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Mathematics in the primary school The approach to teaching calculation methods

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Do it your way! 25 x 19 5% of 86 248 - 99 103 - 98 ½ of 378 1+2+3+4+5+6+7+8+9+10+11=

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Key features of the strategy for mathematics An emphasis on the development of mental calculation A greater focus on the development of number skills and knowledge Informal methods of calculation until children can…..

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Mentally add and subtract any pair of 2-digit numbers For most children during the latter part of year 3 Children will be using a variety of mental methods by this time

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Mental first 56+ 29 or 56 29 + Children stop “saying” the numbers, and start seeing only digits in columns e.g. “6 add 9” instead of “56 add 29”

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2000 - 342 - 105 - 102 197 99

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25x8 or 25 8 x Children relying on written procedures forget how much they can do mentally. 25 x 8 is double 25 x 4

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The calculating repertoire Mental recall of number facts Mental methods of calculation Use of calculators Jottings to record mental calculations Informal written methods Standard written methods

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The calculating continuum Mental Recall Mental Calculations with jottings Informal Methods Expanded Written Methods Standard Written Methods Calculator

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The calculating repertoire Children constantly move up and down the continuum Learning a new method of calculating does not mean other ways are no longer relevant Children should always be looking for calculations they can do wholly or partly mentally

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A structured approach to calculation An approach based on the skills of mental calculation: Remembering number facts Using known facts to derive new ones Familiarity with the number system and relationships between numbers Having a repertoire of mental calculation strategies Understanding of the four operations and how they are related

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Addition and subtraction Partitioning is an important strategy children must learn A number line is a method of informal calculation that works for any size of number, for both operations. Knowing 33+ 25 = 58 leads to the following: 25+ 33 = 58 58 - 33 = 25, 58 - 25 = 33 25+ ? = 58 58 = 33 + ?

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Multiplication and division Multiplication is repeated addition, division is repeated subtraction Doubling, halving, partitioning, and multiplying by 10, 100, 1000 are essential mental strategies Multiplication and division are the inverse of each other 3x4=12 leads to 4x3=12; 12÷3=4; 12÷4=3 and then 6x4=24, etc, and then 30x4=120, 300x4=1200, 120÷4=30 etc

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Moving from informal to formal methods At every stage, teachers first use examples that children can easily do mentally Children then see how the steps in a written procedure link to what they do in their heads They then move to using numbers that cannot easily be dealt with mentally, Partitioning and place value are crucial concepts and estimation of size of answers is essential.

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Now …. The presentation is over. Next either go to Mr Traynor if your child is in year 3 or 4 or to Ms Buttinger if your child is in year 5 or 6. We will answer your questions and go into more depth on any of the teaching methods mentioned e.g. grid method, long division, inverse operations, partitioning. You might want to ask about learning multiplication tables and number bonds, or what does “decomposition” actually mean? Lastly, there are handouts on the table and workbooks to look at.

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