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Teacher’s Guide Sheet 2.1 Concept: Number Patterns Learning Outcomes: 1. Describe the pattern of a given number sequence. 2. Extend number sequence. 3. Complete missing terms in given number sequences. 4. Construct number sequences based on given patterns. Teaching aids: Marbles, bottle caps, pencil, rubber seeds, leaves etc.

Activity 1

Approach Grouping

Aim Introduction of number sequence.

Steps 1. Teacher divides pupils into groups of three. Each group is asked to bring 20 objects, for example 20 marbles.

2. Teacher asks each group to make 4 heaps from the 20 objects. 3. Each group presents the result in front of the class. 4. Teacher explains the concept of number sequence and relates it to the

result of each group. 5. Teacher asks the groups to rearrange the objects to form a number

sequence. Repeat steps (b) and (c) if necessary.

Activity 2

Approach Discussion

Aim To complete the number sequence.

Steps Teacher expands the concept of number sequence. 1. Teacher discusses the different forms of sequences using operations of addition, subtraction, multiplication and division:

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(a) 1 ……. 6 ……. 11 ……. 16, ______, ______, ______ [add] (b) 20 ……. 17 ……. 14, ______, ______, ______, ______ [subtract] (c) 1 ……. 3 ……. 9 ……. 27, ______, ______, ______ [multiply] (d) 36 ……. 12 ……. 4, ______, ______, ______, ______ [divide]

2. Teacher discusses number sequences involved other operations.

(a) 21 , 4

1 , 61 , _______, _______

(b) 21 , 3

2 , 43 , _______, _______

(c) 1, 4, 9, 16, _______, _______

× 3 × 3 × 3

+ 5 + 5 + 5

– 3 – 3

÷ 3 ÷ 3

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Worksheet 2.1 1. Identify whether each group of objects is arranged in sequence (a) (b) (c)

Yes _______ No ________

Yes ________ No ______

Yes ________ No _______

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(d) 2. Complete the following number sequences using addition. (a) (b) (c) (d) 3. Complete the following number sequences using subtraction. (a) (b) (c)

Yes ________ No ________

1 2 3 5

2 4 8 10

10 20 30 50

100 300 400 500

5 4 2 1

10 8 6 2

60 50 40 30

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(d) 4. Complete the following number sequences using multiplication. (a) (b) (c) (d) 5. Complete the following number sequences using division. (a) (b) (c) (d) 6. Complete the following number sequences. (a)

81 71 61 51

1 2 4 16

1 3 9 81

1 4 64 256

10 20 80 160

16 4 2 1

64 32 8 4

81 9 3 1

160 80 40 10

32 30 28 24 22 20

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(b) (c) (d)

11 14 20 26 29

1 2 8 16 64

64 16 4 2 1

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Teacher’s Guide Sheet 2.2 Concept: Prime Numbers Learning Outcomes: 1. Identify the characteristics of prime numbers. 2. Determine whether a given number is a prime number. 3. Determine all the prime numbers less than 100. Teaching aids: Rope, clips, box, two sets flash cards with numbers [1 – 10].

Activity

Approach Game

Aim To identify prime numbers

Steps 1. Teacher hangs one set of the flash cards with numbers 1 – 10 in front of the class.

2. Teacher put the other set of flash cards into a box and asks a pupil to

pick a card from the box.

3. By referring to the hanging flash cards, teacher asks the pupil to state

the numbers which are the divisors of the picked number. Example: the flash card picked by the pupil is . 8

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8 is divisible by 1, 2, 4 and 8. So, 1, 2, 4 and 8 should be stated by the pupil.

4. Steps 2 and 3 are repeated. 5. Teacher asks pupils to record the results in a table as below.

Number with two divisors Number with more than two divisors

2 4

3 6

5 8

7 9

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6. Referring to the above table, teacher explains the concept of prime numbers. (Emphasise that “1” is not a prime number.)

7. Teacher asks pupils to extend the table with numbers such as

11 to 20, 21 to 30, and etc. 8. Teacher makes the conclusion:

1 is not a prime number 2 is the smallest prime number 2 is the only prime number which is an even number Not all odd numbers are prime numbers 9. Pupils try to answer Worksheet 2.2.

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Worksheet 2.2 1. Circle all the prime numbers. 1 13 10 21 17 15 27 11 19 0 16 2 31 29 3 2. Identify the prime numbers. (a) 6 12 17 24 36 (b) 100 111 120 130 44 3. Fill in the blanks with prime numbers in ascending order. (a) 2 3 5 ___ 11 ___ 17 19 (b) 53 59 ___ 67 ___ 73

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Teacher’s Guide Sheet 2.3 Concept: Multiples Learning Outcomes: 1. List the multiples of whole numbers. 2. Determine whether a number is the multiple of another number.

Activity 1

Approach Class

Aim List the multiples of 2 and 3

Steps 1. Teacher asks 2 pupils to stand in front of the class and form the first group.

2. Teacher asks 4 pupils to form the 2nd group. 3. Teacher asks another 6 pupils to form the 3rd group. 4. Teacher asks another 8 pupils to form the 4th group. 5. Teacher asks another 10 pupils to form the 5th group. 6. Teacher lists the number of pupils in each group on the board. 7. Steps 1 to 6 are repeated to form the groups of 3, 6, 9 and 12 (multiples of 3). 8. Teacher makes conclusions as below: (a) multiples of 2 are 2, 4, 6, 8, 10, ... (b) multiples of 3 are 3, 6, 9, 12, …

Activity 2

Approach Question and Answer

Aim To determine whether a number is the multiple of another number

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Steps 1. Teacher asks a pupil to draw the following table on the board.

Selected number Divisor of the selected number

Not a divisor of the selected number

2. Teacher fills the first column with selected number, e.g. 10. Then pupils are requested to determine the divisor and not divisor of the selected number from the list of whole numbers within the range 1 to the selected number (that is 1, 2, 3, 4, 5, 6, 7, 8, 9 and 10 when the selected number is 10).

3. Teacher repeats step 2 with other number, e.g. 12. Results of the activity are as shown in the table below.

Selected number Divisor of the selected number

Not a divisor of the selected number

10 1 2 5

10

3 4 6 7 8 9

12 1 2 3 4 6

12

5 7 8 9

10 11

4. Teacher makes the following conclusion based on the table: (a) 10 is a multiple of 1 10 is a multiple of 2 10 is a multiple of 5 10 is a multiple of 10 (b) 12 is a multiple of 1 12 is a multiple of 2

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12 is a multiple of 3 12 is a multiple of 4 12 is a multiple of 6 12 is a multiple of 12 5. Teacher distributes Worksheet 2.3 to test the pupils.

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Worksheet 2.3 1. Identify the multiples of 2, 5 and 8 from the table below.

2. List the multiples of 3 and 7 referring to the diagram below.

3. Fill in the blanks with the correct multiples. (a) (b)

5 10 15 20

1 13 3 8

7 14 6 16

11 4 9 24

2 17 12 32

3

12

18

5 2030

Multiples of 2: Multiples of 5: Multiples of 8:

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(c) (d) (e) 4. Determine whether the following numbers are multiples of 6. (a) 18

(b) 23

4 12 20 28

6

24

36

7

35

14

15

(c) 48

(d) 15

(e) 2134

5. Determine whether the information in each row of the table is correct by marking the

answer (Yes or No) with a tick ( ).

Number Multiple of the number Yes No

4 16

3 10

5 17

6 24

7 35

8 19

12 12

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Teacher’s Guide Sheet 2.4 Concept: Common Multiples Learning Outcomes: 1. Find the common multiples of two or three whole numbers. 2. Determine whether a number is the common multiple of two or three given numbers. Teaching aids: Nails, rope, flash cards, paper clips, whistle and stop watch.

Activity 1

Approach Competition/ games / question and answer

Aim 1. To find the common multiples of two given numbers 2. To find the common multiples of three given numbers

Steps 1. Pupils are divided into 4 groups (7 to 8 persons in a group). 2. First group and second group choose the flash cards with the multiples

of 2 and 3 respectively and hang them on a rope as shown in Diagram 1. 3. Groups 3 and 4 are the supporters of groups 1 and 2 respectively. 4. Each group (groups 3 and 4) have to identify the numbers which are

common in both groups of multiples. 5. The group that spent less time to give the correct answer will be the

winner. 6. Teacher tells the pupils that numbers that are common in both groups of

multiples shown are 6, 12 and 18. 7. Conclusion by teacher: Common multiples of 2 and 3 are 6, 12, 18, 24…

8. Teacher asks the pupils to identify the multiples of 4 from a bundle of

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flash cards and hang them on a rope. See Diagram 2. 9. Teacher asks pupils to state numbers which are common in the lists of

multiples of 2, 3 and 4. 10. Teacher or pupil then hangs the flash card with the number that has

been stated in step 9 that is ‘12’ on the rope (below the label “Common multiples of 2, 3 and 4”). See Diagram 3.

11. Teacher makes conclusion: The first common multiple of 2, 3 and 4 is 12.

Activity 2

Approach Discussion

Aim To determine whether a number is a common multiple of: (i) two given numbers

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(ii) three given numbers

Steps 1. Teacher writes the number ‘12’ on the board. 2. Teacher asks pupils whether the number is divisible by 2 and 3. 3. If the number ‘12’ is divisible by 2 and 3, 12 is a common multiple of 2

and 3. 4. Steps 1 to 3 are repeated with other numbers. Refer to Table 1. 5. Teacher concludes that steps 1 to 3 can be used as a method to

determine whether a number is a common multiple of other numbers. 6. Steps 1 to 4 are repeated to identify common multiples of three numbers

(2, 3, and 4). Refer to Table 2. 7. Teacher makes a conclusion from the activity in step 6. 8. Teacher asks pupils to answer Worksheet 2.4.

Table 1

Number Divisible by 2 and 3 Not divisible by 2 and 3

16

18

7

12

24

Other numbers ? ?

Columns 2 and 3 are completed by pupils. Teacher chooses other numbers. Teacher makes a conclusion:

A number which is divisible by two numbers is a common multiple of the two numbers.

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Table 2

Number Divisible by 2, 3 & 4 Not divisible by 2, 3 & 4

12

9

24

36

15

14

Other numbers ? ?

Columns 2 and 3 are confirmed by pupils. Teacher chooses other numbers. Teacher makes a conclusion:

A number which is divisible by three numbers is a common multiple of the three numbers.

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Worksheet 2.4 1. Based on the diagram, list the multiples and common multiples of the given numbers.

a) 2 and 6

b) 6 and 12

2. Fill in the blanks with multiples and state the multiples of 3 and 4.

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3. List first three common multiples of the numbers given. (a) First three common multiples of 3 and 4: _______, _______, _______

(b) First three common multiples of 5 and 7: _______, _______, _______

(c) First three common multiples of 3, 5 and 9: _______, _______, _______ 4. Determine whether the given statement is true or false by filling the space with the correct word. Prove your answer.

True/False Proof

(a) 72 is a common multiple of 6 and 7.

(b) 36 is a common multiple of 4 and 8.

(c) 144 is a common multiple of 3, 8 and 12.

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Teacher’s Guide Sheet 2.5 Concept: Lowest Common Multiple (LCM) Learning Outcome: Determine the LCM of two or three given numbers

Activity

Approach Discussion

Aim To find the lowest common multiple of:

(a) two given numbers (b) three given numbers

Steps 1. Teacher asks pupils to find the lowest common multiple of the following numbers using listing method:

(a) 4 and 6 (b) 2 and 3 2. Teacher shows algorithm method to find the LCM.

LCM of 4 and 6 = 2 × 2 × 3 = 12

LCM of 2 and 3 = 2 × 3 = 6 (For cases where both numbers are not divisible by any numbers except

1, teacher explains that the LCM is the product of the two numbers. Pupils are given Worksheet 2.5 and requested to answer questions 1(a) and 1(c).)

(Emphasise that the LCM is the product of the divisors)

(Emphasise that the division is repeated until the quotients are 1)

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3. Teacher shows to the pupils how to find the LCM of (a) 4, 6 and 8

The LCM of 4, 6 and 8 is 2 × 2 × 2 × 3 = 24. (b) 6, 10 and 15

The LCM of 6, 10 and 15 is 2 × 3 × 5 = 30. (c) 2, 3 and 5

The LCM of 2, 3 and 5 is 2 × 3 × 5 = 30. (For cases where three numbers are not divisible by any numbers except

1, teacher explains that the LCM is the product of the three numbers.) 4. Other questions in Worksheet 2.5 are given as homework.

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Worksheet 2.5 1. Find the lowest common multiple (LCM) using the algorithm method: (a) 6, 8

LCM of 6 and 8 is ________. (b) 12, 15 LCM of 12 and 15 is ________. (c) 4, 5 LCM of 4 and 5 is ________. (d) 6, 7 LCM of 6 and 7 is ________.

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2. Find the lowest common multiple (LCM) of the following numbers using the algorithm method.

(a) 2, 8, 10 LCM of 2, 8 and 10 is ________. (b) 6, 9, 12 LCM of 6, 9 and 12 is ________. (c) 4, 9, 36 LCM of 4, 9 and 36 is ________. (d) 5, 10, 14 LCM of 5, 10 and 14 is ________. (e) 12, 14, 27 LCM of 12, 14 and 27 is ________.

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3. Fill in the blanks with suitable numbers. (a) (b)

4. Fill in the blanks with suitable numbers. (a) The lowest common multiple of _______ and 5 is 20. (b) The lowest common multiple of 6 and _______ is 24. (c) The lowest common multiple of _______, 3 and _______ is 12.

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Teacher’s Guide Sheet 2.6 Concept: Factors Learning Outcomes: 1. List factors of whole numbers 2. Determine whether a number is a factor of another whole number Teaching aids: Concrete materials

Activity

Approach Acting/game

Aim 1. To identify whether a number is a factor of another number.

2. To find the factors of given numbers.

Steps 1. Teacher randomly selects six pupils. 2. Teacher asks the six pupils to form a group. 3. Then teacher asks the six pupils to form two groups with equal number

of members. 4. Teacher shows the following table and other pupils are asked to record

the results of steps 2 and 3 by putting a tick ( ) at the appropriate place as shown.

Number of groups with equal number of members

The group/groups can be formed

The group/groups cannot be formed

1

2

3

4

5

6

5. Step 3 is repeated to form three, four, five and six groups and to

complete the table.

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6. Teacher asks pupils to divide 6 by 1, 2, 3, 4, 5 and 6 using the method as below:

7. Based on the table and the divisions in step 6, teacher makes the

conclusion about factors of a number. 8. Teacher asks pupils to repeat steps 1 to 6 using other numbers like 7, 10

… and find the factors of the numbers. 9. Pupils answer the questions in the worksheet in pairs.

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Worksheet 2.6 1. Mark “ ” if true and “ ” if false.

Statement True/False

2 is divisible by 1

6 is divisible by 2

10 is divisible by 5

10 is divisible by 3

12 is divisible by 7

2. State the correct answer by putting a tick ( ) into the appropriate space.

Question Yes No

Is 2 a factor of 6?

Is 3 a factor of 6?

Is 4 a factor of 9?

Is 6 a factor of 20?

Is 10 a factor of 20?

3. Circle the number in the box if it is the factor of the given number.

(a) 8 1 2 3 4 5 6 7 8 9 10

(b) 12 1 2 3 4 5 6 7 8 9 10 12 14 15

(c) 15 1 2 3 4 5 6 7 8 9 10 12 15

(d) 20 1 2 3 4 5 6 7 8 9 10 15 20 25

(e) 32 1 2 4 6 7 8 10 16 30 32

4. Determine the factors of the following numbers. (a) 9 (b) 18 (c) 22

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(d) 25 (e) 30

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Teacher’s Guide Sheet 2.7 Concept: Prime Factors Learning Outcomes: 1. Find prime factor(s) of whole numbers 2. Determine whether a number is a prime factor of another whole number Teaching aids: Manila cards, marker pen, plastic bags, scissors, cellophane tape, string, a hole punch.

Activity

Approach Games

Aim To determine whether a factor is a prime factor and find the prime factor(s) of

a number.

Steps 1. Teacher prepares four sets of flash cards (label as Set 1, Set 2, Set 3 and Set 4) with whole numbers 1 to 18 and a piece of manila card as shown in the diagram.

2. Teacher hangs the manila card in front of the class and asks a pupil to

choose a whole number from Set 1 flash cards and put it into the

Plastic bag

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respective plastic bag. 3. Teacher asks another pupil to choose numbers which are factors of the

selected whole number from Set 2 flash cards and put them into the respective plastic bags.

4. From the list of factors, pupils identify factors which are prime numbers. Then teacher asks a pupil to show the correct answer by placing the appropriate flash cards (select from Set 3) into the respective plastic bags.

5. Finally, a pupil is asked to identify the prime factors and then show the correct answer by placing the appropriate flash cards (select from Set 4) into the respective plastic bags. Following is a possible result of the activity.

6. Repeat the activity by involving other whole numbers. 7. Pupils answer the questions in Worksheet 2.7 in groups of four.

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Worksheet 2.7 1. Determine whether the given statement is true or false. Show your answer using the

symbol “ ”.

Statement True False

2 is a prime factor of 6

7 is a prime factor of 21

3 is a prime factor of 8

5 is a prime factor of 15

3 is a prime factor of 17

2. Use the symbol “ ” to show your answer.

No. Factor Prime factor True False

(a) 2 1, 2 2

(b) 3 1, 3 3

(c) 9 1, 3, 9 1, 9

(d) 12 1, 2, 3, 4, 6, 12 2, 3, 4

(e) 18 1, 2, 3, 6, 9, 18 2, 3

3. Circle the prime factor(s) of the given number.

No. List of factors

(a) 8 1 2 4 8

(b) 10 1 2 5 10

(c) 15 1 3 5 15

(d) 20 1 2 4 5 10 20

(e) 28 1 2 4 7 14 28

4. Fill in the blanks. (a) 14 Factors: _______, _______, _______, _______ Prime factors: _______, _______

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(b) 16 Factors: _______, _______, _______, _______, _______ Prime factor: _______ (c) 21 Factors: _______, _______, _______, _______ Prime factors: _______, _______ (d) 35 Factors: _______, _______, _______, _______ Prime factors: _______, _______ (e) 33 Factors: _______, _______, _______, _______ Prime factors: _______, _______

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Teacher’s Guide Sheet 2.8 Concept: Common Factors Learning Outcomes: 1. Find common factors of two or three whole numbers 2. Determine whether a number is a common factor of two or three given whole numbers Teaching aids: Manila cards, marker pen, plastic bags, scissors, cellophane tape, string, a hole punch.

Activity

Approach Games

Aim 1. To determine whether a number is a common factor of two or three given

whole numbers. 2. To find the common factor(s) of two or three whole numbers.

Steps 1. Prepares six sets of flash cards (label as Set 1, Set 2, Set 3, Set 4, Set 5 and Set 6) with whole numbers 1 to 18 and a piece of manila card as shown in the diagram.

2. Hangs the manila card in front of the class and asks a pupil to choose

three flash cards from Set 1 and put them into the first plastic bag of first, second and third rows.

Plastic bag

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3. Asks another three pupils to determine the factors of the selected whole numbers. They show the correct answer by selecting the related flash cards from Set 2, Set 3 and Set 4, and place them accordingly into the plastic bags.

4. Finally, a pupil is asked to fill the last row of plastic bags by selecting the appropriate flash cards from Set 5 and Set 6. Following is an example of the result of the activity.

5. Teacher explains what common factor is. 6. Repeat the activity by involving other whole numbers (including two

whole numbers) and other pupils. 7. Pupils answer the questions in Worksheet 2.8 in groups of four.

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Worksheet 2.8 1. Show your answer using the symbol “ ”.

Number Factor Common factor True False

(a) 2 3

1, 2 1, 3

1

(b) 4 6

1, 2, 4 1, 2, 3, 6

1, 2

(c) 6 9

1, 2, 3, 6 1, 3, 9

1, 2

(d) 8 9

1, 2, 4, 8 1, 3, 9

1, 3

(e) 12 14

1, 2, 3, 4, 6, 12 1, 2, 7, 14

1, 2

2. Find the common factors of the following numbers. (a) 6: 1, 2, 3, 6 8: 1, 2, 4, 8 Common factors: _______, _______ (b) 5: 1, 5 15: 1, 3, 5, 15 Common factors: _______, _______ (c) 8: 1, 2, 4, 8 20: 1, 2, 4, 5, 10, 20 Common factors: _______, _______, _______ (d) 8: 1, 2, 4, 8 12: 1, 2, 3, 4, 6, 12 18: 1, 2, 3, 6, 9, 18 Common factors: _______, _______ (e) 10: 1, 2, 5, 10 20: 1, 2, 4, 5, 10, 20 25: 1, 5, 25 Common factors: _______, _______

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3. Circle the common factors of the given numbers.

Number Common factor

(a) 8 and 10 1 2 3 4 5 8 10

(b) 6 and 12 1 2 3 4 5 6 12

(c) 10 and 12 1 2 3 4 5 8 10 12

(d) 4, 6 and 8 1 2 3 4 5 6 7 8

(e) 10, 12 and 18 1 2 3 4 5 6 9 10 11 12

4. List the factors and the common factors of the given numbers. (a) 9: _______, _______, _______ 12: _______, _______, _______, _______, _______, _______ Common factors of 9 and 12: _______, _______ (b) 6: _______, _______, _______, _______ 15: _______, _______, _______, _______ Common factors of 6 and 15: _______, _______ (c) 12: _______, _______, _______, _______, _______, _______ 24: _______, _______, _______, _______, _______, _______, _______, _______ Common factors of 12 and 24: _______, _______, _______, _______, _______, _______ (d) 4: _______, _______, _______ 6: _______, _______, _______, _______ 8: _______, _______, _______, _______ Common factors of 4, 6 and 8: _______, _______

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(e) 12: _______, _______, _______, _______, _______, _______ 20: _______, _______, _______, _______, _______, _______ 30: _______, _______, _______, _______, _______, _______, _______,

_______ Common factors of 12, 20 and 30: _______, _______

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Teacher’s Guide Sheet 2.9 Concept: Highest Common Factor (HCF) Learning Outcome: Determine the HCF of two or three given numbers Teaching aids: Manila cards, marker pen, plastic bags, scissors, cellophane tape, string, a hole punch.

Activity 1

Approach Games

Aim 1. To find the highest common factor of: (a) two given numbers (b) three given numbers using listing method.

Steps 1. Prepares eight sets of flash cards (label as Set 1, Set 2, Set 3, Set 4, Set 5, Set 6, Set 7 and Set 8) with whole numbers 1 to 18 and a piece of manila card as shown in the diagram.

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2. Hangs the manila card in front of the class and asks a pupil to choose three flash cards from Set 1 and put them into the first plastic bag of first, second and third rows.

3. Asks another three pupils to determine the factors of the selected whole numbers. They show the correct answer by selecting the related flash cards from Set 2, Set 3 and Set 4, and place them accordingly into the plastic bags.

4. Guide pupils to determine the common factors of the three whole numbers and then randomly select a pupil to fill the plastic bags in fourth row with the appropriate flash cards selected from Set 5 (to fill the first three plastic bags) and Set 6 (to fill other plastic bags in the row).

5. Finally, a pupil is guided to fill the last row of plastic bags by selecting the appropriate flash cards from Set 7 (to fill the first three plastic bags) and Set 8 (to fill the other plastic bag in the row). Following is an example of the result of the activity.

6. Repeat the activity by involving other whole numbers and other pupils. 7. Pupils answer the questions in Worksheet 2.9 in groups of four.

Activity 2

Approach Discussion

Aim To find the highest common factor (HCF) of: (i) two given numbers (ii) three given numbers

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using algorithm method

Steps 1. Teacher shows how to determine the HCF of two and three whole numbers using the algorithm method.

(a) (b)

2. Based on the examples shown, teacher explains how to find the HCF

using the algorithm method. Emphasise that only common divisor is used for each division.

3. Give a few examples and ask the pupils to determine the HCF using both listing and algorithm methods.

4. Let the pupils discuss which method is preferable and why. 5. Pupils answer questions in Worksheet 2.9 in groups of 4.

HCF of 12 and 18 = 2 × 3 = 6

HCF of 12, 18 and 30 = 2 × 3 = 6

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Worksheet 2.9 1. Find the common factors and the highest common factor (HCF) of the following

numbers. (a) 6: 1, 2, 3, 6 10: 1, 2, 5, 10 Common factors: _______, _______ HCF: _______ (b) 5: 1, 5 20: 1, 2, 4, 5, 10, 20 Common factors: _______, _______ HCF: _______ (c) 8: 1, 2, 4, 8 16: 1, 2, 4, 8, 16 Common factors: _______, _______, _______, _______ HCF: _______ (d) 8: 1, 2, 4, 8 14: 1, 2, 7, 14 18: 1, 2, 3, 6, 9, 18 Common factors: _______, _______ HCF: _______ (e) 10: 1, 2, 5, 10 12: 1, 2, 3, 4, 6, 12 30: 1, 2, 3, 5, 6, 10, 15, 30 Common factors: _______, _______ HCF: ______

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2. Complete all the blanks with the factors, common factors and highest common factor of the given numbers.

(a) 6: 1, 2, 3, _______ 9: 1, 3, _______ Common factors: _______, _______ HCF: ______ (b) 4: 1, _______, 4 10: 1, 2, 5, _______ Common factors: _______, _______ HCF: _______ (c) 6: 1, _______, 3, 6 10: 1, _______, 5, 10 Common factors: _______, _______ HCF: _______ (d) 10: 1, _______, 5, 10 12: 1, 2, 3, _______, 6, 12 Common factors: _______, _______ HCF: _______ (e) 12: 1, 2, 3, _______, 6, 12 15: 1, _______, 5, 15 Common factors: _______, _______ HCF: _______

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3. Find the highest common factor (HCF) of the following numbers using algorithm method.

(a) (b)

(c) (d)

(e)

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Test 2.1 Name: __________________________________________________________

Class: __________________________________________________________

1. Complete the following number sequences: (a) 103, 106, 109, 112, _____, _____ (b) 15, _____, 11, 9, _____, 5 (c) 4, 8, _____, 32, _____

(d) 31 , 5

3 , 7 , 7 , 119

2. Fill in the blanks with suitable prime numbers. (a) 11 + _____ + _____ = 16 (b) _____ + 3 + _____ = 10 (c) 14 – _____ – _____ = 4 (d) 19 – _____ – _____ = 9 3. Determine whether the following lists of multiples are correct. Show your answer using

the symbol “ ”.

Number List of multiples Correct Incorrect

4 16, 20, 24, 28, 32, 36

7 21, 28, 34, 42, 49, 56

6 24, 30, 36, 42, 48, 53

8 24, 32, 40, 48, 56, 64

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4. Circle the number (in the brackets) which is the common multiple of the given numbers. (a) 3 and 4

[15, 12, 9] (b) 6 and 8

[24, 12, 20] (c) 5, 6 and 8

[240, 125, 70] (d) 3, 4 and 5

[30, 60, 50] 5. Determine the lowest common multiple of the given numbers: (a) 7 and 8 Answer: (b) 4, 8 and 16 Answer: (c) 3, 4 and 6 Answer:

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Test 2.2 Name: __________________________________________________________

Class: __________________________________________________________

1. Determine whether 6 is the factor of the following numbers and tick the correct answer.

Numbers Yes No

(a) 24

(b) 78

(c) 128

2. List all the factors of the following numbers. (a) 18 (b) 35 (c) 100 3. List all the prime factors of the following numbers. (a) 12 (b) 19 (c) 77

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4. Determine whether the statement is true or false. Show your answer by putting a tick ( ) into the appropriate space.

Statement True False

(a) 3 is the common factor of 15 and 42

(b) 5 is the common factor of 30 and 36

(c) 6 is the common factor of 30, 36 and 136

5. List all the common factors of the following numbers. (a) 12, 18 (b) 25, 35 (c) 21, 28, 35 6. Find the highest common factor (HCF) of the following numbers. (a) 18 and 24 HCF of 18 and 24: _____ (b) 16, 24 and 32 HCF of 16, 24 and 32: _____ (c) 54, 63 and 108 HCF of 54, 63 and 108: _____ 7. 3 is a factor of Q. Q is a factor of 12. State three possible values of Q.

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Answer Worksheet 2.1 1. (a) Yes (b) No (c) No (d) Yes 2. (a) 4 (b) 6 (c) 40 (d) 200 3. (a) 3 (b) 4 (c) 20 (d) 91 4. (a) 8 (b) 27 (c) 16 (d) 40 5. (a) 8 (b) 16 (c) 27 (d) 20 6. (a) 26 (Subtract 2 from the term before it) (b) 17, 23 (Add 3 to get the next term) (c) 4, 32 (Multiply the term before it by 2) (d) 32, 8 (Divide the term before it by 2) Worksheet 2.2 1. 2, 3, 11, 13, 17, 19, 29, 31 2. (a) 17 (b) 111 3. (a) 7, 13 (b) 61, 71 Worksheet 2.3 1. Multiples of 2: 2, 4, 6, 8, 10, 12, 14, 16, 20, 24, 32 Multiples of 5: 5, 10, 15, 20 Multiples of 8: 8, 16, 24, 32 2. Multiples of 3: 3, 6, 9, 21, 42 Multiples of 7: 7, 14, 21, 42 3. (a) 6, 9, 15, 21 (b) 10, 15, 25 (c) 8, 16, 24 (d) 12, 18, 30 (e) 21, 28 4. (a) Yes (b) No (c) Yes (d) No (e) No

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5.

Number Multiple of the number Yes No

4 16

3 10

5 17

6 24

7 35

8 19

12 12 Worksheet 2.4 1. (a) Multiples of 2: 2, 4, 6, 8, 10, 12, 14, 16, 18 Multiples of 6: 6, 12, 18 Common multiples of 2 and 6: 6, 12, 18 (b) Multiples of 6: 6, 12, 18, 24, 30, 36 Multiples of 12: 12, 24, 36 Common multiples of 6 and 12: 12, 24, 36 2. Multiples of 3: 12, 15, 24 Multiples of 4: 16, 20 Common multiples of 3 and 4 are 12 and 24. 3. (a) First three common multiples of 3 and 4: 12, 24, 36 (b) First three common multiples of 5 and 7: 35, 70, 105 (c) First three common multiples of 3, 5 and 9: 45, 90, 135 4. (a) False (b) False (c) True Worksheet 2.5 1. (a) 24 (b) 60 (c) 20 (d) 42 2. (a) 40 (b) 36 (c) 36 (d) 70 (e) 756

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3. (a) (b)

4. (a) 4 or 20 (b) 8 or 24 (c) 2, 4 or 4, 6 or 6, 12 Worksheet 2.6 1.

Statement True/False

2 is divisible by 1

6 is divisible by 2

10 is divisible by 5

10 is divisible by 3

12 is divisible by 7 2.

Question Yes No

Is 2 a factor of 6?

Is 3 a factor of 6?

Is 4 a factor of 9?

Is 6 a factor of 20?

Is 10 a factor of 20? 3. (a) 1, 2, 4, 8 (b) 1, 2, 3, 4, 6, 12 (c) 1, 3, 5, 15 (d) 1, 2, 4, 5, 10, 20 (e) 1, 2, 4, 8, 16, 32 4. (a) 1, 3, 9 (b) 1, 2, 3, 6, 9, 18 (c) 1, 2, 11, 22 (d) 1, 5, 25 (e) 1, 2, 3, 5, 6, 10, 15, 30 Worksheet 2.7 1. True, True, False, True, False

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2. (a) True (b) True (c) False (d) False (e) True 3. (a) 2 (b) 2, 5 (c) 3, 5 (d) 2, 5 (e) 2, 7 4. (a) Factors: 1, 2, 7, 14 (b) Factors: 1, 2, 4, 8, 16 Prime factors: 2, 7 Prime factor: 2 (c) Factors: 1, 3, 7, 21 (d) Factors: 1, 5, 7, 35 Prime factors: 3, 7 Prime factors: 5, 7 (e) Factors: 1, 3, 11, 33 Prime factors: 3, 11 Worksheet 2.8 1. (a) True (b) True (c) False (d) False (e) True 2. (a) Common factors: 1, 2 (b) Common factors: 1, 5 (c) Common factors: 1, 2, 4 (d) Common factors: 1, 2 (e) Common factors: 1, 5 3. (a) 1, 2 (b) 1, 2, 3, 6 (c) 1, 2 (d) 1, 2 (e) 1, 2 4. (a) 9: 1, 3, 9 (b) 6: 1, 2, 3, 6 12: 1, 2, 3, 4, 6, 12 15: 1, 3, 5, 15 Common factors: 1, 3 Common factors: 1, 3 (c) 12: 1, 2, 3, 4, 6, 12 (d) 4: 1, 2, 4 24: 1, 2, 3, 4, 6, 8, 12, 24 6: 1, 2, 3, 6, Common factors: 1, 2, 3, 4, 6, 12 8: 1, 2, 4, 8 Common factors: 1, 2 (e) 12: 1, 2, 3, 4, 6, 12 20: 1, 2, 4, 5, 10, 20 30: 1, 2, 3, 5, 6, 10, 15, 30 Common factors: 1, 2 Worksheet 2.9 1. (a) Common factors: 1, 2 (b) Common factors: 1, 5 HCF: 2 HCF: 5 (c) Common factors: 1, 2, 4, 8 (d) Common factors: 1, 2 HCF: 8 HCF: 2

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(e) Common factors: 1, 2 HCF: 2 2. (a) 6: 1, 2, 3, 6 (b) 4: 1, 2, 4 9: 1, 3, 9 10: 1, 2, 5, 10 Common factors: 1, 3 Common factors: 1, 2 HCF: 3 HCF: 2 (c) 6: 1, 2, 3, 6 (d) 10: 1, 2, 5, 10 10: 1, 2, 5, 10 12: 1, 2, 3, 4, 6, 12 Common factors: 1, 2 Common factors: 1, 2 HCF: 2 HCF: 2 (e) 12: 1, 2, 3, 4, 6, 12 15: 1, 3, 5, 15 Common factors: 1, 3 HCF: 3 3. (a) HCF: 8 (b) HCF: 6 (c) HCF: 6 (d) HCF: 15 (e) HCF: 12 Test 2.1 1. (a) 115, 118 (b) 13, 7 (c) 16, 64 (d) 5, 9 2. (a) 2, 3 (b) 2, 5 (c) 3, 7 or 5, 5 (d) 3, 7 or 5, 5 3. (a) Correct (b) Incorrect (c) Incorrect (d) Correct 4. (a) 12 (b) 24 (c) 240 (d) 60 5. (a) 56 (b) 16 (c) 12 Test 2.2 1. (a) Yes (b) Yes (c) No 2. (a) 1, 2, 3, 6, 9, 18 (b) 1, 5, 7, 35 (c) 1, 2, 4, 5, 10, 20, 25, 50, 100 3. (a) 2, 3 (b) 19 (c) 7, 11

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4

Statement True False

(a) 3 is the common factor of 15 and 42

(b) 5 is the common factor of 30 and 36

(c) 6 is the common factor of 30, 36 and 136 5 (a) 1, 2, 3, 6 (b) 1, 5 (c) 1, 7 6 (a) 6 (b) 8 (c) 9 7. 3, 6, 12