Transcript Mental Calculation

1
LEARNING TO CALCULATE
MENTALLY
What is mental calculation?
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
Number sense
3
‘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
Calculating mentally involves:
5
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
6
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
7

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
8
Addition:
36 + 22
54 + 34

Subtraction:
68 – 32
62 – 38

Multiplication:
36 x 5
42 x 5

Division:
91 ÷ 7
96 ÷ 6
192 ÷ 8

Key Stage 1 - halving
9
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 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.
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
1
Seminar
Induction
Developing Maths Concepts: the four operations
Q14, 15, 17
Consider the mathematical ideas which underpin mental
calculation
2
Seminar
Learning to calculate mentally
Q14, Q15, Q23
Define mental calculation and consider why it is
important
3
Seminar
Learning to calculate mentally
Q14, Q15 Q17
Identify three mental calculation strategies and explore
their relative efficiency/ versatility using calculation
examples
Q14, Q15 Q17
Explore the knowledge skills and understanding needed
to make use of each of your chosen strategies
Lead lecture – assignment guidance
4
Seminar
Learning to calculate mentally
Plan the content of your guidance paper
5
Seminar
Progression from mental to written methods
Q14, Q15, Q25
Consider how jottings support your chosen strategies
Start to draft your guidance paper
Lead lecture - Talk and Learning
6
7
Seminar
Progression from mental to written methods
Seminar
Progression from mental to written methods
Assignment due date
Q1, 2, 4, 6, 7
Q14, Q15, Q25
Q14, Q15, Q25
(a) (b)
Final draft and proof read
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