Digitized by the Internet Archive in 2016 with funding from University of Alberta Libraries https://archive.org/details/puremathematics101albe Module 1 Statistics and Data Tables Pure Mathematics 10 Module 1: Statistics and Data Tables Student Module Booklet Learning Technologies Branch ISBN 0-7741-2135-1 This document is intended for You may find the following Internet sites useful: Students y • Alberta Learning, http://www.learning.gov.ab.ca Teachers y • Learning Technologies Branch, http://www.learning.gov.ab.ca/ltb • Learning Resources Centre, http://www.lrc.learning.gov.ab.ca Administrators The use of the Internet is optional. Exploring the electronic information superhighway can be Home Instructors educational and entertaining. However, be aware that these computer networks are not censored. General Public Students may unintentionally or purposely find articles on the Internet that may be offensive or inappropriate. As well, the sources of information are not always cited and the content may not be Other accurate. Therefore, students may wish to confirm facts with a second source. ALL RIGHTS RESERVED Copyright © 2 002, the Crown in Right of Alberta, as represented by the Minister of Learning, Alberta Learning, 11160 Jasper Avenue, Edmonton, Alberta T5K 0L2. All rights reserved. Additional copies may be obtained from the Learning Resources Centre. No part of this courseware may be reproduced in any form, including photocopying (unless otherwise indicated), without the written permission of Alberta Learning. Every effort has been made both to provide proper acknowledgement of the original source and to comply with copyright law. If cases are identified where this effort has been unsuccessful, please notify Alberta Learning so that appropriate corrective action can be taken. IT IS STRICTLY PROHIBITED TO COPY ANY PART OF THESE MATERIALS UNDER THE TERMS OF A LICENCE FROM A C OLLECTIVE OR A L ICENSING BODY. iUiNmIrVoEeRiSTIVT YA F L IMB RR AFRRYT A Welcome y Pure Mathematics 1 0 Module 1 Statistics and Data Tables Module 2 Patterns and Relations Module 3 Algebra Module 4 Number Connections Welcome to Module 1. We hope Module 5 you’ll enjoy your study of Statistics and Data Tables. Trigonometry Pure Mathematics 10 contains five modules. Work through the modules in the order given, since several concepts build on each other as you progress in the course. High School Mathematics Courses Pure Mathematics 10 is the first course in the Pure Mathematics 10-20-30 sequence of courses. Many students who take the Pure Mathematics 10-20-30 will also choose to take Mathematics 31. Another sequence of courses is Applied Mathematics 10-20-30. How Do the Sequences Differ? Each sequence of courses is designed for students with different mathematical strengths and interests. The Pure Mathematics 10-20-30 sequence is intended for students who are strong in mathematical theory and algebra. The Applied Mathematics 10-20-30 sequence is better suited to students who prefer to solve mathematical problems using numerical reasoning or geometry. Each sequence of courses is designed for students with different career plans. Students who plan to take courses such as commerce, engineering, physics, and engineering technologies in post-secondary education will need to take Pure Mathematics 30 in high school. Some of these students will also need to take Mathematics 3 1 . Can I T ransfer to the Applied Mathematics Sequence of Courses? You should be aware that the applied and pure mathematics courses do have some topics in common; other topics are independent. Applied Topics Common Topics Pure Topics • linear programming • spreadsheets • irrational numbers • data tables and trends • line segments and linear • exponents • design and layout • scaling • polynomial and rational expressions • metric and imperial measure graphs • mathematical expectation • triangles • data presentation • surveys • growth patterns • vectors and matrices • linear and non-linear systems • periodic, fractal, and recursive • financial mathematics • operations on functions patterns • quadratic functions • mathematical reasoning • financial decision making • circle geometry • exponential and logarithmic • the bell curve • cfuonncitciso ns • costing and design problems • combinations • trigonometric functions If y ou want to transfer from the Pure Mathematics 10-20-30 sequence to the Applied Mathematics 10-20-30 sequence at a f uture time, you won’t have to repeat the topics that are common to pure mathematics and applied mathematics. If y ou decide to transfer to the Applied Mathematics sequence of courses after successfully completing Pure Mathematics 10, you may take the 3-credit course called Applied Mathematics 10b or you may take the 5-credit course called Applied Mathematics 10. If y ou decide to transfer after successfully completing Pure Mathematics 20, you will take the 5-credit course called Applied Mathematics 20b. The two bridging courses are shown in the following diagram: Pure Mathematics 30 (5) r q r f Applied Mathematics 10 MathAepmpaltiiecds 20 MathAepmpaltiiecds 30 L V. (5) J J J (5) v (5) Mathematical Processes Throughout the course you will be expected to do the following: • communicate mathematically • connect mathematical ideas to everyday experiences and to concepts in other disciplines • develop and use estimation strategies • develop and use mental math strategies • develop and use problem-solving strategies • reason and justify your thinking • select and use appropriate technologies as tools to solve problems • use visualization to assist in processing information, making connections, and solving problems Mathematical Process B C ommunication K C onnection This icon shows which mathematical | E stimation process you are expected to perform. B M ental Math El Problem Solving B R easoning B T echnology B V isualization In order to develop these mathematical processes more fully, you are encouraged to ask someone who is also taking Pure Mathematics 10 to be your study partner. You will find that having a f riend to discuss mathematics with will make your studying more enjoyable. You are also encouraged to record your mathematical ideas in a j ournal. Here are some suggestions for organizing your journal: • Keep a section on new concepts and procedures you have learned. Get in the habit of describing new concepts, procedures, and strategies in your own words. If y ou are having difficulty, write your questions in your journal before discussing them with your teacher or study partner. Record useful ways to help you remember what a concept means. Make graphic organizers (such as context webs, Venn diagrams, or organizational charts) to help you connect mathematical ideas. • Keep a section on your mathematical accomplishments. This can include solutions to problems that you are proud of solving. It can also include landmark events, such as when you finally grasped a d ifficult concept (an “aha!”) or when you first used a c alculator or spreadsheet program in a n ew way. • Keep a section on mathematics in the everyday world. This could include newspaper articles, cartoons, and descriptions of careers that require a mathematical background. Resources You Will Need In order to complete Pure Mathematics 10 successfully, you will need to have access to the following resources, which can be purchased through the Learning Resources Centre: • the MATHPOWER™ 10 textbook and data disks, Western Edition, published by McGraw-Hill Ryerson (1998) • a g raphing calculator Any of the following graphing calculators may be used: Texas Instruments TI-83, TI-83 Plus, TI-86, TI-89, TI-92, or TI-92 Plus; Casio Algebra FX-2.0, CFX-9850 GA-Plus, CFX-9850 G, CFX-9800 G, or FX-9700 series; Sharp EL-9600C, EL-9600, EL-9200, or EL-9300; or Hewlett-Packard HP 39g (only approved for 2001-2003 school years). Note: Some calculators are no longer commercially manufactured. • spreadsheet program Any of the following spreadsheet programs may be used: ClarisWorks™ 4.0 (or higher) for Macintosh or for Windows, Microsoft® Access 97 and Microsoft® Excel 97 for Windows (a part of Microsoft® Office Professional 95 or Microsoft® Office Professional 97). Note: Examples in this course show the TI-83 graphing calculator and the ClarisWorks ™ 4 .0 spreadsheet program where applicable. The screen shots in this module have been reprinted by permission from Apple Computer, Inc. You will need access to a computer (mandatory) and a v ideocassette player (optional). Finally, you will need the following resources, which can be purchased locally: • a mathematical instrument set (compass, protractor, ruler, and triangles) • a b inder in which to respond to the questions asked • a b inder for journal writing Other Visual Cues In addition to the Mathematical Process icon described earlier, you will find other visual cues throughout this course. Read the explanations given to discover what each icon prompts you to do. Use the Internet Refer to the View a to explore a textbook. videocassette. topic. Remember: Iny Internet website address Answer the Use the Computer givseunb j einc t t htios c mhoadnuglee. is questions in the Data Bank. \ Assignment Booklet. CONTENTS Evaluation Activity 1: Sampling Techniques Activity 1: Analysing Data 2 6 in 2 Ta0bl es 27 Strategies for Completing Activity 2: Inferences and Bias a M odule 11 Activity 2: Creating and Modifying Tables Follow-up Activities 14 Activity 3: Using a C omputer Database Extra Help 41 14 15 Enrichment Follow-up Activities 48 Extra Help 17 48 Conclusion 17 Enrichment Assignment Conclusion 535 2 Assignment 53