Maths form 1

Whole Numbers

1

1. Teacher displays cards showing different ways of writing whole numbers by

different civilizations and asks students: “Students, can you tell me what are these?”

Teacher accepts all responses and may ask students to read aloud the numbers that are familiar to them.

2. Teacher points to the displayed cards and says:

“These are the different ways of writing whole numbers for examples the Arabic, Chinese, Indian, Roman and others. The number system we use today is the Hindu-Arabic system. In this system there are 10 symbols namely 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9. These symbols are called digits.”

3. Teacher writes the numbers 0, 1, 2, 3, …, 9 and the word “digits” on the board.

Learning Area Whole Numbers Learning Objective

Understand the Concept of Whole Numbers

Learning Outcome

Count, read and write whole numbers.

Resources Cards with numbers used by different civilizations. Diagrams showing 1- 10 objects.

Vocabulary

Whole number, count, read, write

one, two, three, … ten

eleven, twelve, thirteen, … twenty-one, twenty-two, twenty-tree, twenty-four, twenty-five, twenty-six, …

Focus

Contextual Learning, Communication in Mathematics and Multiple Intelligences.

Introductory ActivitiesIntroductory Activities

Mathematics Teaching Scripts – Form 1

2

“Today we will learn how to count, read and write whole numbers.” 1. Teacher shows the class cards with diagrams containing 1 – 10 objects (in order) and

pastes every one of them on the board. Eg.

2. Refer to card 1(one object).

“How many (objects) are there?” 3. Students count the objects and say aloud the numbers. Ask a student to come out and

write the number in numerals and in words on the board. “Write the number of (objects) on the board.” “Can you spell ‘one’ and write it on the board?” 4. Repeat with cards containing diagrams with 2 – 10 and 0

objects. 5. Teacher shows a card without any object and asks:

“How many (objects) are there?” Expected answer: no objects or nothing.

“There are zero objects?”

Teacher writes 0 in numerals and in words. 6. Teacher points to the numbers written on the board

0 – zero , 1 – one, 2 – two, 3 – three, 4 – four, 5 – five, 6 – six, 7 – seven, 8 – eight, 9 – nine, 10 – ten and asks students to say the numbers.

“Let’s say it together, zero, one, two … ten.”

“What is the number after 10?” 7. Teacher asks students to fill in the blanks with numerals (up

to 20). “Ali, can you fill in the blanks with the correct numerals?” 1, 2, 3, …, 10, …

“Can you write the numbers in words?” 8. Repeat similar activities for numbers 21 to 30.

Expected responses : There is one pumpkin There are two pumpkins.

Number of objects in numerals – 1 Number of objects in words -one

Expected responses: 11 – eleven 12 – twelve 13 – thirteen 14 – fourteen 15 – fifteen 16 – sixteen 17 – seventeen 18 – eighteen 19 – nineteen 20 – twenty

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9. Teacher emphasises that numbers over twenty are written with hyphen.

“Students, numbers over twenty is written with a hyphen, for example twenty-one, thirty-two and thirty- nine?”

10. Teacher points to the numbers written on the board (0,1,2, 3, …, 30) and says:

“Students, we have learnt how to count, read and write numbers from 0 to 30.” “Can you give me a number larger than 30?”

Teacher accepts all responses from the students and continues writing the numbers on

the board ( 0,1,2, …, 21,22,23, …, 31, ..,45, …, 100,…, 1200, … Teacher asks students:

“Is there an end to these numbers?”

Teacher accepts all responses from the students and says:

“These numbers are called whole numbers.”

Teacher writes the word ‘Whole Numbers’ on the board. 11. Teacher explains to the students the use of number line to represent whole numbers. “We can use a number line to represent whole numbers.”

Teacher draws a number line on the board and explains:

“We label the point on the left with zero and the rest of the points, in order, with the numbers 1,2, 3, 4, and so on.” “The arrow indicates that the number can continue in that direction forever.”

Teacher leads the students to sing songs with numbers. “Class, let us sing this song together.” Eg. One little, two little, three little soldiers Four little, five little, six little soldiers Seven little, eight little, nine little soldiers Ten little soldier boys …

ClosureClosure

0 1 2 3 4


4

Ask students to record the use of numerals around the.

“Class, mathematics and numbers are all around us. Now look around you and give as many examples as possible of situations using numbers, especially whole numbers.”

Eg. There are 6 windows in my house. My age is 13.

My house number is 43.

Additional ActivitiesAdditional Activities

Whole Numbers

5

Learning Area

Whole Numbers

Learning Objective


Learning Outcome

Count, read and write whole numbers.

Resources Interlocking blocks and manila cards Focus

Communication in Mathematics, Contextual Learning.

1. Count on and count back the number of students in the class.

“Let us count the attendance of the day. We shall begin with Ali (name of 1st student). Start with number one, the other students please count on with 2, 3……… and so on.”

“Now, we have (45) students in our class. Let us count back. Ali, start with number 45 and the others please count back with 44, 43, and so on.”

1. Revision from the previous day’s lesson.

Teacher writes a few numbers (0 – 30) in numerals on the board, one at a time and asks students to read it.

“Ah Beng, read the numbers on the board.” “Now, write down the numbers in words on the board.”

Repeat the activities with other students.

Teacher shows the following diagram by using interlocking blocks or manila cards.

“Fauzi, count the number of cubes in the diagram. How many cubes are there?”

“Write the number in numerals and in words on the board.”

Procedures



6

Write the numbers on the board and repeat with 50, 60,…, 100, 200, 300, …, 1000.

3. Teacher writes “48” on the board.

“Mei Ling, can you please read this number and write it down in words?”

Repeat with other numbers (<10 000) such as 57, 85, 93, 35, 240, 408, 386, 4715, 5209 and 8008.

“Kumar, write a number not more than 10 000 in words on the board.”

“Azizah, read the given number and write it down in numerals.”

Repeat the activity with other students.

“Ali, please write a 5 digit number on the board.” “Laila, can you please read the number and write it in words.”

Teacher repeats the activity to include 5, 6, and 7 digit numbers.

4. Teacher introduces skip counting in context.

“If you have RM30 in your savings, and you save RM10 per week, how much money would you have after one week, two weeks… ?”

“If your parents give you RM280 to spend and you only spend RM5 a day, how much money would you have after one day, two days …?”

“There are 23 pots of baby orchids in the garden. Everyday the gardener plants 10 more pots of baby orchids.” “How many pots of baby orchids are there in the garden after 1 day, 2 days, 3 days…?

5. Students have a competition on how to write and read whole numbers. Divide the class into two groups.

“Class we are going to have a competition.” “Each student from group 1 will write a number less than 10 000 in words on a board/ paper.” “Student from the other group will read the number and write the number in numerals.”

Teacher chooses a student in group 1 to show his / her number to a student in group 2.

“Omar, show your number to Chong Meng.” “Lui Kai, please read the number and write it in numeral.”

Repeat this activity with other students. Reverse the role of group 1 and group 2.

Forty, fifty, sixty, seventy, eighty, ninety, one hundred, two hundred,…, one thousand. Forty-eight One hundred and Thirty –five Four hundred and eight One thousand five hundred and sixty-eight Eight thousand and eight.

Whole Numbers

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“23 can be represented by this way.:

“How many tens are there?” “How many ones are there?”

“235 can be represented by ..”

“How many hundreds are there?” “How many tens are there?” “How many ones are there?” “We will continue our lesson tomorrow and learn about place values of digits. Please read the textbook before the next lesson.”

Closure

Expected answer: 2 tens 3 ones

Expected answer: 2 hundreds, 3 tens, 5 ones


8

Teacher guides her students to explore the use of numbers in various forms in their daily activities.

“Class, here are some examples of numbers in different forms. Can you write these numbers in another form? Try and think of some events and write the date of the events in various forms. Here is an example.”

World War 2 – 1941- MCM XLI Teacher writes the above example on the board.

Different forms of Numbers

Arabic Roman Arabic Roman Arabic Roman

1 I 10 X 100 C 2 II 20 XX 200 CC

3 III 30 XXX 300 CCC

4 IV 40 XL 400 CD 5 V 50 L 500 D

6 VI 60 LX 600 DC

7 VII 70 LXX 700 DCC

8 VIII 80 LXXX 800 DCCC

9 IX 90 XC 900 DCCCC or CM

1 000 M

Additional Activities

Whole Numbers

9

Learning Area

Whole Numbers

Learning Objective


Learning Outcome

Identify place value and value of each digit in whole numbers

Vocabulary Ones, tens, hundreds, thousands, ten thousands, hundred thousands, million, billion, digit

Place value, value of the digit

Resources Interlocking blocks of units and tens or strips of unit, tens and hundreds made from manila cards. Unit Ten Hundred

Focus

Communication in Mathematics, Multiple Intelligences, Contextual

Learning.

Teacher repeats activity for closure of the previous lesson.

“What is the number represented by the diagram?”

“How many tens are there?” “How many ones are there?”


Expected answer: 3 tens, 6 ones


10

1. Teacher shows number 236 by using strips/ blocks.

“What is the number represented by the diagram?”

2. Teacher writes the number 236 on the board. 2 3 6

“How many hundreds are there?” “How many tens are there?” “How many ones are there?”

3. Teacher fills the blanks with the words ‘hundreds, tens and ones’ 2 3 6

“The value of 2 is 200 and the place value is hundreds. The value of 3 is 30 and the place value is tens.

The value of 6 is 6 and the place value is ones.”

“Every digit in a number has its place value and value.”

4. Teacher shows 4, 5, 6 and 7 digit numbers to the class. Numbers involving real-life situations should be used: E.g.: The number of students in the school.

Example 1:

“What is the place value of 9?” “What is the value of the digit 9?”

Hundreds Tens Ones

Thousandss

1 3 8 9

Hundreds Tens Ones

Expected answer: 2 hundreds, 3 tens, 6 ones

Expected answer: ones 9

Expected answer: 236

Whole Numbers

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5. Teacher shows the table below on the board.

Thousands Hundreds Tens Ones

“Students we have learnt about place values; ones, tens, hundreds, and thousands.”

6. Teacher fills in a digit to the left of the place value ‘thousands’.


6 1 3 8 9

“Students, can you read this number?”

“What is the place value of six?” 7. Teacher writes down ten thousand in the appropriate box.

Ten Thousands


6 1 3 8 9

8. Repeat this procedure with place values of ‘hundred thousand’ and ‘million’. Example: 593 146

“Noor Aini, what is the place value of the underlined digit?”

“What is the value of the underlined digit?”

9. Repeat with other digits.

“Tze Lee, read the number and write it down in words?”

“Why do you read it this way?”

10. Repeat with other examples.

Expected answer: sixty-one thousand three hundred and eighty-nine

Ten thousands

Expected answer: Ten thousand 90 000

Expected answer: Five hundred and ninety-three thousand, one hundred and forty-six.

Expected answer: The place value of five is hundred thousands….


12

1. Forming the largest and the smallest numbers.

“Every digit in a number has a place value and value. The position of a digit in a number is very important because it determines the value of the digits.”

“Form a four-digit number with the following digits 5, 3, 7, 8” “ What is the largest number?” “What is the smallest number?”

“If you are given these digits: 3, 9, 8, 9, 2 , form the smallest and the largest five-digit number.”

Explore from the Internet.

“Find out from the Internet how to write one billion in numeral.”

Give the following tables to make students aware the system of writing whole numbers.

“Class, this is a table showing place values of numbers. You can use this table to guide you to write whole numbers in numerals.”

Million Thousand Hundred

Hundred Million

Ten Million

Unit Hundred Thousand

Ten Thousand

Unit Hundred Ten Unit

ClosureClosure

Whole Numbers

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Learning Area Whole Numbers Learning Objectives


Learning Outcome

Rounding Whole Numbers

Vocabulary

Round Number line Estimate Round up Round down

Resources

Number line

Focus

Communication in Mathematics, Multiple intelligences.

Teacher introduces estimation in context with a recent event.

“During the school assembly, the principal said that there are about 1300 students in our school. Do you think that our school has exactly 1300 students?” “If not, what may be the possible number of students in the school?”

Students’ responses are to be used for further discussion.

Teacher starts the lesson by mentioning the number of students in the class.

“There are 33 students in class today.” 1. Teacher shows the diagram of a number line below.

“33 is in between 30 and 40, but it is closer to 30 than 40.” “We can say that there are about 30 students in the class.”

“We are rounding the number 33 to 30, to the nearest ten because it is nearer to 30.”

“This means that we are rounding down the number.” 2. Repeat the same activity when there are 38 students in a class.

30 40 33


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“38 is in between 30 and 40, but it is closer to 40 than 30.” “We can say that there are about 40 students in the class.”

“We are rounding the number 38 to 40, to the nearest ten. We are rounding up the numbers.”

3. Teacher discusses the value of 35.

“35 is exactly halfway between 30 and 40.” “35 is rounded up to 40.”

“To round whole numbers: First, look at the digit to the right of the place to which you are rounding.

If the digit is 5 or more, add 1 to the digit in the place to be rounded and replace all the digits to the right with zeroes. If the digit is less than 5, maintain the digit that needs to be rounded and replace all the digits to the right with zeroes.

Teacher gives general rule on how to round a number: The digit that needs to be rounded remains the same.”

4. Teacher writes the following number on the board.

“Now let us round the number given to the nearest hundred.”

“Which digit has a place value of hundred?” (8) “Look at the digit to the right of digit 8.” “Is the digit 5 or more than 5?”

“Digit 6 is more than 5, So we add 1 to the digit 8 and replace the digits to the right with zeroes. Hence 23 867 is rounded up to 23 900 to the nearest hundred.”

30 40 38

23 867 Students might give the answer of 238 when rounding to the nearest hundred, teacher should explain why it is wrong by asking the student to read aloud 23 847 and 238 and ask them to compare their values.

23 867

Add 1 to get 9 to the nearest hundred

Greater than 5

Replace with zero

Whole Numbers

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5. Teacher should also use the number line to explain the answer.

6. Teacher repeats activity 5 with different numbers such as 56 493 rounding to the nearest thousand.

56 493

“Now let us round the number given to the nearest thousand”. “Which digit has a place value of thousand?”

Expected answer: 6

“Look at the digit to the right of digit 6”. “Is the digit 5 or more?”

“Digit 4 is less than 5, So digit 6 remains the same and the digit to the right are replaced with zeroes. Hence 56 493 is rounded down to 56 000 to the nearest thousand.”

Teacher should encourage students to check the answer using the number line.

7. Relate rounding to estimation. “We can use rounding to help us estimate numbers.” Teacher gives a few examples.

a) Last week’s attendance of Form 1 Jujur: Monday - 27 Tuesday - 29 Wednesday - 31 Thursday - 32 Friday - 30

Teacher concludes:

“There are about 30 students in the class each day. Class, do you agree with that statement?”

23 800 23 847 23 900

23 850

56 493

Digit 6 remains the same

less than 5

Replace with zero


16

Class No of students Number of

students rounded to the nearest ten

A 43 B 38 C 53

“Aishah, please estimate the total number of students in Form 1?” Expected answer:There are about 130 students in Form 1 Teacher gives a few numbers to be rounded to the nearest tens, hundreds, thousands and ten thousands without using the number line.

“Look at your answer to the question given at the beginning of the lesson?” “Do you think that our school has exactly 1 300 students?”

Expected answer: No “What is the possible number of students in the school?”

Expected answer: Any number between 1250 to 1349.

“Is your friend’s answer acceptable?” “If not, please give an acceptable answer?”

ClosureClosure

Whole Numbers

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Learning Area Whole Numbers Learning Objectives

Perform computations and solve problems involving addition and subtraction of whole numbers.

Learning Outcome

Add whole numbers. Solve problems involving addition of whole numbers.

Recourses Interlocking blocks, place-value cards and calculators.

Key words and phrases

add addition total sum plus subtract subtraction difference minus regroup carry

Focus

Communication in Mathematics, Constructivism, Multiple Intelligence

1. Teacher introduces a problem related to students' everyday experiences. “Ali has 5 marbles and Meng Tat has 8 marbles. How many marbles do they have?”

2. Teacher asks a student

“Maniam, what is your answer?”

Expected answer: 13

“How did you get your answer?”

Expected answer: By adding mentally or by counting on

3. “Class, let us try out these questions.” Teacher reads out the following questions (one by one) to be answered by individual

students.

i. 5 + 3; 3 + 8; 6 + 8; 9 + 4; ii. 10 + 30; 40 + 40; 60 + 90; 200 + 500; 700 + 900; iii. 43 + 20; 48 + 50; 57 + 70; 200 + 79; 36 + 200; 348 + 300; 725 + 400;

4. “How did you get the answer?”

Expected answer: Counting on.

5. “Today, we are going to learn how to add larger numbers using different methods.”



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1. Concrete materials or drawings are used to develop the process and the language of addition and subtraction.

“There are 65 boys and 72 girls in the Mathematics Club. How many students are there in the club altogether?”

“Can you write the problem in mathematical form?”

"Yes, we add the two numbers, 65 and 72. We write 65 plus 72."

2. Teacher guides the students to write '65 + 72 =' on the board and in their exercise book. "Using the blocks or drawings provided, place 6 tens and 5 ones, then add 7 tens and 2 ones.”

3. A student comes forward to demonstrate with the guidance of the teacher.

“Adding the ones, we have 5 ones and 2 ones giving 7 ones.”

“Add the tens. 6 tens and 7 tens gives 13 tens.”

Hundreds Tens Ones

Hundreds Tens Ones

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“Regrouping the tens. Exchange 10 tens for a hundred.”

“The sum is one hundred and thirty-seven.”

“65 plus 72 is 137. There are altogether one hundred and thirty-seven students.”

4. Teacher completes the equation '65 + 72 = 137' on the board.

“We can also write the addition in column form.”

Hundreds Tens Ones

Hundreds Tens Ones

Hundred Tens Ones 6 5

+ 7 2

Hundreds Tens Units


20

“The total is one hundred and thirty seven.” “We must remember to add the columns up from right to left.”

“Add the ones. 5 ones and 2 ones equals 7 ones.”

“Add the tens. 6 tens and 7 tens equals 13 tens.” “Regroup the tens. Exchange 10 tens for a hundred.”

Hundred Tens Ones 6 5

+ 7 2 7

Hundreds Tens Units

Hundreds Tens Ones

Hundred Tens Ones 1 6 5

+ 7 2 3 7

Hundred Tens Ones 1 6 5

+ 7 2 1 3 7

Hundreds Tens Ones

Whole Numbers

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5. “Class, we can use another method to find the answer for 65 + 72.” Teacher writes on the board

65 + 72 “We start with 65 and count on 66, 67.” 65 + 2 = 67

Teacher writes on the board 67+ 70

“Here, we add the tens to 67 by counting on.” “We count on 67, 77, 87,…,137.”

“So the sum is 137.”

6. “We can also add 65 and 72 this way.” “We add the ones of the numbers first.” Teacher writes on the board

5 + 2 = 7 “Then we add the tens.” 60 + 70 = 130 “Work out the total for the ones and tens. 7 + 130, The sum is 137.”

7. Try out the different methods of addition on these questions:

i. 2 465 + 3 726 ii. 3 527 + 1 076

8. “Most of us are more familiar with writing addition in the column form. We add

the ones, the tens, the hundreds, the thousands, and so on separately, from right to left. Regrouping may be necessary during the process.”

9. Try out the different methods of addition with this question.

“The area of East Malaysia is 198 069 square kilometers, whereas the area of West Malaysia is 131 678 square kilometers. Find the area of Malaysia.”

“Add the ones. 9 ones and 8 ones gives 17 ones.”

“Regrouping the ones. Exchange 10 ones for a ten.” “Add the tens. 1 ten, 6 tens and 7 tens gives 14 tens.” “Regrouping the tens. Exchange 10 tens for a hundred.”

Teacher points at 130 followed by 7

198069

+ 131678

198069

+ 131678

7

1

1 198069 + 131678

47

1


22

“Add the hundreds. 1 hundred, 0 hundred and 6 hundreds gives 7 hundreds.”

“Add the thousands. 8 thousands and 1 thousands gives 9 thousands.”

“Add the ten thousands. 9 ten thousands and 3 ten thousands gives 12 ten thousands.”

“Regrouping the tens thousands. Exchange 10 tens thousands for a hundred thousand.”

“Add the hundred thousands. 1 hundred thousand, 1 hundred thousand and 1 hundred thousand gives 3 hundred thousands.”

“The total is 3 hundred and twenty-nine thousand, seven hundred and forty-seven.”

“All the three methods will give the same answer.”

“Which method do you prefer? Why?”

1 198069

+ 131678

9747

1

1 198069

+ 131678

29747

1 1

1 198069

+ 131678

329747

1 1

1 198069

+ 131678

747

1

Whole Numbers

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1. “Find the total cost of buying a computer and a printer.”

“We should have an estimation of the amount required so that we have enough money to buy.”

“Do you think it is close to RM 3000? Can anyone give a better estimation? You may try by rounding off 3299 and 1625 to the nearest thousand.”

“Yes, 3 thousands and 2 thousands make 5 thousands. RM 5000 sounds reasonable to us.”

“Find the exact cost of buying the computer and the printer.”

“Is RM 5000 a useful rough approximation of the exact cost of RM4924?”

2. Repeat with other examples of addition of 2 or 3 whole numbers.

“Use the skill of estimation by adding rounded

numbers to check the reasonableness of the exact calculations.”

“The second 'sum' is obviously not correct because 2 thousands and 6 thousands make 8 thousands but the answer given here is about 9 thousands.”

10. Students attempt several questions involving the addition of two or three whole numbers on the board and in their exercise books.

3. Show the students some 'sums'. They may be taken from students' work.

“Some mistakes may have been made. Can you spot them?”

ClosureClosure

RM3299 RM1625

Students are encouraged to use calculators to check their answers when they are adding large numbers or a list of numbers.

186

+ 272

458

4096

+ 512

4608

2109

+ 5699

8808


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4. “Use pencil-and-paper to answer the following questions. Use calculators to check your answers.”

4 900 718 + 899 654 =

238 + 4507 + 2933 + 640 + 1427 =

5. Students should be exposed to mental and speed addition if they have mastered the basic skills in addition.

“Look at the following examples. By rearranging the numbers, we may be able to answer the questions easily.”

24 + 9 = 24 + 10 − 1

328 + 75 = 328 + 100 − 25

64 + 37 + 36 + 18 + 13 = 64 + 36 + 37 + 13 + 18

1. Find some questions from puzzle books to be used as additional activities in the

class or after school.

Additional ActAdditional Act ivitiesivities

Whole Numbers

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Learning Area Whole Numbers

Learning Objectives

Perform computations and solve problems involving addition and subtraction of whole numbers.

Learning Outcomes

Subtract whole numbers. Solve problems involving subtraction of whole numbers.

Resources Interlocking blocks, place-value cards, calculators

Vocabulary subtract subtraction difference minus

take away borrow inverse

Focus Communication in Mathematics, Constructivism, Multiple Intelligence

1. Teacher introduces problems related to students' everyday experience. Different situations are used to develop the concept of subtraction as a process to find the remainder after 'take away', missing addend, part of the whole, difference in comparison. Concepts of subtraction as the inverse of addition should also be developed.

“Can you write the following problems in mathematical form? You may use different ways to write the same problem.”

“Hassan has 7 rambutans. Idris gives him 2 more rambutans. How many rambutans does Hasan have?”

Students are expected to write '7 + 2 = ? “Class, this example is known as joined problems in addition” “Now try this example. Hassan has some rambutans. Idris gives him 2 more rambutans. Now he has 9 rambutans. How many rambutans did Hassan have in the beginning?”

Students may write '? + 2 = 9' or '9 − 2 = ?'

“Now class, this problem is known as missing addend.”

“Hassan has 7 rambutans. Idris gives him some more rambutans. Now Hassan has 9 rambutans. How many rambutans did Idris give Hassan?"

Expected answer: 7 + ? = 9

“ N o w , t h i s p r o b l e m i s a l s o k n o w n a s m i s s i n g a d d e n d . ”“ N o w , t h i s p r o b l e m i s a l s o k n o w n a s m i s s i n g a d d e n d . ”

“Hassan has 9 rambutans. He eats 2 rambutans. How many rambutans are left?”“Hassan has 9 rambutans. He eats 2 rambutans. How many rambutans are left?”



26

Expected answer: 9 – 2 = 7 “Class, this type of subtraction is known as take away. Let us try another problem.”

“Hassan has some rambutans. He ate 2 rambutans. He has 7 rambutans left. How many rambutans did Hassan have in the beginning?”

Expected answer: ? – 2 = 7

“Hassan has 9 rambutans. He ate some rambutans. He has 7 rambutans left. How many rambutans did Hassan eat?”

Expected answer: 9 - ? = 7

“This example is known as missing addend.”

“The problem that I am going to read to you now is known as ‘Part-part-whole problem’. Try and write the mathematical sentence and solve the problem.” “Hassan has 2 rambutans and 7 mangosteens. How many fruits does he have?”

Expected answer: 2 + 7 = 9

“Hassan has 9 fruits. 2 are rambutans, the rest are mangoesteens. How many mangoesteens does Hassan have?”

Expected answer: 9 – 2 = 7 or 2 + ? = 9

Teacher writes the following problem on the board and reads it the problems back to the students.

“Hassan has 9 rambutans. Idris has 2 rambutans. How many more rambutans does Hassan have than Idri?”

“Hassan has 2 more rambutans than Idris. Hassan has 9 rambutans. How many rambutans does Idris have?”

“Idris has 2 less rambutans than Hassan. He has 7 rambutans. How many rambutans does Hassan have?”

“Class, try and solve these problems. These problems are known as compare problems.”

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1. Concrete materials or drawings are used to develop the process and the language of subtraction.

“There are 213 Form 1 students in Sekolah Bestari. 87 of them are boys. How many girls are there?”

“Can you write the problem in mathematical form?”

“Yes, we can write '87 + ? = 213' or '213 −− 87 = ?”

2. Teacher guides the students to write '213 − 87 =' on the board and their exercise book.

A student comes forward to demonstrate with the guidance of the teacher. “Using the blocks or drawings provided, put out 2

hundreds, 1 ten and 3 ones.”

“We are going to take away 8 tens and 7 ones.”

“There are not enough ones to be taken away. Regroup the tens. Exchange 1 ten for 10 ones.”

“Take away 7 ones.”

Hundreds Tens Ones

Hundreds Tens Ones

Hundreds Tens Ones

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28

“There are not enough tens to be taken away. Regrouping the hundreds.

Exchange 1 hundred for 10 tens.”

“Now, take away 8 tens.”

“There are one hundred and twenty-six left.”

“So, there are 126 girls.”

Teacher completes the equation '213 − 87 = 126' on the board. “We can record the above process of subtraction in the column form.”

“Regrouping the tens. Exchange 1 ten for 10 ones.”

“13 ones minus 7 ones gives 6 ones.”

“Subtract the tens. There are not enough tens to be subtracted.”

“Regrouping the hundreds. Exchange 1 hundred for 10 tens.”

“Subtract the ones. There are not enough ones to be subtracted.”

213

− 87

Hundreds Tens Ones

Hundreds Tens Ones

213

− 87

6

0 13 − −

Whole Numbers

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“10 “tens” minus 8 “tens” gives 2 “tens.”

“There are many ways of reading this:

213 minus 87 equals 126, The difference between 213 and 87 is 126” answer is one hundred and twenty-six.”

Several examples like this should be discussed, terms like subtract, subtraction, minus, take away, difference should be used.

Students should learn different methods of addition to acquire an understanding of the process of subtraction and the skill on computation.

“The area of East Malaysia is 198069 square kilometers, whereas the area of West Malaysia is 131678 square kilometers. What is the difference between the area of East Malaysia and the area of West Malaysia?”

Teacher accepts students' responses and writes the question '198069 − 131678 =' on the board.

“You may use any working to find the answer.”

Teacher explains each step of the working to students.

“Here is a method that can be associated with 'count down' when we 'take away'.”

198 069 − 100 000 = 98 069

98 069 − 30 000 = 68 069

68 069 − 1000 = 67 069

67 069 − 600 = 66 469

“1 ‘hundred’ minus 0 ‘hundred’ gives 1 ‘hundred’ .The answer is one hundred and twenty-six.”

213

− 87

26

0 13 − −

1 10 − −

213

− 87

126

0 13 − −

1 10 − −

count down 30 thousands: 98 thousands, 88 thousands, 78 thousands, 68 thousands.

count down 70: 469, 459, 449, 439, 429, 419, 409, 399.


30

66 469 − 70 = 66 399

66 399 − 8 = 66 391

“This method involves ‘count on’ starting with the smaller number.”

“First count on to 190 000.”

131 678 + 2 = 131 680

131 680 + 20 = 131 700

131 700 + 300 = 132 000

132 000 + 8000 = 140 000

140 000 + 50 000 = 190 000

190 000 + 8000 = 198 000

198 000 + 60 = 198 060

198 060 + 9 = 198 069

“We have added 2 + 20 + 300 + 8000 + 50 000 + 8000 + 60 + 9 = 66 391.”

“Since 131 678 + 66 391 = 198 069, therefore 198 069 −− 131 678 = 66 391.”

“We can also count on directly to 198 069.”

131 678 + 1 = 131 679 to make 9 ‘ones’

131 679 + 90 = 131 769 to make 6 ‘tens’

131 769 + 300 = 132 069 to make 0 ‘hundreds’

132 069 + 6000 = 138 069 to make 8 ‘thousands’

138 069 + 60 000 = 198 069 to make 9 ‘ten thousands’

“We have added 1 + 90 + 300 + 6000 + 60 000 = 66 391.”

“Since 131 678 + 66 391 = 198 069, therefore 198 069 −− 131 678 = 66 391.”

“Most of us are more familiar writing subtraction in the column form and then we subtract the corresponding ones, the tens, the hundreds, the thousands, and so on separately. Regrouping may be necessary during the process.”

“Next, count on to 198 069.”

198069

− 131678

Or just add another 8069.

Whole Numbers

31

“Subtract the ones. 9 ones minus 8 ones gives 1 one.”

“Carry 1 thousand to become 10 hundreds, and carry 1 hundred to become 10 tens, making 7 thousands, 9 hundreds, and 16 tens.”

“Subtract the tens. 16 tens minus 7 ones give 9 tens.”

“Subtract the ten thousands, 90 thousands minus 30 thousand gives 60 thousands.”

“Subtract the hundreds, 9 hundreds minus 6 hundreds gives 3 hundreds.”

“Subtract the thousands, 7 thousands minus 1 thousand gives 6 thousands.”

198069

− 131678

1

198069

− 131678

91

9 16 7 10 -- -- --

198069

− 131678

391

9 16 7 10 -- -- --

198069

− 131678

6391

9 16 7 10 -- -- --

198069

− 131678

66391

9 16 7 10 -- -- --


32

Teacher discuss with the students the advantages and disadvantages of each method.

“All the three methods will give the same correct answer.”

“Which method do you like most? Why?”

Students attempt several questions involving subtraction of two or three whole numbers on the board and in their exercise books.

1. Students are encouraged to have a rough estimation of the answer before carrying out the actual calculation.

2. Students should use estimation to check the reasonableness of the exact calculation.

3. Students are encouraged to use calculators to check their answers when they are subtracting large numbers or a list of numbers.

“Use pencil-and-paper to answer the following questions. Use calculators to check your answers.”

4 900 718 − 899 654 =

2 384 507 − 52 933 − 640 148 =

4. Students sholud be exposed to mental and speed subtraction if they have master the basic skills in subtraction.

“Look at the following examples. By rearranging the numbers, we may be able to make the questions easier.”

24 − 9 = 24 − 10 + 1

328 − 87 = 328 − 100 + 13

264 + 437 − 75 − 64 − 27 = 264 − 64 + 437 − 23 − 75

“Subtract the hundred thousands, 100 thousands minus 100 thousand gives 0.”

“The difference is sixth-six thousands, three hundreds and ninety-one.”

ClosureClosure

198069

− 131678

66391

9 16 7 10 -- -- --

Whole Numbers

33

Use concrete materials to develop the concept of multiplication and introduce the terms associated with multiplications. 1. Teacher shows multiplication table on the board.

2 x 1 = 2 3 x 1 = 3 … 9 x 1 = 9 2 x 2 = 4 3 x 2 = 6 … 9 x 2 = 18 . . . . 2 x 10 = 20 … 9 x 10 = 90 “Class, can you recognise this table?” “This is a multiplication table” “All the important multiplication facts are shown on the table. I am sure all of you have memorized these multiplication facts. “Now we shall have an activity to see who can answer the questions quickly and correctly. Put up your hand if you know the answer to the question.” “What is 6 x 7 equals to?”

Teacher repeats with other numbers.

“Class it is very important that you memorize all the multiplication facts on the table. Please make sure that all of you can recite all the multiplication facts correctly and fluently.”

Learning Area Whole Numbers Learning Objective

Perform computations and solve problems involving multiplication and division of whole numbers.

Learning Outcome

Multiply whole numbers. Solve problems involving multiplications of whole numbers.

Resources 3 packets of 4 buns.

Vocabulary add addition total sum plus subtract subtraction difference minus regroup carry

Focus

Communication in Mathematics, Constructivism, Multiple Intelligence

INTRODUCTORY ACTIVITIESINTRODUCTORY ACTIVITIES


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1. Show students 3 packets of 4 buns or any other suitable concrete materials.

“How many packets of 4 buns are there?” (There are 3 packets of 4 buns.) 2. Teacher writes: 3 x 4 on the board. 3. “In mathematics this is read as 3 times 4.” 4. “How many buns are there altogether?” “How did you get the answer?” 5. Teachers writes: 3 x 4 = 4 + 4 + 4 = 12 6. “Class, read aloud three times four equals 12.” “The product of 3 and 4 is 12” 7. Teacher gives the following situation:

P R O C E D U R EP R O C E D U R E

x =

x =

Whole Numbers

35

10. Teacher points at diagram 1 and 2.

Teacher accepts all methods shown by students.

8. Ask a student to read aloud. “Tan Ping, Fill the blanks and read aloud the mathematical sentence”

9. Repeat with diagram 3.

11. “Is 6 x 3 the same as 3 x 6?” (The value is the same but 6 x 3 refers to 6 groups of three and 3 x 6 refers to 3 groups of six)

“Muthu, what is the product of 8 x 6?” “Chin Wah, is 6 x 8 equals to 8 x 6?”

12. “8 times 6 is also read as 8 multiplied by 6” 13. Teacher arrange 36 identical books into groups of 12.

“Class, I have three sets of 12 books, how many books are there altogether?” “There are many ways to get the answer. We can count the books or add repeatedly.”

“Sally, count the books. How many books are there altogether?” “Johnny, add 12 + 12 + 12. What is you answer?”

Teacher writes the answer on the board. “Class, read aloud, three times twelve equals thirty-six.” “Can anyone show us how to get the answer using other methods?”

14. Teacher separates the books so that each set shows 10 books and 2 books.

3 x 10 = 30 3 x 2 = 6


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15. “How many books are there in these three sets of two books?”

Teacher shows the multiplication of three times two in the algorithm. Tens Ones 1 2 x 3 6

16. “How many books are there in these three sets of ten books?”

Teacher shows the multiplication of three sets of tens in the algorithm. Tens Ones 1 2 x 3 6

3 0 3 6

17. Teacher gives other examples of multiplications ( 1 digit multiplied by 2 digits that does not involve regrouping).

18. “Now we are going to use the same method to find the product of 4 x

21.” Teacher writes 4 x 21 on the board.

“Can anyone show the class how to get the answer?”

19. Teacher gives examples which involve regrouping such as: Tens Ones 1 7 x 4 2 8

4 0 6 8

3 x 2

3 x 10

7 x 4 = 28

10 x 4 = 40

Whole Numbers

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20. Teacher refers to the following examples on the board. “Class, we can simplify the steps as follows.”

1 2 2 1 1 7 x 3 x 4 x 4 6 4 2 8

3 0 2 0 4 0 3 6 2 4 6 8

1 2 2 1 12 7 x 3 x 4 x 4 3 6 2 4 6 8

21. “Class, solve these questions by using the simplified method within 15 minutes.”

Questions involving multiplications of a single digit number and a number less than a thousand are given.

22. “Class, we have learnt how to find the product of 4 x 17 by the

algorithm, can you show the class how to get the product of 17 x 4?”

23. “Amir, is 4 x 17 equals to 17 x 4?” “We are more familiar with algorithm to find the product of 4 x 17

and wee know that 4 x 17 = 17 x 4. To find the product of 17 x 4, we can always write it this way”

1 7 x 4

“Class, please try these questions on the board” Teacher wri tes the following questions on the board.

i) 128 x 7 ii) 5 x 23 iii) 27 x 9

4 x 7 ones = 28 ones regrouping 2 tens and 8 ones. 2 tens carried forward.

C L O S U R EC L O S U R E

Documents

Maths form 1