Essential Mathematics for the Australian Curriculum builds on established learning sequences and teaching methods to provide an authoritative and practical interpretation of all content strands, substrands and content descriptions. It also covers essential prior knowledge and includes some extension topics. The essential foundations of the series: * The three interconnected content strands are incorporated into 11 units of work that can be completed in the school year * Let's Start activities provide context and foundation for topics * Every question is grouped according to the four proficiency strands of the new Australian Curriculum: Understanding, Fluency, Problem-solving and Reasoning * Problem-solving and Reasoning questions are included in every exercise * Enrichment questions in each exercise, and investigations, challenges and puzzles in every chapter reflect curriculum aims by extending students in depth * Literacy and numeracy skills, thinking skills, creativity and ICT activities (including dynamic geometry and calculator activities) are incorporated and encouraged in every chapter.

 

This book is part of a book series called Essential Mathematics .

There are 704 pages in this book. This book was published 2011 by Cambridge University Press .

Dr Michael Evans is Head of Mathematics at Scotch College and also actively involved in the Victorian Curriculum and Assessment Authority. His interest in mathematics extends to the Mathematics Olympiad Team. David Greenwood teaches at Scotch College and has special expertise in the creative use of graphics calculators. Professor Peter Jones from Swinburne University has taken a keen interest in secondary school mathematics and has also had a key role in the development of the new course of study. Dr Kay Lipson's experience extends through secondary and tertiary courses. She is currently a lecturer in statistics at Swinburne University. Jenny Vaughan writes information books and educational television programmes for children.

This book has the following chapters: About the authors; Introduction and how to use this book; 1 Whole numbers; Pre-test; 1. 1 Numbers systems; 1. 2 Place value; 1. 3 Addition and subtraction; 1. 4 Addition and subtraction algorithms; 1. 5 Multiplication; 1. 6 Multiplying larger numbers; 1. 7 Division; 1. 8 Estimating and rounding; 1. 9 Order of operations; Investigation; Puzzles and challenges; Review; Chapter summary; Multiple-choice questions; Short-answer questions; Extended-response questions; 2 Geometry; Pre-test; 2. 1 Pointslines and angles; 2. 2 Measuring angles; 2. 3 Angles at a point; 2. 4 Transversal lines and parallel lines; 2. 5 Problems with parallel lines; 2. 6 Circles and constructions; 2. 7 Designs with circles and lines; 2. 8 Dynamic geometry; Investigation; Puzzles and challenges; Review; Chapter summary; Multiple-choice questions; Short-answer questions; Extended-response questions; 3 Number properties and patterns; Pre-test; 3. 1 Factors and multiples; 3. 2 Highest common factor and lowest common multiple; 3. 3 Divisibility; 3. 4 Prime numbers; 3. 5 Powers; 3. 6 Prime decomposition; 3. 7 Squares and square roots; 3. 8 Number patterns; 3. 9 Spatial patterns; 3. 10 Tables and rules; 3. 11 The number plane and graphs; Investigation; Puzzles and challenges; Review; Chapter summary; Multiple-choice questions; Short-answer questions; Extended-response questions; 4 Fractions and percentages; Pre-test; 4. 1 What are fractions?; 4. 2 Equivalence and simplification; 4. 3 Mixed numbers; 4. 4 Ordering fractions; 4. 5 Adding fractions; 4. 6 Subtracting fractions; 4. 7 Multiplying fractions; 4. 8 Dividing fractions; 4. 9 Fractions and percentages; 4. 10 Percentage of a number; 4. 11 Expressing a quantity as a proportion; Investigation; Puzzles and challenges; Review; Chapter summary; Multiple-choice questions; Short-answer questions; Extended-response questions; 5 Algebra; Pre-test; 5. 1 Introduction to algebra; 5. 2 Evaluating expressions; 5. 3 Equivalent expressions; 5. 4 Like terms; 5. 5 Multiplying and dividing expressions; 5. 6 Expanding brackets; 5. 7 Applying algebra; Investigation; Puzzles and challenges; Review; Chapter summary; Multiple-choice questions; Short-answer questions; Extended-response questions; 6 Decimals; Pre-test; 6. 1 Decimals and place value; 6. 2 Rounding decimals; 6. 3 Addition and subtraction of decimals; 6. 4 Multiplying and dividing by powers of 10; 6. 5 Multiplication of decimals; 6. 6 Division of decimals; 6. 7 Decimals and fractions; 6. 8 Decimals and percentages; Investigation; Puzzles and challenges; Review; Chapter summary; Multiple-choice questions; Short-answer questions; Extended-response questions; Semester Review 1; 7 Negative Numbers; Pre-test; 7. 1 Integers; 7. 2 Adding and subtracting positive integers; 7. 3 Adding and subtracting negative integers; 7. 4 Multiplication and division of integers; 7. 5 Order of operations; 7. 6 Substituting integers; 7. 7 The number plane; Investigation; Puzzles and challenges; Review; Chapter summary; Multiple-choice questions; Short-answer questions; Extended-response questions; 8 Statistics and probability; Pre-test; 8. 1 Summarising data numerically; 8. 2 Dot plots and column graphs; 8. 3 Line graphs; 8. 4 Scatter plots; 8. 5 Stem-and-leaf plots; 8. 6 Pie charts and divided bar graphs; 8. 7 Describing chance; 8. 8 Theoretical probability; 8. 9 Experimental probability; Investigation; Puzzles and challenges; Review; Chapter summary; Multiple-choice questions; Short-answer questions; Extended-response questions; 9 Polygons solids and transformations; Pre-test; 9. 1 Polygons; 9. 2 Triangles; 9. 3 Constructing triangles; 9. 4 Triangle angle sum; 9. 5 Quadrilaterals; 9. 6 Quadrilateral angle sum; 9. 7 9. 7 Symmetry ; 9. 8 Reflection and rotation; 9. 9 Translation; 9. 10 Drawing solids; 9. 11 Nets and the Platonic solids; Investigation; Puzzles and challenges; Review; Chapter summary; Multiple-choice questions; Short-answer questions; Extended-response que