Author(s): Merle Green
This book provides a structured and clear interpretation of the Australian mathematics curriculum, detailing what a child is required to know by the end of Year 3. It covers the syllabus topic by topic, explaining what is to be taught and how it is being taught in Australian classrooms. It is a comprehensive, well-presented and easy to understand book which provides an ideal reference for parents to consult when they wish to provide assistance in supporting the development of their child's mathematical understanding. The Australian mathematics curriculum caters for the acquisition of basic concept skills and processes. It contains three content strands, each divided into a number of sub-strands or topics, which set out what needs to be learnt. ‘The Number and Algebra’ and ‘Measurement and Geometry’ strands each have 4 sub-strands, and the ‘Statistics and Probability’ strand has been divided into 2 substrands. Entwined with these are the four proficiency strands of Understanding, Fluency, Problem solving and Reasoning, which determine how the content is studied and developed so that mathematical learning and understanding continue to progress over the years. It is most important for a child to be aware that each sub-strand is not an isolated topic but is interrelated with the others, and also with other subjects, for example, science and geography. Technology such as computers, touch pad applications and calculators should be utilised as an aid, when appropriate. In Year 3, the emphasis is on mathematical experiences that are meaningful in real life. These experiences should build on learning acquired from Kindergarten through Year 2. Students should be encouraged to select appropriate procedures in problem solving, to justify and give reasons for their choice, and to assess the reasonableness of their answers. Each day of our lives, we use many mathematical concepts and processes, usually without our realising that we are doing it. We constantly have to solve problems which require mathematical thinking whether spatial, involving manipulating numbers, or needing an understanding of measurement in one form or another. The over-riding aim of the Australian curriculum is to develop confident students who are able to use their knowledge and understanding of mathematics effectively and efficiently in their everyday lives, regardless of where they live. This book supports that aim. The Australian National Curriculum, developed by ACARA, states that, by the end of Year 3, students should be able to do the following: recognise the connection between addition and subtraction. solve problems using efficient strategies for multiplication. model and represent unit fractions. represent money values in various ways. identify symmetry in the environment. match positions on maps with given information. recognise angles in real life situations. interpret and compare data displays. count to and from 10 000. classify numbers as either even or odd. recall addition and multiplication facts for single digit numbers. correctly count out change from financial transactions. continue number patterns involving addition and subtraction. use metric units for length, mass and capacity. tell the time to the nearest minute. make models of three-dimensional objects. conduct chance experiments and list possible outcomes. carry out simple data investigations. How to use this book Each of the sub-strands within the three major strands is dealt with separately. The ‘Number and Place Value’ sub-strand and the ‘Units of Measurement’ sub-strand are so large, that the author has further subdivided these topics. Parents and teachers are introduced to activities which develop a real understanding of the different aspects of mathematics in an enjoyable and meaningful way. Understanding develops through completing these activities. Offer every opportunity for practical hands-on experiences in real life - measuring the correct amount of ingredients whilst cooking, comparing supermarket price labels for the best value when shopping, or discussing what quantities to buy for the family. These experiences are invaluable because they show children how important and relevant mathematical skills are to their own lives. This book introduces the language which students are expected to use and the stages through which they pass on the way to acquiring understanding. The emphasis is on discovery and the development of the ability to accurately identify which processes can be used to solve real life problems - and to justify those choices. It is very important to interlink the sub-strands as much as possible. They are not separate, isolated entities. Each topic is followed by 5 graded assessments involving both paper and pencil tests and practical activities. They enable parents and teachers to check to what extent concepts have been grasped. LEVEL 1 covers the basic ideas in a topic, using similar examples to those given in the chapter, and is designed to build confidence. Refer back to the appropriate page if difficulties occur. LEVELS 2 & 3 are of average difficulty. They give opportunity to consolidate and extend the basic ideas. They involve choosing and using appropriate strategies in more difficult examples. Page referrals are again given. All Year 3 students should try to complete the first 3 levels. LEVEL 4 has more challenging problems. No page referrals have been given. Students are encouraged to select for themselves which page to refer to, should difficulties arise. LEVEL 5 is an extension level, included to challenge those students who are more gifted at Maths. These problems frequently require more than one process for the solution, or involve a number of steps. No page referrals have been given. SOLUTIONS ARE GIVEN AT THE END OF THE BOOK. For parents: This book tells you what your teacher does not have the time to explain to you - the steps and stages by which each strand in Mathematics will be taught in Australian Schools. It will give you the confidence to support your children by reinforcing what is being taught at school, and to correctly provide assistance where weaknesses are identified. For teachers: This book summarises the steps and stages by which Australian children acquire necessary mathematical skills and concepts. It eliminates the need to wade through lengthy curriculum documents, and it provides a clear, easy to follow summary for teachers to use, which they can also confidently recommend to parents, as it supports classroom activities and exercises. For student primary teachers: This book provides a concise record of the steps to be taken and the activities suggested to support the acquisition of mathematical concepts. It is the perfect reference book for teaching practice, and during the early years of teaching, when there is so much to learn. The Australian mathematics curriculum caters for the acquisition of basic concept skills and processes. It contains three content strands: Number and Algebra, Measurement and Geometry, and Statistics and Probability. Each of these are divided into a number of sub-strands or topics, which set out what needs to be learnt. Entwined with these are the four proficiency strands of Understanding, Fluency, Problem solving and Reasoning, which determine how the content is studied and developed so that mathematical learning and understanding continue to progress over the years. This book generally follows the basic format of the Australian Curriculum Mathematics, which provides that by the end of Year 2, students should be able to do the following: Recognise increasing and decreasing number sequences involving 2’s, 3’s and 5’s. Represent multiplication and division by grouping into sets. Associate collections of Australian coins with their value. Identify the missing element in a number sequence. Recognise the features of three-dimensional objects. Interpret simple maps of familiar locations. Explain the effects of one-step transformations. Make sense of collected information. Count to and from 1 000. Perform simple addition and subtraction calculations using a range of strategies. Divide collections of objects into halves, quarters and eighths. Order shapes and objects using informal units. Tell the time to the quarter hour. Use a calendar to identify the date and the months included in the seasons. Draw two-dimensional shapes. Describe outcomes for everyday events. Collect data from relevant questions to create lists, tables and picture graphs. Understanding, Fluency, Problem Solving and Reasoning are a central part of Mathematics content across the three major strands (Number and Algebra, Measurement and Geometry, and Statistics and Probability). These are generally treated as individual chapters. Because the Number and Algebra sub-strand is quite extensive, it has been broken up into several parts for convenience, so as not to present the child with a daunting amount of information to access in one chapter. At the end of each chapter there is a series of tests, generally ranging through: EASIER AVERAGE DIFFICULT EXTENSION. There will be differences from school to school, as teachers tend to select topics in varying sequences. Some students may be involved in accelerated promotion, enrichment or remedial activities. Completing a chapter involves careful marking of answers from the solutions given at the end of the book. If a student gets any answer wrong, then it is very important to find out why they were wrong before moving onto the next level. In some instances it is difficult to test young children with pencil and paper tests, such as with 3D shapes. Suggestions have been made for practical evaluation strategies. These will include such activities as estimating in the Measurement strand, recognising shapes and reading the time. Even in the Number and Algebra strand, practical testing can be more appropriate, e.g. half fill this glass, share these Smarties between the members of a family. Many students will find that they can do much of the work in a particular strand before the end of Year 1. There are a number of avenues to follow: Make sure the child understands all the other strands in this text. After a period of time, say 3 or 4 weeks, do the test again to see that the information has been retained. Go to work in the next book in this series. This will require careful monitoring. About the Exercises At the end of each sub-strand (or part of a sub-strand) there are usually six exercise pages. These exercises are carefully graded in accordance with the Year 2 Curriculum content and are laid out as follows: Two pages of EASIER questions. Two pages of AVERAGE questions. One page of DIFFICULT questions. One page of EXTENSION questions All the question pages have very thorough full-page solutions at the end of the book. This book contains some revision of Year 1 Maths. It contains more written exercises especially in the Number and Algebra strand.