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Maths the Modern Way!! Addition and Subtraction St Teresa’s Primary School with Essex County Council The Primary National Strategy Basis of teaching since 1999 – based on extensive research and proven success Daily entitlement to maths lesson Key features Progression carefully set out Interactivity – use of models, images, games, practical activities Focus on mental skills as well as written Vocabulary, problem solving, communication, explanation and reasoning There is no “right way” to work!! Children exposed to a range of methods. Methods selected will depend upon the situation and the numbers involved, including when to use calculators. Children make decisions about methods and draw on a range of strategies and approaches when applying Maths in context. Children in same class could be using different methods to others depending on their ability, confidence and stage of mathematical development. Addition Foundation Stage (Reception) Counting and recognising numbers Counting on using number lines or apparatus Recall of facts and number bonds Numbers to 10, then beyond. Key Stage 1 Year 1 Introduce + and = signs to record calculations done mentally Securing bridge over 10s boundary Mental recall of facts Numbers extend to 30, 40… Recognise patterns in 100 square (+10, +1) Splitting numbers and recombining The Importance of Place Value Place Value Runaround! Key Stage 1 Year 2 Extension of Year 1 Introduction of partitioning Adding significant digits first How to Partition 35 + 72 30 5 30 + 70 = 100 5+ 2= 7 100 + 7 = 107 70 2 Try these by partitioning!! 45+67 154+78 327+198+23 This can work with any size of number – is it efficient to use this method for this? 40187+63742+31243 10005+12010+3000 Key Stage 2 The Numberline!! 67 + 32 67 + 10 + 10 + 10 + 2 67 77 87 97 99 Expanded Addition (Introduced Year 3) 43+25 43 + 25 60 8 68 Try this method with these!! 254+167 423+541 Standard Method 63+39 63 + 39 12 90 1 02 + 63 39 2 1 63 + 39 1 02 1 You may like to try these problems using some of the methods that we have used so far. 623+12 352+231+101 16+746+233 The Roundabouts of Harlow FINISH 1 1 2 4 11 8 5 9 2 3 5 12 7 6 1 10 START Subtraction Foundation Stage (Reception) Counting and recognising numbers Counting back using numberlines or apparatus Recall of facts and number bonds Numbers to 10, then beyond. Key Stage 1 Year 1 Introduce - and = signs to record calculations done mentally Mental recall of facts Subtracting 10 from “teens” number Recognise patterns in 100 square (-10, -1) Splitting numbers and recombining Key Stage 1 Year 2 Extension of Year 1 Crossing 10s boundary with numbers to 20,30…. (crossing 100s boundary in Y3) May use splitting of numbers/partitioning to assist in calculation (e.g. 27–15 = 27–5–2–8) Key Stage 2 The Numberline!! 67 - 32 67 - 10 - 10 - 10 - 2 -2 35 -10 37 ANSWER!!! -10 47 -10 57 67 OR…. 67 - 32 +10 +10 32 42 +10 52 +5 62 67 10 + 10 + 10 + 5 = 35 +10 +8 32 40 +10 50 10 + 10 + 8 + 7 = 35 +7 60 67 Complementary Addition +10 +8 32 40 +10 50 10 + 10 + 8 + 7 = 35 67 - 32 8 to 4 0 2 0 to 6 0 7 to 6 7 35 +7 60 67 The Standard Method Decomposition Introduced from Year 3 Linked initially with use of images and practical apparatus to secure understanding of how place value is being used in the calculation Lots of stages where children can make errors Not always the most efficient method to use If children can obtain an answer using another method, that is OK. 33 - 17 Can I do this mentally? Shall I use a written method? Which written method is most appropriate to use for these numbers? 33 - 17 33 - 17 33 - 17 33 - 17 I’m going to partition the numbers. 33 - 17 33 - 17 = 30 + 3 - 10 + 7 33 - 17 33 - 17 30 + 3 = - 10 + 7 33 - 17 33 - 17 30 + 3 = - 10 + 7 I start with the units, so I need to take away 7 small cubes. But I only have 3 of them. I’ll break up one of the 10s into 10 units. 33 - 17 33 - 17 30 + 3 = 20 + 13 - 10 + 7 = - 10 + 7 I’ve now got 2 lots of 10, so that’s 20, as well as 13 units, so let’s write it down to show what I am doing. 33 - 17 33 - 17 30 + 3 = 20 + 13 - 10 + 7 = - 10 + 7 Now I can take away 7! 33 - 17 33 - 17 30 + 3 = 20 + 13 - 10 + 7 = - 10 + 7 6 33 - 17 33 - 17 30 + 3 = 20 + 13 - 10 + 7 = - 10 + 7 6 Now I can take away 10! 33 - 17 33 - 17 30 + 3 = 20 + 13 - 10 + 7 = - 10 + 7 10 + 6 33 - 17 33 - 17 30 + 3 = 20 + 13 - 10 + 7 = - 10 + 7 10 + 6 =16 Have a Go! There is some base 10 apparatus in the tables if you would like to run through using this to be clear about the process involved. 42 – 27 51 – 29 90 - 36 There will be examples like this… 75 – 32 where no exchange is needed, but partitioning is still useful as children are more successful at working with tens and units separately. - 75 70+5 32 = 30+2 20+3 = 23 Next stages will involve increasing the number of digits in the numbers (HTU, the ThHTU), working with apparatus, then without, to ensure children are secure with place value before moving on to the final stage. Often this would be taught side by side with the more expanded method so that children can see how they relate. 271 200+70+ 1 200+60+11 -158 = 100+50+ 8 = 100+50+ 100+10+ 6 1 6 1 6 1 8 3=113 6 1 271 2 7 1 2 7 1 2 7 1 2 7 1 -158 - 1 5 8 - 1 5 8 - 1 5 8 -1 5 8 3 1 3 1 1 3 Why the additional steps? Why the additional steps? 2 1 6 3 0 4 - 3 2 0 7 1 1 6 3 0 4 - 3 2 0 7 1 3 0 0 7 Why the additional steps? 2 1 6 3 0 4 - 3 2 0 7 1 1 6 3 0 4 - 3 2 0 7 1 3 0 0 7 3 0 0 0 5 - 4 8 5 7 3 0 0 0 5 - 4 8 5 7 3 4 8 5 2 Maths the Modern Way!! Addition and Subtraction St Teresa’s Primary School with Essex County Council