PREFACE Over 40 years, calculators have evolved from being computational devices for scientists and engineers to becoming important educational tools. What began as a tool to answer numerical questions has evolved to become an affordable, powerful and flexible environment for students and their teachers to explore mathematical ideas and relationships. CASIO’s invention of a graphics screen on scientific calculators almost 30 years added significant educational power to these devices. Following many years of advice from experienced teachers, the CASIO fx-9860GII series of calculators include substantial mathematical capabilities, innovative use of a graphics screen for mathematical purposes and extensive use of natural displays of mathematical notation. Continuing this evolutionary process, the CASIO fx-CG 20 includes a colour graphics screen and innovative applications to enhance its educational value. This publication comprises a series of modules to help make best use of the opportunities for mathematics education afforded by these developments. The focus of the modules is on the use of the calculators in the development of students’ understanding of mathematical concepts and relationships, as an integral part of the development of mathematical meaning for the students. The calculator is not just a device for computation, once the mathematics has been understood. It is now best thought of as a laboratory in which students can experiment with mathematical ideas and deepen their understanding of the mathematics involved. The similarities between the two calculator models allows users of either calculator to make use of the modules, except for three special modules which require the enhanced features of the CASIO fx-CG 20, the colour graphics calculator. The mathematics involved in the modules spans a wide range from the early years of secondary school to the early undergraduate years, and we leave it to the reader to decide which modules suit their purposes. Although mathematics curricula vary across different countries, we are confident that the mathematical ideas included in the modules will be of interest to mathematics teachers and their students across international boundaries. The modules are intended for use by both students and teachers. Each module contains a set of Exercises, focusing on calculator skills relevant to the mathematics associated with the module. In addition, a set of exploratory Activities is provided for each module, to illustrate some of the ways in which the calculator can be used to explore mathematical ideas through the use of the calculator; these are not intended to be exhaustive, and we expect that teachers will develop further activities of these kinds to suit their students and their particular curriculum. The Notes for Teachers in each module provide answers to exercises, as well as some advice about the classroom use of the activities (including answers where appropriate). Permission is given for the reproduction of any of the materials for educational purposes. Some of these materials are based on earlier materials written by the authors and published by the Mathematical Association of Western Australia, to whom we express our gratitude for permitting the materials to be more widely published in the present form. We are also grateful to CASIO for supporting the development of these materials, and appreciate in particular the assistance of Mr Yoshino throughout the developmental process. We hope that users of these materials enjoy working with the calculators as much as we have enjoyed developing the materials and we wish both teachers and their students a productive engagement with mathematics through the use of these fine calculators. Barry Kissane and Marian Kemp Murdoch University, Western Australia Table of Contents Module 1: Introduction to the calculators ································································· 1 Modes and p ·························································································· 1 Input mode ································································································· 2 Entering and editing commands ········································································ 3 Menus ······································································································ 4 Recalling and editing commands ······································································· 6 Scientific notation ························································································ 7 SET UP ···································································································· 7 Memories ·································································································· 9 Exercises and Notes for teachers ····································································· 11 Module 2: Functions ························································································· 13 Symbols ·································································································· 13 Graphs ···································································································· 13 Tables ···································································································· 16 Tracing and zooming graphs ·········································································· 17 Evaluating functions ···················································································· 20 Tracing and zooming tables ··········································································· 20 Interpreting graphs automatically ····································································· 22 Exercises, Activities and Notes for teachers ························································ 24 Module 3: Exploring functions ············································································ 27 A family of functions ··················································································· 27 Animation of graphs ···················································································· 28 Piecewise functions ····················································································· 30 Composite functions ···················································································· 30 Inequalities ······························································································ 31 Polar graphs ····························································································· 32 Conics ···································································································· 34 Exercises, Activities and Notes for teachers ························································ 36 i Module 4: Data analysis ····················································································· 39 Entering and editing data ·············································································· 39 Summarising data numerically ········································································ 40 Displaying data graphically ··········································································· 42 Frequency data ·························································································· 45 Categorical data ························································································· 45 Bivariate data ···························································································· 47 Comparing groups ······················································································ 49 Data transformations ··················································································· 50 Sorting bivariate data ··················································································· 51 Exercises, Activities and Notes for teachers ························································ 53 Module 5: Geometry ························································································· 56 Drawing and changing objects ········································································ 56 Changing the view ······················································································ 58 Showing the coordinate plane ········································································· 59 Constraints ······························································································· 60 Constructions ···························································································· 61 Sequences of constructions ············································································ 63 Saving and retrieving your work ······································································ 64 Making measurements ················································································· 65 Displaying measurements ············································································· 67 Constraining measurements ··········································································· 69 Other geometric activities ············································································· 70 Exercises, Activities and Notes for teachers ························································ 71 Module 6: Trigonometry ···················································································· 74 Trigonometry and right triangles