LEARNING TO CALCULATE MENTALLY

What is mental calculation?

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Learning intentions2

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 sense3

‘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 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

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Calculating mentally involves:

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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

Types of mental calculation strategies

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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

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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

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Addition:36 + 2254 + 34

Subtraction:68 – 3262 – 38

Multiplication:36 x 542 x 5

Division:91 ÷ 796 ÷ 6192 ÷ 8

Key Stage 1 - halving9

Independent study task: Why is being able to calculate mentally important ?10

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?

Week Session Content Standards Suggested timeline for your maths assignment

1SeminarInductionDeveloping Maths Concepts: the four operations

Q14, 15, 17 Consider the mathematical ideas which underpin mental calculation

2SeminarLearning to calculate mentally Q14, Q15, Q23 Define mental calculation and consider why it is

important

3SeminarLearning to calculate mentally

Lead lecture – assignment guidance

Q14, Q15 Q17 Identify three mental calculation strategies and explore their relative efficiency/ versatility using calculation examples

4SeminarLearning to calculate mentally Q14, Q15 Q17 Explore 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 methods Q14, Q15, Q25 Consider how jottings support your chosen

strategies

Start to draft your guidance paper

6Lead lecture - Talk and LearningSeminarProgression from mental to written methods

Q1, 2, 4, 6, 7Q14, Q15, Q25

Final draft and proof read

7SeminarProgression 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