OpenStax-CNX module: m31086 1 Different kinds of numbers ∗ Siyavula Uploaders This work is produced by OpenStax-CNX and licensed under the † Creative Commons Attribution License 3.0 1 MATHEMATICS 2 Grade 8 3 THE NUMBER SYSTEM 4 (Natural and whole numbers) 5 Module 1 6 DIFFERENT KINDS OF NUMBERS CLASS ASSIGNMENT1 • Discover the number system step by step.... 1. General: Dierent 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 ∗ Version 1.1: Aug 7, 2009 7:55 am -0500 † http://creativecommons.org/licenses/by/3.0/ http://cnx.org/content/m31086/1.1/ OpenStax-CNX module: m31086 2 Prime numbers ={..................................................} Compound ={..................................................} numbers Denition: ........................................................................................ Denition: ................................................................ . . .. . .. . .. . ................................................... . . .. ..... ... ... ... ............ .. . ..... Table 1 Prime numbers + Compound numbers = Natural numbers 3. Divisibility rules Do you recall that Figure 1 In each instance, select a number that is divisible by the given divisor and try to deduce a rule for each instance. Number Divisor 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 Divisibility rule Table 2 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: http://cnx.org/content/m31086/1.1/ OpenStax-CNX module: m31086 3 • 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 rst 6 cube numbers. 13. Explain : Square numbers. Write down the rst 10 square numbers. HOMEWORK ASSIGNMENT 1 1. Write the denition 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 rst 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 rst four multiples of 12 ........................................................................... 4.4 The rst four square numbers ........................................................................... Learning unit 1 Assessment 1.1 Assessment by myself: of myself: Assessment by Teacher: I can. . . 1 [U+F04A] [U+F04B] [U+F04C] 2 3 4 continued on next page http://cnx.org/content/m31086/1.1/ Critical1 Outcomes 2 3 4 OpenStax-CNX module: m31086 4 give examples of different types of numbers; (Lo 1.1) Critical and creative thinking dene prime numbers; (Lo 1.1) Collaborating dene compound numbers; (Lo 1.1) Organising en managing apply divisibility rules; (Lo 1.2.6) Processing of information continued on next page http://cnx.org/content/m31086/1.1/ OpenStax-CNX module: m31086 5 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) Table 3 [U+F04A] good [U+F04B] Comments by the learner: average [U+F04C] My plan of action: not so good My marks: continued on next page http://cnx.org/content/m31086/1.1/ OpenStax-CNX module: m31086 6 I am very satised with the standard of my work. < Date : I am satised 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 4 Comments by parents: Comments by teacher: Signature: Signature: Date : Table 5 http://cnx.org/content/m31086/1.1/ Date : OpenStax-CNX module: m31086 7 7 Assessment 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 condence 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, classies 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); Table 6 8 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. 10; 11 √ 2; 3; 4; 5; 6; 7; 8; 9; √ ×××××××× • • • • • 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. F 48 = {1, 2, 3, 4, 6, 8, 12, 16, 24, 48} http://cnx.org/content/m31086/1.1/ OpenStax-CNX module: m31086 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. x 3 (number)3 : 1, 8, 27, 64, 125, 216 13. x 2 (number)2 : 1, 4, 9, 16, 25, 36, 49, 64, 81, 100 8.1 HOMEWORK ASSIGNMENT 1 1.1: , b 6= 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, :1, :6, :1, :2, :1, 6 9, 15, 21, 25, 27, 33, 35 12, 18, 24, 30, 36 2, 3, 4, 6, 12 3 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 http://cnx.org/content/m31086/1.1/ 8

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