Learning to Calculate Mentally

1. Learning to Calculate Mentally What is mental calculation?

2. Learning intentions • To understand the central place of mental calculation in mathematics • To consider the need for knowledge of number facts, an understanding of key concepts and a range of skills in order to calculate mentally • To identify the range of mental strategies pupils may use to calculate mentally • To make appropriate choices about which strategy to use. • To develop an understanding of the structural laws which underpin mental calculation • To develop an understanding of how jottings can be used to support, record and explain calculation • To develop knowledge, understanding and skills in mathematics

3. Number sense ‘a well organised conceptual framework of number information that enables a person to understand numbers and number relationships and to solve mathematical problems that are not bound by traditional algorithms’ (Bobis 1996) Bobis, J. (1996). Visualisation and the development of number sense with kindergarten children. In Mulligan, J. & Mitchelmore, M. (Eds.) Children's Number Learning : A Research Monograph of the Mathematics Education Group of Australasia and the Australian Association of Mathematics Teachers. Adelaide: AAMT

4. Threlfall, 1998 Number sense……finding an approach to solving a problem using mental calculation involves; • how you see the numbers as a composite of parts (and in relation to the question) • seeing the numbers and their proximity to others • how the numbers connect with your current knowledge and understanding • how you see how the numbers can be changed

5. Calculating mentally involves: • Use of mental calculation strategies • Use of rapid recall facts and other knowledge, skills and understanding (including ‘number sense’) • May involve pencil and paper jottings

6. Types of mental calculation strategies Children use established mathematical knowledge and understanding to apply: general strategies when using one-digit and two-digit numbers particular strategies to special cases

7. Counting on and back in steps of constant size • Addition: 4 + 16 or 16 + 4 • Subtraction: 504 – 6 The difference between 2004 and 2009 • Multiplication: How many wheels are there on 3 cars? • Division: 35 ÷ 5

8. Partitioning in tens and ones • Addition: 36 + 22 54 + 34 • Subtraction: 68 – 32 62 – 38 • Multiplication: 36 x 5 42 x 5 • Division: 91 ÷ 7 96 ÷ 6 192 ÷ 8

9. Key Stage 1 - halving

10. Independent study task: Why is being able to calculate mentally important ? Work with your study group on this collaborative reading task referring to: • Thompson, I. (2010) ‘Getting your head around mental calculation’, in Thompson (ed.) Issues in Teaching Numeracy in Primary Schools, Buckingham, OUP pp. 161-173 (in reading pack) Consider: • What mental calculation is • Why it is important • What we need to focus on in supporting children to become good mental calculators • When and why you use mental calculation in your everyday life.

11. What is your next step in preparing for your assignment/learning about calculation? What are you feeling confident about? Where might you need support and from whom/what?

13. Marking criteria Your guidance paper should: • Clearly explain what is meant by mental calculation and why it is important. • Demonstrate secure understanding of the mathematical knowledge, skills and concepts which underpin each strategy chosen. • Provide a range of mental calculations from both KS1 and KS2, covering all four operations and using appropriate numbers. • Exemplify and explain how different strategies can have different levels of versatility and efficiency. • Be effective as a guidance paper in terms of the clarity with which ideas are presented