© Crown copyright 2007 Mathematics at St. Hilary School ~ Calculation Strategies Tuesday 27 th of January 2009

© Crown copyright 2007

Mathematics at St. Hilary School

~ Calculation Strategies

Tuesday 27th of January 2009


Format of mathematics session:1) Brief introduction to mathematics at

St. Hilary School2) Mathematics in the Foundation

Stage (EYFS)3) Calculation strategies, and how they

are taught (addition, subtraction, multiplication, division)


Recent history of mathematics ...

• Numeracy strategy first introduced in 1999 – comprehensive learning objectives and strict lesson structure (including a compulsory mental starter and plenary).

• This has continuously evolved over the past 8 years, where many teachers have taken the initiative and made it their own.

• Renewed framework for English and mathematics introduced in 2008 – main changes are longer


The Renewed Framework ... Encourages flexibility in the organisation of the curriculum

and the structure of literacy and mathematics lessons

Structures learning over sequences of lessons as well as within lessons – promotes learning being built over time

Raises expectations for all children, especially those at greatest risk of underachievement

Uses assessment more effectively to inform and direct teaching and learning

Adds breadth and strengthens pedagogy to include a clearer focus on inclusion, the use of ICT, using and applying mathematical skills and knowledge, the teaching of early reading, speaking, listening and learning, and developing core areas of learning in literacy and mathematics


Our classrooms provide rich mathematical environments ... mathematics is learnt by children exploring and making sense of concepts

all children can explore and develop their thinking and understanding children should work on ‘rich learning’ tasks in different ways and to

different depths, discussing their work with each other as well as with the teacher

‘rich learning’ tasks will enable children to think mathematically, to reason and to communicate

children will need time to develop mathematical understanding and skills, especially number and how it works

Equipment is provided to scaffold their learning, like stabilisers on a bike. It is then adapted, and finally taken

away as confidence and skill levels improve.


The Teaching of Blocked Units

These strands are put

together into units of

teaching ...

Using and applying mathematics

Knowing and using number facts

Counting and understanding number

Calculating

Understanding shape

Measuring

Handling data


Block A

Counting,

partitioning

and calculating

Block B

Securing number

facts, understanding

shape

Block C

Handling

data and measures

Block D

Calculating,

measuring and

understanding

shape

Block E

Securing number

facts, relationships

and calculating



Calculating



Understanding shape


Measuring

Handling data



Calculating

Measuring



Calculating

Understanding shape

The ‘using and applying of

mathematics’ is now integral in every unit,

either as a main focus, or as a starter / plenary – the children are continually

practising what they are learning.


Requirements:“Children must be supported in developing their understanding of Problem Solving, Reasoning and Numeracy in a broad range of contexts in which they can explore, enjoy, learn, practise and talk about their developing understanding. They must be provided with opportunities to practise and extend their skills in these areas and to gain confidence and competence in their use.”

EYFS statutory guidance 2007

Problem-Solving, Reasoning and Numeracy in the Foundation Stage


ADDITIONEarly stages

• Practical activities and discussions. Recognising numbers. Count objects up to 10. Find one more than a number. Count in ones and tens. Relate addition to combining two groups of objects. Count along a number line to add numbers. Begin to use + and = signs in a number sentence.


• Mental Strategies & Informal Methods Looking for pairs that make 10 then 20, 30 etc.

16 + 12 + 4= Using a number square, count on the units then the tens –

Get your Number Squares out

Adding ‘nearly’ numbers – To add 9 add 10 then subtract 132 + 9 = 32 +10 =42 -1 =41

Using a number line, bridging through a multiple of 10 e.g 27 + 8 +3 +5

_______________________________________________ 27 30 35

Mid-stages


Mid-stages• Formal Methods – Start to emerge:

Add using partitioning: 47 + 34 = 40 + 7 +30 + 4= Add units 4 + 7 = 13 Add tens 40 + 30 = 70 Total 70 + 13 = 83

Expanded Method: 47 + 34 = TU T U 47 40 + 7 34 30 + 4 70 + 3 = 83 10

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Later stages

• Standard Methods HTU HTU . t h

147 347 . 36

+ 534 126 . 17

683 473 . 53

1 1 1


SUBTRACTIONEarly stages

• Practical activities and discussion. Count backwards in number rhymes or stories. Count back from a given number. Begin to relate subtraction to take away. Find one less than a number. Counting back in tens Count backwards along a number line to take away. Begin to use the – and = signs to record mental additions.


Mid-stages• Mental Strategies & Informal Methods Using a number square, partition the number, then count back the

units then the tens. Subtracting ‘nearly’ numbers – To take 9 take 10 then add 1

32 - 9 = 32 -10 =22 +1 =23

Using a number line, bridging through a multiple of 10 e.g 63 – 26 37 47 57 60 63 -10 -10 -3 -3 Recognise when to count on- when 2 numbers are close together

106 – 98= 2 6 =8 _________________________

98 100 106


Mid-stages• Methods which lead to Standard Methods Can also use counting on: 374 22 100 74 =

196 - 178 ___________________________________ 178 200 300 374 Expanded Method – Exchanging 10 43 – 27= T 10 U T U 40 + 3 30 + 13 20 + 7 20 + 7 10 + 6 = 16

This leads to understanding how the standard written method works.

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Later stages

• Standard MethodsCan you remember those good old fashioned maths lessons?!!

343 65. 08

- 297 - 37. 35


MULTIPLICATIONEarly stages

• Practical Activities

Counting in twos, fives and tens.

Using activities to recognise doubles and halves.

Using equipment to give lots of practice of making groups of.


Mid-stages• Mental Strategies & Informal Methods Using arrays. ●●●● 2 x4 means 2 lots of/ groups of 4 ●●●● 2 x 4 =8 OR 4 x2 is 4 lots of/ groups of 2 ●● ●● 4 x 2 =8 Therefore demonstrating ●● that multiplication can be ●● done in any order. Partitioning e.g. 4 x 13 = 4 x 3 = 12 4 x 10 = 40 Total 12 + 40 =52 Counting on using our tables. They really need to know tables!!


Later stages• Methods which lead to Standard Methods Use easy sums to help with harder: 30 x 40 = take off zeros 3 x 4 = 12 put zeros back on = 1200 7 x 0.8 = we know 7 x 8 =56 therefore 10 x smaller = 5.6

The grid method: 33 x 248 1) First partition & put numbers in grid 200 40 8 2) Multiply each number together, 30 = remembering to use easier sums to 4 = help, take off zeros & add them _____ back on. 3) Total each row & then add together.


Later stages Standard Methods – Can you remember them?! Short Multiplication 7 x 48 48 x 7

Long multiplication 67 x 36 67 x 36 (6 x 67) 0 ( 30 x 67) Total

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DIVISIONEarly stages

• Practical Activities. Counting back in tens, twos and fives.

Know halves ... half of 6 is 3


Mid-stages• Mental Strategies & Informal Methods Counting on and back using tables Understanding division as sharing e.g if 20 sweets are shared

between 4 people:

Understanding division as grouping e.g. How many groups of 5 are there in 20? (Using apparatus and then our tables)

Using arrays ●●●●● 10 divided into 2 groups = 5 in each group

●●●●● ●●

OR 10 divided into 5 groups = 2 ●●

●●

●●

●●


Mid-stages• Mental Strategies & Informal Methods (Contd) Repeated subtraction 12 ÷ 3 means how many 3’s in 12, therefore

keep subtracting 3’s : 12 - 3 = 9, 9 – 3 = 6 etc.

__-3____-3____-3____-3___ How many 3’s? = 4

0 3 6 9 12

Start to understand remainders and if you need to round up or down

e.g If I have 14 eggs, how many egg boxes will I need?

14 ÷ 6 = 2 remainder 2 2 full egg boxes and 2 in the other.

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Later stages• Standard Methods Remember these?

• Short Multiplication 237 ÷ 6

• Long Multiplication 427 ÷ 24


Children should develop habits Children should develop habits as:as:

pattern sniffers ……… experimenters …. tinkerers

……. inventors ………visualisers ………conjecturers

and be able to:

investigate… deduce… communicate… reason…

analyse… scrutinize… discuss…. explore...

decipher… solve problems…

formulate…


Thank you so much for

attending – your interest

means a lot to us and your

children!

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© Crown copyright 2007 Mathematics at St. Hilary School ~ Calculation Strategies Tuesday 27 th of January 2009