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© Crown copyright 2007 Mathematics at St. Hilary School ~ Calculation Strategies Tuesday 27 th of January 2009
© Crown copyright 2007 Format of mathematics session: 1)Brief introduction to mathematics at St. Hilary School 2)Mathematics in the Foundation Stage (EYFS) 3)Calculation strategies, and how they are taught (addition, subtraction, multiplication, division)
© Crown copyright 2007 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
© Crown copyright 2007 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
© Crown copyright 2007 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.
© Crown copyright 2007 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
© Crown copyright 2007 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 Using and applying mathematics Counting and understanding number Calculating Using and applying mathematics Knowing and using number facts Understanding shape Using and applying mathematics Measuring Handling data Using and applying mathematics Calculating Measuring Counting and understanding number Knowing and using number facts 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.
© Crown copyright 2007 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
© Crown copyright 2007 ADDITION Early 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.
© Crown copyright 2007 Mental Strategies & Informal Methods Looking for pairs that make 10 then 20, 30 etc = 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 = =42 -1 =41 Using a number line, bridging through a multiple of 10 e.g _______________________________________________ Mid-stages
© Crown copyright 2007 Mid-stages Formal Methods – Start to emerge: Add using partitioning: = = Add units = 13 Add tens = 70 Total = 83 Expanded Method: = TU T U = DWO-EN-19
© Crown copyright 2007 Later stages Standard Methods HTU HTU. t h
© Crown copyright 2007 SUBTRACTION Early 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.
© Crown copyright 2007 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 = =22 +1 =23 Using a number line, bridging through a multiple of 10 e.g 63 – Recognise when to count on- when 2 numbers are close together 106 – 98=2 6 =8 _________________________
© Crown copyright 2007 Mid-stages Methods which lead to Standard Methods Can also use counting on: = ___________________________________ Expanded Method – Exchanging – 27= T 10 U T U = 16 This leads to understanding how the standard written method works DWO-EN-19
© Crown copyright 2007 Later stages Standard Methods Can you remember those good old fashioned maths lessons?!!
© Crown copyright 2007 MULTIPLICATION Early 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.
© Crown copyright 2007 Mid-stages Mental Strategies & Informal Methods Using arrays. ●●●● 2 x4 means 2 lots of/ groups of 4 ●●●● 2 x 4 =8 OR 4 x2is 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 =52 Counting on using our tables. They really need to know tables!!
© Crown copyright 2007 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 = 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 ) 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.
© Crown copyright 2007 Later stages Standard Methods – Can you remember them?! Short Multiplication 7 x x 7 Long multiplication 67 x x 36 (6 x 67) 0 ( 30 x 67) Total DWO-EN-19
© Crown copyright 2007 DIVISION Early stages Practical Activities. Counting back in tens, twos and fives. Know halves... half of 6 is 3
© Crown copyright 2007 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 ●● ●●
© Crown copyright 2007 Mid-stages Mental Strategies & Informal Methods (Contd) Repeated subtraction 12 ÷ 3 means how many 3’s in 12, therefore keep subtracting 3’s : = 9, 9 – 3 = 6 etc. __-3____-3____-3____-3___ How many 3’s? = 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 DWO-EN-19
© Crown copyright 2007 Later stages Standard Methods Remember these? Short Multiplication 237 ÷ 6 Long Multiplication 427 ÷ 24
© Crown copyright 2007 Children should develop habits as: pattern sniffers ……… experimenters …. tinkerers ……. inventors ………visualisers ………conjecturers and be able to: investigate… deduce… communicate… reason… analyse… scrutinize… discuss…. explore... decipher… solve problems… formulate…
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