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MIP2601 Exam pack 2024(Questions and answers)
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MIP2601 EXAMPACK 2024
QUESTIONS AND
ANSWERS
FOR ASSISTANCE CONTACT
EMAIL:gabrielmusyoka940@gmail.com
, Mathematics for Intermediate Phase Teachers I
MIP 2601
Year module
Department of Mathematics Education
BAR CODE
Define tomorrow
UNISA
, 2
Contents
INTRODUCTION ..................................................................................................................................... 5
MODULE MIP1501 LEARNING UNIT 1 ......................................................................................... 10
NUMERATION SYSTEMS ................................................................................................................................ 10
INTRODUCTION ............................................................................................................................................... 10
1.1. THE HISTORY OF NUMBERS ................................................................................................... 10
1.2 THE HINDU-ARABIC NUMBER SYSTEM .................................................................................. 14
1.2.1 Base 60 number system ................................................................................................................ 14
1.2.2 Base 12 number system ................................................................................................................ 15
1.2.3 The base 10 number system ......................................................................................................... 16
1.3 THE REAL NUMBER SYSTEM .................................................................................................. 17
1.3.1 Natural numbers ............................................................................................................................ 17
1.3.2 Integers .......................................................................................................................................... 17
1.3.3 Rational numbers ........................................................................................................................... 18
1.3.4 Irrational numbers .......................................................................................................................... 20
1.3.5 Non-real or imaginary numbers ..................................................................................................... 21
1.3.6 Absolute value ............................................................................................................................... 21
1.3.7 Summary of the real and complex number systems ..................................................................... 22
TEST YOUR KNOWLEDGE.............................................................................................................................. 22
CONCLUSION ................................................................................................................................................... 23
ADDITIONAL LEARNING EXPERIENCES .................................................................................................. 23
MODULE MIP1501 LEARNING UNIT 2 .......................................................................................... 24
NUMBER SENSE .............................................................................................................................................. 24
INTRODUCTION ............................................................................................................................................... 24
2.1 THE DEVELOPMENT OF NUMBER SENSE ............................................................................. 24
2.1.1 The meaning of numbers ............................................................................................................... 25
ACTIVITY 2.1.1(a) ......................................................................................................................................... 27
2.1.2 The properties of numbers ............................................................................................................ 30
2.1.3 Types of numbers .......................................................................................................................... 32
2.2 CHANGE IN NUMBERS .............................................................................................................. 37
2.2.1 Conceptual fields ........................................................................................................................... 38
2.2.2 Calculation methods and strategies .............................................................................................. 42
TEST YOUR KNOWLEDGE.............................................................................................................................. 49
CONCLUSION ................................................................................................................................................... 49
ADDITIONAL LEARNING EXPERIENCES ...................................................................................................... 50
MODULE MIP1501 LEARNING UNIT 3 ........................................................................................ 51
PROBLEM SOLVING ........................................................................................................................................ 51
INTRODUCTION ............................................................................................................................................... 51
3.1 HIGHER ORDER NUMERICAL REASONING ........................................................................... 51
3.1.1 Level 1: Mathematical knowledge ................................................................................................. 52
, 3
3.1.2 Level 2: Routine Procedures ......................................................................................................... 54
3.1.3 Level 3: Complex Procedures ....................................................................................................... 56
3.1.4 Level 4: Problem Solving ............................................................................................................... 58
3.2 NUMBER PROBLEMS ................................................................................................................ 61
3.2.1 The situational nature of number problems................................................................................... 62
3.2.2 The construction of number problems ........................................................................................... 66
3.2.3 Critical problem solving skills ......................................................................................................... 70
3.2.4 Heuristics ....................................................................................................................................... 73
A Brief History of Heuristics .......................................................................................................................... 73
Why Do We Use Heuristics? ........................................................................................................................ 73
Types of Heuristics........................................................................................................................................ 74
Heuristics Can Lead to Bias ......................................................................................................................... 74
A Word From Verywell .................................................................................................................................. 75
TEST YOUR KNOWLEDGE.............................................................................................................................. 75
CONCLUSION ................................................................................................................................................... 75
ADDITIONAL LEARNING EXPERIENCES ...................................................................................................... 76
MODULE MIP1501 LEARNING UNIT 4 ........................................................................................... 77
RATIONAL NUMBERS ...................................................................................................................................... 77
INTRODUCTION ............................................................................................................................................... 77
4.1 THE FRACTIONAL CONCEPT ................................................................................................... 78
4.1.1 Common fractions .......................................................................................................................... 81
4.1.2 Decimal fractions ........................................................................................................................... 84
4.1.3 Percentage ..................................................................................................................................... 88
4.2 COMMON FRACTIONS .............................................................................................................. 90
4.2.1 The learning of common fraction calculations ............................................................................... 91
4.2.2 Algorithms in operating on fractions .............................................................................................. 93
4.2.3 Calculations with decimal fractions ............................................................................................. 101
CONCLUSION ................................................................................................................................................. 102
ADDITIONAL LEARNING EXPERIENCES .................................................................................................... 102
MODULE MIP1501 LEARNING UNIT 5 ...................................................................................... 103
COMPARING QUANTITIES ............................................................................................................................ 103
INTRODUCTION ............................................................................................................................................. 103
5.1 PROPORTIONAL REASONING ............................................................................................... 104
5.2 RATIO ........................................................................................................................................ 115
5.3 RATE AS A SPECIAL FORM OF RATIO .................................................................................. 118
CONCLUSION ................................................................................................................................................. 120
ADDITIONAL LEARNING EXPERIENCES .................................................................................................... 121
MODULE MIP1501 LEARNING UNIT 6 ....................................................................................... 122
TECHNOLOGY IN LEARNING NUMBERS .................................................................................................... 122
INTRODUCTION ............................................................................................................................................. 122
6.1 TECHNOLOGICAL TOOLS ....................................................................................................... 123
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