# Learning to Calculate Mentally

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LEARNING TO CALCULATE MENTALLYWhat is mental calculation?*

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

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

Threlfall, 1998

Number sensefinding 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

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Calculating mentally involves:* Use of mental calculation strategiesUse of rapid recall facts and other knowledge, skills and understanding (including number sense)May involve pencil and paper jottings

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

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

Partitioning in tens and ones*Addition:36 + 2254 + 34

Subtraction:68 3262 38

Multiplication:36 x 542 x 5

Division:91 796 6192 8

Key Stage 1 - halving*

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 isWhy it is importantWhat we need to focus on in supporting children to become good mental calculatorsWhen and why you use mental calculation in your everyday life.

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 ContentStandardsSuggested timeline for your maths assignment1SeminarInductionDeveloping Maths Concepts: the four operationsQ14, 15, 17Consider the mathematical ideas which underpin mental calculation 2SeminarLearning to calculate mentallyQ14, Q15, Q23Define mental calculation and consider why it is important

3SeminarLearning to calculate mentally

Lead lecture assignment guidanceQ14, Q15 Q17Identify three mental calculation strategies and explore their relative efficiency/ versatility using calculation examples

4SeminarLearning 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

5SeminarProgression from mental to written methodsQ14, Q15, Q25Consider how jottings support your chosen strategies

Start to draft your guidance paper

6Lead lecture - Talk and LearningSeminarProgression from mental to written methodsQ1, 2, 4, 6, 7Q14, Q15, Q25Final draft and proof read7SeminarProgression from mental to written methods

Assignment due dateQ14, 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

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