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From Counting to Calculation (Two digit addition)

From Counting to Calculation (Two digit addition). Paul Swan pswan@iprimus.com.au p.swan@ecu.edu.au. Proficiency & Content Strands. Australian Curriculum. Understanding (conceptual) Fluency Number and Algebra. Consider. 28 + 37. Three Strategies. Split one 20 + 37 + 8 Or 28 + 30 + 7

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From Counting to Calculation (Two digit addition)

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  1. From Counting to Calculation (Two digit addition) Paul Swan pswan@iprimus.com.au p.swan@ecu.edu.au

  2. Proficiency & Content Strands

  3. Australian Curriculum • Understanding (conceptual) • Fluency • Number and Algebra

  4. Consider 28 + 37

  5. Three Strategies • Split one 20 + 37 + 8 • Or 28 + 30 + 7 • Split both 20 + 30 + 8 + 7 Adjust and compensate 30 + 27 – 2

  6. A closer look • 20 + 30 +8 + 7 • How do you add 20 and 30? • How do you add 8 and 7?

  7. 8 and 7 • 8 + 8 – 1 (Near doubles) • Relies on knowing doubles • Adjust and compensate • 7 + 7 + 1 (Near doubles) • 8 + 2 + 5 (bridge ten) • Relies on make to ten strategy • Ability to partition (7 = 2 and 5)

  8. Pre-requisite • Children need to be secure in counting • 5 principles of counting • See p. 12 FSiM: Number-Understand whole number. • Quick check • Snap +/– 1 • See p. 24 Card Capers

  9. Further pre-requisite • Commutative property of addition • 3 + 6 = 6 + 3 • Think BIG count small • Count 3 not 6 • Dominoes ideal material • Match dice – subitising

  10. Adding 1, 2, 3 or 0: Counting on

  11. Counting on 1, 2, 3, 0 • Accounts for 64 addition facts

  12. Partitioning • Splitting or breaking up numbers • Tools • Partitioning board • Number window (frame) • Counters • Cuisenaire rods • Make to ten

  13. Partition board 2 5

  14. CuisenairePartitioning Ten

  15. Ten Frames • What do you see?

  16. Part Part Whole WHOLE Part Part 9 5 4 See p. 20 FSiM: Number - Understand Operations

  17. Make to ten

  18. Partitions or bonds to ten

  19. Make to Ten • Serves as an anchor point • Pre-requisite for bridge ten • 8 + 7 • 8 + 2 + 5 • By this stage start introducing subtraction

  20. Celebrity Heads • Playing cards to crowns

  21. Link + and – 6 10 Part 4 WHOLE Part WHOLE Part

  22. Understand Operations • Subtraction is the inverse of addition • A common subtraction strategy is to think addition • However subtraction more difficult • Language issues

  23. Doubles

  24. All Doubles

  25. Near Doubles

  26. All Near Doubles

  27. Dominoes game • Separate all the doubles and near doubles. • Turn over (face down) • Pick one up • State Total • Grid paper may be used to develop doubles

  28. Bridge ten - start with 9 and …

  29. Tens Frame - Ideal tool 9 and 6 Becomes 10 and 5

  30. Summary of StrategiesDeveloping Fluency through games

  31. Summary of StrategiesDeveloping Fluency through games • CD • Containing: • Teacher notes • Video • IWB or computer software • Printable student materials • Assessment materials

  32. Assessment • What strategies are being taught and used? • Common Assessment task(s)

  33. Games • 7 cards • Observe strategies being used. • Mary’s Game (p. 20 Dice Dilemmas) • Improves speed and accuracy • Flipper (p. 28/29 Card Capers)

  34. Westwood One Minute Basic Facts Tests

  35. Westwood Analysis

  36. For multiplication and division

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