Visible maths : using representations and structure to enhance mathematics teaching in schools / Peter Mattock.

Includes bibliographical references (pages 305-306).

10. Representing irrational numbers

11. Introducing algebra

12. Simplifying algebraic expressions

13. Multiplying algebraic expressions

14. Expanding and factorising algebraic expressions

15. Equations and representations

16. Further algebraic manipulations

17. Frequently asked and anticipated questions. Customer notice: this book contains a large amount of full colour images, therefore any digital version would be better rendered by being viewed using a device with a colour display. --Amazon.co.uk

2. Representing fractions and decimals

3. Addition and subtraction with integers

4. Multiplication and division of integers

5. Powers and roots

6. Operations with fractions and decimals

7. Laws of arithmetic

8. Order of operations

9. Accuracy and numerical representations

Peter Mattock's Visible Maths: Using representations and structure to enhance mathematics teaching in schools supports teachers in their use of concrete and pictorial representations to illustrate key mathematical ideas and operations. Viewing the maths lesson as an opportunity for pupils to develop a deep understanding of mathematical concepts and relationships, rather than simply to follow fixed processes that lead to 'the answer', is increasingly recognised as the pinnacle of best practice in maths education. In this book, Peter Mattock builds on this approach and explores - in colourful detail - a variety of visual tools and techniques that can be used in the classroom to deepen pupils' understanding of mathematical operations. Covering vectors, number lines, algebra tiles, ordered-pair graphs and many other representations, Visible Maths equips teachers with the confidence and practical know-how to take their pupils' learning to the next level. The book looks at the strengths, and flaws, of each representation so that both primary and secondary school teachers of maths can make informed judgements about which representations will benefit their pupils. The exploration begins at the very basics of number and operation, and extends all the way through to how the representations apply to algebraic expressions and manipulations. As well as sharing his expert knowledge on the subject, Peter draws on relevant research and his own experience of using the representations in order to support teachers in understanding how these representations can be implemented effectively. Visible Maths also includes a glossary covering the key mathematical terms, as well as a chapter dedicated to answering some of the questions that may arise from the reading of the book. Furthermore, the accompanying diagrams and models are displayed in full colour to illustrate the conceptual takeaways and teaching techniques discussed. Suitable for teachers of maths in primary and secondary school settings. Chapters include: 1. Different representations of whole numbers