Session 4 - Addition and Subtraction (Year 1) PDF

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Summary

Tutor - Amanda ...

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Addition and Subtraction (Mental maths) LO: To understand the rationale for the teaching of mental maths To know that there are a range of mental addition and subtraction strategies

Why Teach Mental Maths? = It is statutory (Links to teaching standard 1 becoming fluent) = Contributes to improved problem-solving skills = Develops effective ‘number sense’ = Most calculators are done in the head in real life = Improves estimation skills = Theoretically, they should help children develop towards informal written methods and then standard methods

Curriculum: Key Stage 1 The NC makes reference to pupils using concrete objects and pictorial representations when carrying out mental calculations Moyer (2001) points out that: - Manipulative materials are objects designed to represent explicitly and concretely mathematical ideas that are abstract. They have both visual and tactile appeal and can be manipulated by learners through hands-on experiences. (p.176) - Pictorial representations are visual representations of the concrete manipulatives e.g. circles to represent coins, number lines, pictures of objects etc.

Laws of arithmetic Commutative law 4+3=3+4 4x3=3x4

// (b + a) = (a + b) // (b x a) = (a x b)

Associative Law 2 + (3 + 4) = (2 + 3 ) + 4

//

a + (b + c) = (a + b) + c

What skills are needed for effective mental maths? An understanding of the relationships between numbers Why don’t we memorise number facts rather than learning relationships between them? Learning about relationships leads to understanding of concepts such as compensation Can help children remember a forgotten fact

How does counting forwards and backwards help in mental calculations? ● Counting forwards and backwards in ones, tens, hundreds is essential for effective mental maths calculation ● Counting on (addition) and counting back (subtraction) are linked with movements along a number line ● Children taught counting starting from any number e.g. 7,17, 27 ● A hundred square provides children with a strong image that supports counting in ones and tens e.g. online resource

Number line As children develop their understanding of the number system, progression in the level of sophistication of a number line is needed for both teaching and learning Number tracks are superseded by marked number lines An empty number line allows for the modelling of mental calculation

Addition and Subtraction strategies There is a range and variety of possible methods for A and S and the following mental strategies are identified in the National Strategies booklet Teaching Children to Calculate Mentally (DfE, 2010:p26) -

Counting forwards and backwards Reordering Partitioning (using multiples of 10 and 100) Partitioning (bridging through multiples of 10) Partitioning (compensating which is also referred to as ‘rounding and adjusting’ Partitioning ( using near doubles) Partitioning (bridging through numbers other than 10)

Bridging through multiples of 10 75 + 8 = 70 + 10 + 3 = 83 47 + 6 = 40 + 10 + 3 = 53

Re-ordering, Compensating and Partitioning

Other examples: 1. Calculate 386 + 243 using partitioning 300 + 200 = 500 80 + 40 = 120 6+3=9 500 + 120 + 9 = 629  2. Calculate 247 + 245 using near doubles 245 + 245 = 490 + 2 = 492   3. Calculate 513 - 198 using compensation 513 - 200 = 313 + 2 = 315

Student example: Scott calculates 27 + 28 “ Two 20s is 40...7 and 8...if theres 7...take 3 from the 8 which makes it into a 1...3 taken off 8 leaves 5...so the answer is 55…” More efficient would be doubles or compensation so: -

27 + 30 = 57 - 2 = 55 27 + 27 = 54 + 1 = 55

Inverse relationship Why might children find it difficult to recognise the inverse relationship between addition and subtraction? -

Prior learning Not realise that they can be used in similar ways Consider the strategies used by Chris and Scott. Chris and Scott’s strategies are not the exact opposite of each other. Many countries partition only the second number when adding, e.g. 27 + 20 + 8, to avoid this....