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Developing Mathematical Thinking in Addition and Subtraction

Developing Mathematical Thinking in Addition and Subtraction. Checking Understanding. What strategies could you use?. Count up from / back from. Empty number line actual or imagined. round and compensate eg 42 – 30 then +1. Subtraction 42 - 29. Decomposition?.

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Developing Mathematical Thinking in Addition and Subtraction

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  1. Developing Mathematical Thinking in Addition and Subtraction

  2. Checking Understanding

  3. What strategies could you use? Count up from / back from. Empty number line actual or imagined round and compensate eg 42 – 30 then +1 Subtraction 42 - 29 Decomposition? conserve number ie 42 – 29 = 43 - 30 29 42 30 43

  4. Strategies for calculation • 5006 – 3562 • 5006 - 99 • 5006 – 4958 How would your pupils solve these? • 2704 + 3562 • 2704 + 5998 • 2704 + 96 They all start with the same number Efficiency of calculation – it depends on the relationship between the numbers involved I can use addition, subtraction, multiplication and division when solving problems, making best use of the mental strategies and written skills I have developed. MNU 1-03a

  5. Should it make a difference if this was written horizontally as 6000 – 2369? Is decomposition the most sensible strategy here? Checking Understanding Subtract: 6,000 – 2,369 Do you encourage and discuss informal jottings which pupils use? Do pupils develop understanding of the process using practical material? How can we encourage understanding and develop learning?

  6. Applying Strategies A concert is taking place. 6003 tickets are on sale. 5997 tickets sell in a week. How many tickets remain on sale ? Is decomposition the most sensible strategy here? How can we help pupils in solving word problems? Development and progression FIRST Level - ‘solving word problems involving the four number operations‘

  7. Time – a further complication. A common error – 2h 40 mins. Why? George took 7 hours 55 minutes to travel from Glasgow to London. Eric took 9 hours 15 minutes to drive the same journey. How much longer did Eric take? How can we encourage understanding and develop learning?

  8. Properties of Number • Inverses The inverse of + is - eg family of four facts 5+2 = 7 2+5 = 7 7–2 = 5 7-5 = 2 Do you encourage your pupils to make the links? Knowing one fact means you know four.

  9. Properties of Number • Identity: An important mathematical concept identity of + and - is 0 e.g. Does it matter how many items are in the cup? 2 + 0 = 2 6 - 0 = 6 Progression to formal algebra + 0 = - 0 = x + 0 = x a - 0 = a

  10. Support for progression in mathematics http://www.ltscotland.org.uk/curriculumforexcellence/mathematics/outcomes/moreinformation/developmentandprogression.asp

  11. Next steps What informationwillyou share with colleagues? What might you or your staff do differently in the classroom? What impact will this have on your practice? What else can you do as to improve learning and teaching about number

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