Square, Cube & Roots: More Examples (I)

2011, 28 Jan: Activity - Questions for Discussion

Workbook Page 3

Question 15:

(a) Find the prime factorisation of the following numbers and write your answers in index notation.

(i) 27

(ii) 99

(iii) 135

(b) Hence, find

(i) the HCF of 27, 99 and 135 in prime factorisation form

(ii) the LCM of 27, 99 and 135 in prime factorisation form

Question 14:

(a) Find the prime factorisation of 3375 and write your answer in index notation.

(b) Hence, deduce and write down

(i) the smallest 2-digit number that is a factor of 3375

(ii) the largest 2 digit number that is a factor of 3375

(iii) the smallest 3-digit number that is a factor of 3375

(iv) the smallest 4-digit number that is a factor of 3375

Question 17:

(a) Find the smallest possible value of

(i) a whole number y if it leaves a remainder of 3 when divided by 5, 6 or 9

(ii) a whole number z if it leaves a remainder of 2 when divided by 4, 5 or 6

(b) Hence, calculate the

(i) HCF of y and z

(ii) LCM of y and z

Lesson 2 (02) Investigation - Family "DO"

Family "DO":
58, 74, 102, 50, 46, 282

(a) Describe as many relationship(s) as you could about the numbers.
(b) Add 3 members to Family "DO" that satisfy the relationship(s) you described in (a)

Note: In your description, comment

• Are the numbers even or odd? or there is no pattern at all?
• Are there prime numbers in this family?
• What are these numbers divisible by?
• What are the common factors of these numbers? How do you find them?
• What is the highest common factor? How do you find it?
• What is the lowest common multiple? How do you find it?

Lesson 2 (02) Investigation - Family "RE"

Family "RE":
75, 305, 200, 130, 155, 550

(a) Describe as many relationship(s) as you could about the numbers.
(b) Add 3 members to Family "RE" that satisfy the relationship(s) you described in (a)

• Are the numbers even or odd? or there is no pattern at all?
• Are there prime numbers in this family?
• What are these numbers divisible by?
• What are the common factors of these numbers? How do you find them?
• What is the highest common factor? How do you find it?
• What is the lowest common multiple? How do you find it?

Lesson 2 (02) Investigation - Family "MI"

Family "MI":
80, 150, 400, 530, 1000, 370

(a) Describe as many relationship(s) as you could about the numbers.
(b) Add 3 members to Family "MI" that satisfy the relationship(s) you described in (a)

• Are the numbers even or odd? or there is no pattern at all?
• Are there prime numbers in this family?
• What are these numbers divisible by?
• What are the common factors of these numbers? How do you find them?
• What is the highest common factor? How do you find it?
• What is the lowest common multiple? How do you find it?

Lesson 2 (02) Investigation - Family "FA"

Family "FA":
87, 210, 249, 303, 705, 966

(a) Describe as many relationship(s) as you could about the numbers.
(b) Add 3 members to Family "FA" that satisfy the relationship(s) you described in (a)

• Are the numbers even or odd? or there is no pattern at all?
• Are there prime numbers in this family?
• What are these numbers divisible by?
• What are the common factors of these numbers? How do you find them?
• What is the highest common factor? How do you find it?
• What is the lowest common multiple? How do you find it?

Lesson 2 (02) Investigation - Family "SO"

Family "SO":
64, 100, 240, 304, 396, 516

(a) Describe as many relationship(s) as you could about the numbers.
(b) Add 3 members to Family "SO" that satisfy the relationship(s) you described in (a)

• Are the numbers even or odd? or there is no pattern at all?
• Are there prime numbers in this family?
• What are these numbers divisible by?
• What are the common factors of these numbers? How do you find them?
• What is the highest common factor? How do you find it?
• What is the lowest common multiple? How do you find it?

Lesson 2 (02) Investigation - Family "LA"

Family "LA":
81, 90, 234, 504, 333, 1350

(a) Describe as many relationship(s) as you could about the numbers.
(b) Add 3 members to Family "LA" that satisfy the relationship(s) you described in (a)

• Are the numbers even or odd? or there is no pattern at all?
• Are there prime numbers in this family?
• What are these numbers divisible by?
• What are the common factors of these numbers? How do you find them?
• What is the highest common factor? How do you find it?
• What is the lowest common multiple? How do you find it?

Lesson 2 (02) Investigation - Family "TI"

Family "TI":
72, 138, 174, 420, 612, 702

(a) Describe as many relationship(s) as you could about the numbers.
(b) Add 3 members to Family "TI" that satisfy the relationship(s) you described in (a)

• Are the numbers even or odd? or there is no pattern at all?
• Are there prime numbers in this family?
• What are these numbers divisible by?
• What are the common factors of these numbers? How do you find them?
• What is the highest common factor? How do you find it?
• What is the lowest common multiple? How do you find it?

20110118: We have a Problem

In S1-02, there are 4 groups.
3 groups have 6 members, 1 group has 5 members.
Every member contribute points to the group score.

To be fair to the group with 5 members only, 2 suggestions were given:

Suggestion 1: Ben suggested to find the average of the total points contributed by the members
Suggestion 2: Dexter suggested multiply the points of the 3 groups by 5 and the points of the group with 5 members by 6.

Are both suggestions workable.
Justify your answer.