LEARNING TO CALCULATE MENTALLYWhy is mental calculation important?

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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

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:3 + 12 35 + 22 + 15 + 8 =

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:23 + 9 + 9 =74 + 58 =2.9 + 3.8 =

Subtraction:34 – 9 =236 – 99 =

Multiplication97 x 3£6.99 x 8

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KS 1 addition

Independent Study Task7

Work with your study group on the collaborative reading task referring to:

Haylock, D. and Thangata, F. (2007) Teaching Primary Mathematics, pp. 125-129 (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

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KS1 or KS2 mental calculation?

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 + 30 = ?, 40 + ? = 100, 56 - ? = 10; record calculations in a number sentence, using the symbols +, -, x , ÷ and = correctly [for example, 7 + 2 = 9] .

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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, 3000 - 1997, 4560 + 998]

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?

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