with carrying and

repeated subtraction with removing up to 500. It is based on [Example 9], [Example 13],

[Example 14] and [Example 16]. The focal and difficult point is same as [Example 9],

[Example 13]and [Example 14].

Carry 1 at Tens when there are 10 at Ones; Carry 1 at Hundreds when there are 10 at Tens.

Remove 1 at Tens if there is insufficient at Ones; Remove 1 at Hundreds if there isinsufficient at Tens.

Before explain [Example 17], let pupils do some revision:

1) repeated addition with carrying up to 500;

2) repeated subtraction with removing up to 500.

When explaining this example, let pupils look at the Abacus Calculation demonstration



i. The first step is384 - 56, first subtract numbers at Tens. Then subtract

numbers at Ones, not enough beads at Ones, so remove 1at Tens. Equals

to 328.

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ii. The second step is 328 + 172, first add numbers at Hundreds. Then add

numbers at Tens. Then add numbers at Ones, Carry 1 at Tens when there

are 10 at Ones. There are 9 at Tens, carry 1 at Hundreds. Equals to 500.

iii. The third step is 500 -8, not enough beads at Ones, remove 1 at Tens, there

is zero at Tens, remove 1 at Hundreds. Equals to 492.

Repeated addition with carrying and repeated subtraction with removing is the difficult point.

Teachers should explain the process step by step to make pupils manage it.


1) 384 56 + 172 - 8, how to do it?

2) Firstly, up 384;

3) Minus 56, first down 5 at Tens;Then down 6 at Ones, not enough beads at Ones, so remove 1 at Tens;

4) Plus 172, first up 1 at Hundreds;

Then up 7 at Tens;

Then up 2 at Ones, not enough beads at Ones, so carry 1 at Tens;

5) Minus 8, not enough beads at Ones, so remove 1 at Tens, there is zero at

Tens, remove 1 at Hundreds.

6) Equals to 492.

[Example 18 ]Mental Calculation 487-194=293

Explanation

This example is 3-digit number subtract 3-digit number in mental calculation up to 500. It is

to be taught based on skill in [Example 16]and[Example 17].

Focal and difficult point is the memorization of beads for numbers with 3 unit-place number,

especially the memorization of bead image at Hundreds.

Before proceeding to the teaching, teacher may let the pupils do some revision:

1) Listen to the 3-digit numbers and memorize the numbers.

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Look at the 3-digit numbers and memorize the numbers.

2) Listen to the 3-digit numbers and interpret the numbers.

Look at the 3-digit numbers and interpret the numbers.

3) Mental Calculation of 3-digit numbers up to 500.

When explaining this example, let pupils look at the Mental Calculation demonstration



i. The first step : subtract the numbers at Hundreds;

ii. The second step: subtract the numbers at Tens, not enough beads, so

remove 1 at Hundreds.

iii. The third step: subtract the numbers at Ones;

This is the first time for pupils touch the mental calculation of 3-digit numbers.


1) 487-194, how to do it?

2) Ready, close your eyes and cover your head;3) 487, simulate fingers up 487;

4) Minus 194, first down 1 at Hundreds; then down 9 at Tens, not enough beads,

so remove 1 at Hundreds; then down 4 at Ones

5) Equals to 293.

2.3.4 Addition up to 1000[Example 19] Abacus Calculation 254+631=876

Explanation

This example is to be taught based on addition up to 500. Focal and difficult point of the

teaching is: addition on numbers in the same place value.

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Before proceeding to the teaching, teacher may let the pupils do these questions:

1) 127 + 145 =

2) 308 + 170 =

3) 161 + 49 + 107 =4) 132 + 120 + 214 =




i. The first step: add the numbers at Hundreds, 2 + 6 = 8;

ii. The second step: add the numbers at Tens, 4 + 3 = 7;iii. The third step: add the numbers at Ones, 5 + 1 = 6.


1) 245 + 631, how to do it ?

2) First up 245;

3) Plus 631,

First up 6 at Hundreds,

Then up 3 at TensThen up 1at Ones.

4) Equals to 876.

[Example 20 ]Abacus Calculation 364+219+417=1000

Explanation

This example is the repeated addition of 3 numbers of 3-digit number up to 1000. It is to be

taught based on addition up to 500 and the [Example 19]. The focal and difficult point is :

addition the numbers at Ones, carry 1 at Tens when there are 10 at Ones, if there are 9 at

Tens, carry 1 at Hundreds, if there are 9 at Hundreds, carry 1 at Thousands.

Before proceeding to the teaching, teacher may let the pupils do these questions:

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1) 377 + 259 =

2) 408 + 179 =

3) 614 + 208 =

4) 326 + 174 =




i. The first step: 364 + 219

First add the numbers at Hundreds, 3 + 2;

Then add the numbers at Tens, 6 + 1;

Then add the numbers at Ones,4 + 9, not enough beads at Ones, so carry 1at Tens, equals to 583.

ii. The second step: 583 + 417

First add the numbers at Hundreds, 5 + 4;

Then add the numbers at Tens, 8 + 1;

Then add the numbers at Ones,3 + 7, not enough beads at Ones, so carry 1

at Tens, there are 9 at Tens, so carry 1 at Hundreds, there are 9 at

Hundreds, so carry 1 at Thousands, equals to 1000.

Please remind pupils especially: carry 1 at Tens when there are 10 at Ones; carry 1 at

Hundreds when there are 10 at Tens; carry 1 at Thousands when there are 10 at Hundreds.


1) 364 + 219 + 417, how to do it?

2) First up 364;

3) Plus 219,


Then up 1 at Tens,

Then up 9 at Ones, not enough beads at Ones, so carry 1 at Tens;

4) Plus 417,


Then up 1 at Tens,

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Then up 7 at Ones, not enough beads at Ones, so carry 1 at Tens,

There are 9 at Tens, so carry 1 at Hundreds,

There are 9 at Hundreds, so carry 1 at Thousands;

5) Equals to1000.

Example 21 Mental Calculation 367 + 529 = 896

Explanation

This example is to be taught based on mental addition up to 500. Focal and difficult point is

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Module Year 2