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.