LEARNING TO CALCULATE MENTALLY Why is mental calculation important? 1

Learning intentions 2  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

Why is mental calculation so important?  ‘Most calculations in real life are done in the head rather than on paper’ (Thompson 2010 p163)  ‘… mental calculation is important because it promotes number sense’. (Maclellan 2001 p148)  ‘Confidence in mental procedures enables the pupil to deal with numerical situations in a flexible and efficient way that is determined by numbers and operations involved’ (Haylock and Thaganta 2007 p125)  ‘ … the ability to calculate mentally forms the basis of all methods of calculation and has to be maintained and refined’ (DfES 2006 p40)

Re-ordering  Addition: =  Subtraction: 47 – 12 – 7 = 36 – 9 – 1 – 5 =  Multiplication: 4 x 7 = 9 x 3 x 10 =  Division: 60 ÷ 5 ÷ 3 = 42 ÷ 2 ÷ 7 =

Compensating  Addition: = = =  Subtraction: 34 – 9 = 236 – 99 =  Multiplication 97 x 3 £6.99 x 8

KS 1 addition 6

Independent Study Task 7 Work with your study group on the collaborative reading task referring to:  Haylock, D. and Thangata, F. (2007) Teaching Primary Mathematics, pp (in reading pack) Use the guidance and questions in your reading log to help structure your discussions and tasks. Record your discussion and thinking in the log for reference in the next seminar

KS1 or KS2 mental calculation? 8 How can the National Curriculum help? KS1  develop rapid recall of number facts: know addition and subtraction facts to 10 and use these to derive facts with totals to 20, know multiplication facts for the x2 and x10 multiplication tables and derive corresponding division facts, know doubles of numbers to 10 and halves of even numbers to 20  develop a range of mental methods for finding, from known facts, those that they cannot recall, including adding 10 to any single-digit number, then adding and subtracting a multiple of 10 to or from a two-digit number; develop a variety of methods for adding and subtracting, including making use of the facts that addition can be done in any order and that subtraction is the inverse of addition  carry out simple calculations of the form = ?, 40 + ? = 100, 56 - ? = 10; record calculations in a number sentence, using the symbols +, -, x, ÷ and = correctly [for example, = 9].

9 KS2  recall all addition and subtraction facts for each number to 20  work out what they need to add to any two-digit number to make 100, then add or subtract any pair of two-digit whole numbers; handle particular cases of three-digit and four-digit additions and subtractions by using compensation or other methods [for example, , ]  recall multiplication facts to 10 x 10 and use them to derive quickly the corresponding division facts  double and halve any two-digit number  multiply and divide, at first in the range 1 to 100 [for example, 27 x 3, 65 ÷ 5], then for particular cases of larger numbers by using factors, distribution or other methods

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?

WeekSession Content Standards Suggested timeline for your maths assignment 1 Seminar Induction Developing Maths Concepts: the four operations Q14, 15, 17Consider the mathematical ideas which underpin mental calculation 2 Seminar Learning to calculate mentallyQ14, Q15, Q23Define mental calculation and consider why it is important 3 Seminar Learning to calculate mentally Lead lecture – assignment guidance Q14, Q15 Q17Identify three mental calculation strategies and explore their relative efficiency/ versatility using calculation examples 4 Seminar Learning to calculate mentallyQ14, Q15 Q17Explore the knowledge skills and understanding needed to make use of each of your chosen strategies Plan the content of your guidance paper 5 Seminar Progression from mental to written methodsQ14, Q15, Q25Consider how jottings support your chosen strategies Start to draft your guidance paper 6 Lead lecture - Talk and Learning Seminar Progression from mental to written methods Q1, 2, 4, 6, 7 Q14, Q15, Q25 Final draft and proof read 7 Seminar Progression from mental to written methods Assignment due date Q14, Q15, Q25 (a) (b)

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