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  • Mathematics for Primary School Teachers

  • © Saide, with the Wits School of Education, University of the Witwatersrand

    Permission is granted under a Creative Commons Attribution

    licence to replicate, copy, distribute, transmit, or adapt this work

    freely provided that attribution is provided as illustrated in the

    citation below. To view a copy of this licence visit

    http://creativecommons.org/licences/by/3.0/

    or send a letter to Creative Commons, 559 Nathan Abbott Way,

    Stanford, California, 94305, USA.

    Citation Sapire, I. (2010). Mathematics for Primary School Teachers. Saide and the Wits School of

    Education, University of the Witwatersrand, Johannesburg.

    ISBN: 978-0-9869837-5-7

    School of Education,

    University of the Witwatersrand

    Tel +27 11 717 3001

    www.wits.ac.za

    23 St Andrew’s Road

    Parktown

    2193 Johannesburg

    South Africa

    Saide

    Tel +27 11 4032813

    E-mail: info@saide.org.za www.saide.org.za P O Box 31822

    Braamfontein

    2017 Johannesburg

    South Africa

    http://creativecommons.org/licenses/by/3.0/ http://www.wits.ac.za/ http://www.saide.org.za/ http://creativecommons.org/licenses/by/3.0/

  • MATHEMATICS FOR PRIMARY SCHOOL TEACHERS _______________________________________________________________________________________________

    Contents

    About the course “Mathematics for Primary School Teachers” .......... 1

    Unit 1: Space and Shape ......................................................................... 5

    Introduction .............................................................................................................................. 5 The raw material of geometric shapes ..................................................................................... 5 Plane figures .......................................................................................................................... 11 Polygons and other plane figures ........................................................................................... 22 Space figures ......................................................................................................................... 32 Pattern work and transformations........................................................................................... 42

    Unit summary .......................................................................................51

    Assessment ......................................................................................... 52

    Unit 2: Numeration ................................................................................. 53

    Introduction ............................................................................................................................ 53 Multi-base ............................................................................................................................... 62 Developing number concept ................................................................................................... 71 Number systems we use at school ......................................................................................... 77 Reasoning, algebra and number patterns .............................................................................. 84

    Unit summary .......................................................................................91

    Assessment ......................................................................................... 92

    Unit 3: Operations .................................................................................. 93

    Introduction ............................................................................................................................ 93 Background and algorithms for addition and subtraction ........................................................ 94 Background and algorithms for multiplication and division ................................................... 101 Multiples, factors and primes: divisibility rules ...................................................................... 108 Problem-solving, word problems and order of operations .................................................... 117

    Unit summary ..................................................................................... 123

    Assessment ........................................................................................ 124

    Unit 4: Fractions ................................................................................... 125

    Introduction .......................................................................................................................... 125 Fractions and wholes: introductory concepts and activities .................................................. 126 Further activities in the teaching of fractions ........................................................................ 135 Equivalent fractions and comparison of fractions ................................................................. 144 Categories of the whole – a review of concepts and apparatus ........................................... 153 Apparatus ............................................................................................................................. 156 Rational numbers ................................................................................................................. 164

  • Unit summary ..................................................................................... 174

    Assessment ........................................................................................ 175

    Unit 5: Statistics ................................................................................... 176

    Introduction .......................................................................................................................... 176 Random numbers, population and sample ........................................................................... 178 Graphical forms of data representation ................................................................................ 181 Measures of central tendency .............................................................................................. 189 Misleading statistics ............................................................................................................. 192 Statistics in the classroom .................................................................................................... 194

    Unit summary ..................................................................................... 196

    Assessment ........................................................................................ 197

    Unit 6: Size and Measurement ............................................................ 198

    Introduction .......................................................................................................................... 198 Introduction to concepts and relevant ideas ......................................................................... 198 Conservation of size – some practical exercises .................................................................. 204

    Unit summary ..................................................................................... 210

    Assessment ........................................................................................ 211

  • MATHEMATICS FOR PRIMARY SCHOOL TEACHERS

    1

    About the course “Mathematics for Primary School Teachers”

    Mathematics for Primary School Teachers has been digitally published by Saide, with the

    Wits School of Education. It is a revised version of a course originally written for the

    Bureau for In-service Teacher Development (Bited) at the then Johannesburg College of

    Education (now Wits School of Education).

    The course is for primary school teachers (Foundation and Intermediate Phase) and

    consists of six content units on the topics of geometry, numeration, operations, fractions,

    statistics and measurement. Though they do not cover the entire curriculum, the six units

    cover content from all five mathematics content areas represented in the curriculum.

    Unit 1 Space and Shape

    This unit presents an analytical approach to the study of shapes, including the make-up of

    shapes, commonalities and differences between shapes and a notation for the naming of

    shapes.

    On completion of the unit students should be able to:

     Identify and describe fundamental properties of shapes.

     Differentiate between and illustrate two dimensional (2-D) and three dimensional (3- D) shapes.

     Categorize and compare two dimensional (2-D) and three dimensional (3-D) shapes.

     Describe and design patterns using tessellations and transformations.

    Unit 2 Numeration

    This unit is designed to give insight into a few specially chosen ancient numeration

    systems. After the presentation of historic numeration systems, there is an in-depth look

    at the Hindu-Arabic numeration system, still in use today, with its base ten and place

    value.

    On completion of the unit students should be able to:

     Record numbers using a range of ancient numeration systems.