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### Transcript of Mathematics for Primary School Teachers Materials/Teacher...¢  Mathematics for Primary...

• 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

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

• 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.