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Different kinds of numbers

Module by: Siyavula Uploaders. E-mail the author

MATHEMATICS

Grade 8

THE NUMBER SYSTEM

(Natural and whole numbers)

Module 1

DIFFERENT KINDS OF NUMBERS

CLASS ASSIGNMENT1

  • Discover the number system step by step....

1. General: Different kinds of numbers

Provide an example of each of the following numbers:

  • Natural numbers N = {..................................................}
  • Counting numbers N0 = {..................................................}
  • Integers Z+ = {..................................................}

Z- = {..................................................}

  • Rational numbers Q = {..................................................}
  • Irrational numbers Q’ = {..................................................}
  • Real numbers R = {..................................................}

2. Natural numbers

Table 1
Prime numbers ={..................................................} Compound numbers ={..................................................}
Definition: ........................................................................................…………..................................................…………..................................................………….......... Definition: ................................................................…………..........................................................................…………..................................................…………..........

Prime numbers + Compound numbers = Natural numbers

3. Divisibility rules

Do you recall that

Figure 1
Figure 1 (Picture 1.png)

In each instance, select a number that is divisible by the given divisor and try to deduce a rule for each instance.

Table 2
  Number Divisor Divisibility rule
3.1   2  
3.2   3  
3.3   4  
3.4   5  
3.5   6  
3.6   8  
3.7   9  
3.8   10  
3.9   11  

4. Determine by which numbers (1.3.1 - 1.3.9) 61 226 is divisible and provide a reason for each.

5. Explain what you understand the following terms to mean:

5.1 Multiple:

5.2 Factor:

5.3 Prime number:

5.4 Prime factor:

5.5 Even numbers and odd numbers:

  • How do you determine the factors of a number? Look at the following.....e.g. F24 = {1; 2; 3; 4; 6; 8; 12; 24} 1 x 24; 2 x 12; 3 x 8; 4 x 6

6. Determine the factors of 48.

7.Write out all the multiples of 6 between 23 and 56.

8. Determine the prime numbers between 17 and 78.

9 Determine all odd compound numbers between 16 and 50.

10 Write down all the factors of 50 that are prime numbers.

11. Write down all the factors of 50 that are compound numbers.

12. Explain: Cube numbers. Write down the first 6 cube numbers.

13. Explain : Square numbers. Write down the first 10 square numbers.

HOMEWORK ASSIGNMENT 1

1. Write the definition for each of the following:

1.1 Rational number:

1.2 Prime number:

1.3 Compound numbers:

1.4 Prime factors:

2. Select from {0; 1; 2; 3; 4; ... ; 36} and write down:

2.1 The first two compound numbers

2.2 Odd numbers that are not prime numbers

2.3 Multiples of 6

2.4 Factors of 12

2.5 Prime factors of 12

2.6 Factors of 36

3. Which of the following numbers -9/3; 7/0; 0; 3; -9; 16; 2 1/3 are:

3.1 Integers?

3.2 Rational numbers?

3.3 Non-real numbers?

4. Tabulate the following:

4.1 Natural numbers < 5 ...........................................................................

4.2 Prime numbers < 10 ...........................................................................

4.3 The first four multiples of 12 ...........................................................................

4.4 The first four square numbers ...........................................................................

Learning unit 1 Assessment 1.1

Table 3
Assessment of myself:   by myself:   Assessment by Teacher:
I can…     1 2 3 4   Critical Outcomes 1 2 3 4
give examples of different types of numbers; (Lo 1.1)                     Critical and creative thinking        
define prime numbers; (Lo 1.1)                     Collaborating        
define compound numbers; (Lo 1.1)                     Organising en managing        
apply divisibility rules; (Lo 1.2.6)                     Processing of information        
determine multiples of a number; (Lo 1.2.6)                     Communication        
determine factors of a number; (Lo 1.2.6)                     Problem solving        
determine prime numbers and prime factors; (Lo 1.2.6)                     Independence        
determine even and odd numbers. (Lo 1.1)                              

good average not so good

Table 4
Comments by the learner:     My plan of action:     My marks:
I am very satisfied with the standard of my work.     <   Date:      
I am satisfied with the steady progress I have made.         Out of:      
I have worked hard, but my achievement is not satisfactory.         Learner:      
I did not give my best.     >          
Table 5
Comments by parents:   Comments by teacher:
     
     
     
Signature: Date:   Signature: Date:

Assessment

Table 6
Learning outcomes(LOs)
 
LO 1
Numbers, Operations and RelationshipsThe learner will be able to recognise, describe and represent numbers and their relationships, and to count, estimate, calculate and check with competence and confidence in solving problems.
Assessment standards(ASs)
 
We know this when the learner :
1.1 describes and illustrates the historical and cultural development of numbers;
1.2 recognises, classifies and represents the following numbers in order to describe and compare them:1.2.3 numbers written in exponent form; including squares and cubes of natural numbers and their square roots and cube roots;1.2.6 multiples and factors;1.2.7 irrational numbers in the context of measurement (e.g. square and cube roots on non-perfect squares and cubes);

MemorandumACTIVITY 1

2. {2, 3, 5, 7, . . . }

Two factors: 1 and itself

{4, 6, 8, 9, . . . }

More than 2 factors

  • Own choice: Ends on even numbers
  • Sum of all the numbers ÷ 3
  • Last numbers ÷ 4: e.g. 84 ÷ 4 = 21
  • Ends on 0 / 5
  • Divisible by 2 and 3
  • Last 3 numbers ÷ 8: e.g. 3 720 ÷ 8 = 90
  • Add all the numbers ÷ 9
  • Ends on 0
  • e.g. 2 6 8 2 + 8 = 10, 10 – 10 = 0

0 ÷ 11 = 0, 4 + 6 = 10

4. 2; 3; 4; 5; 6; 7; 8; 9; 10; 11

√ × × × × × × × × √

  • Count on, e.g. in 3’s: Number ÷ 3
  • Number that can divide into another number
  • Number with 2 factors: 1 and itself
  • Prime number that can divide into another number
  • Even: (Ends on even numbers) [divisible by 2]

Uneven: (Not divisible by 2)

6. F48 = {1, 2, 3, 4, 6, 8, 12, 16, 24, 48}

7. {24, 30, 36, 42, 48, 54}

8. {19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73}

9. {21, 25, 27, 33, 35, 39, 45, 49}

10. {2, 5}

11. {10, 25, 50}

12. x³ (number)³: 1, 8, 27, 64, 125, 216

13. x² (number)²: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100

HOMEWORK ASSIGNMENT 1

1.1: , b ≠ 0 (Decimal: recurring or ends)

  • :Number with factors: 1 and itself
  • :Number with more than two factors
  • :Prime number that can divide onto a number
  • :4, 6
  • :1, 9, 15, 21, 25, 27, 33, 35
  • :6, 12, 18, 24, 30, 36
  • :1, 2, 3, 4, 6, 12
  • :2, 3
  • :1, 2, 3, 4, 6, 9, 12, 18, 36
  • :-, 0, 3, -9, 16
  • :-, 0, 3 -9, 16, 2
  • :
  • :1, 2, 3, 4
  • :2, 3, 5, 7
  • :12, 24, 36, 48
  • :1, 4, 9, 16

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