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Calculation up to 100. Presentatie titel. Okahandja, June 2014. Rotterdam, 00 januari 2007. As in calculation <10 and calculation <20, it ´s in calculation <100 very important learners learn how to solve problems by making use of structures . We all know now three phases :

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  1. Calculation up to 100 Presentatie titel Okahandja, June 2014 Rotterdam, 00 januari 2007

  2. As in calculation <10 and calculation <20, it´s in calculation <100 very important learnerslearnhow to solveproblemsbymakinguse of structures. • We all knownowthreephases: • Addition and subtractionbycounting (noteffective at last) • Addition and subtractionbyusing models (smart teaching materials) • Addition and subtraction in a formalway. • This last phase is the finalphase.

  3. 10 frames

  4. 10 frames

  5. Classroom number line 1 - 100

  6. Classroom number snake 1 - 100

  7. Number snake 1-100, combined with the empty number line

  8. Sun-game

  9. Empty number line

  10. Strategies calculation up to 100Intermezzo: How did you do it? Solve the problems and write down your calculations. Show the way you find your answer! • 43 + 35 = • 58 + 26 =  • 85 – 32 =  • 72 – 37 = • Solve

  11. The calculations of the learners of Elim Primary School in Windhoek

  12. The strategies used by the learners of Elim Primary School in Windhoek • In grade 3: Counting one-by-one, Stepwise addition and subtraction/ Stringing, Splitting, Digit algorithm • In grade 4: Stepwise addition and subtraction/ Stringing, Splitting, Digit algorithm • In grade 5: Digit algorithm what about your strategies?

  13. Stepwise addition and subtraction/Stringing 45 + 28 = Joan has read 45 pages in her book. Today she reads 28 pages. • 45 + 20 = 65 65 + 25 = 70 70 + 23 = 73

  14. Stepwise addition and subtraction/Stringing 84 – 27 = I cut 27cm off a ribbon measuring 84 cm. How much is left?

  15. Stepwiseaddition and subtraction/Stringing • 47 + 25 47 + 3 = 50, 50 + 20 = 70, 70 + 2 = 72 • 47 + 25 47 + 20 = 67, 67 + 3 = 70, 70 + 2 = 72 • 47 + 25 47 + 20 = 67, 67 + 5 = 72

  16. Stepwise addition and subtraction/Stringing • Teaching materials supporting stepwise addition/subtraction (stringing) • Numberline • Number snake • Sun-game • 100-beads/bottle caps string • Empty number line

  17. Splitting or Column calculation.This strategy is based on number value. • 47 + 25 40 + 20 = 60, 7 + 5 = 12, 60 + 12 = 72

  18. Splitting or Column calculation 47 25 + 60 12 + 72 47 + 25 40 + 20 = 60, 7 + 5 = 12, 60 + 12 = 72

  19. Splitting or Column calculation

  20. Splitting or Column calculation • Teaching materials, supporting splitting or column calculation • 10-frames

  21. Strategie 4: Digit algorithm

  22. Smart strategies (a higher level of calculation)The Grandstand problem (in case of addition) • 56 + 27 • 56 + 27 = 53 + 30 = 83 3

  23. Smart strategies The Scale problem (in case of subtraction) • 68 – 29 • 68 – 29 = 69 – 30 = 39 +1 +1

  24. Smart strategies Jumping too far and back (learners think of the nearest decade) • 45 + 28 = 45 + 30 – 2 = • 82 – 37 = 82 – 40 + 3 =

  25. Which strategie do you choose? A book with 84 pages. You are reading at the bottom of page 37. How many pages still to read? The black t-shirt costs N$ 92 and the grey t-shirt costs N$ 69. How much more expensive is the black t-shirt? N$ 92 N$ 69

  26. The basic strategies: 1 Stepwise addition and subtraction/ Stringing • Starts with flexible counting • The ‘large number line’: 10 – 20 – 30 – 40 – 50 – 60 – 70 – 80 – 90 – 100 • The ‘small number line’: 1 – 2 – 3 – 4 - 5 – 6 - 7 – 8 – 9 – 10 – 11 – 12 - ….- 33 – 34 – 35 – 36 – 37 – 38 – 39 - 40- etc • Use of the empty number line as a ‘notation scheme’ and ‘paradigm’

  27. The basic strategies: 2 Splitting/ column calculation • Starts with place value • Use of the 10-frames as a ‘paradigm’ • Use of the ‘column notation scheme’ emphasises the place value

  28. The teaching-learning-trajectory Basic strategies for all learners: • Stepwise addition and subtraction/ Stringing. The most natural way of addition and subtraction • Splitting/Column calculation. You need to know if the numbers get bigger ad you want to add and subtract without a calculator Additional: • Smart calculation

  29. Discussion & Exercises • Discussion • Exercises 46 + 23 = 58 + 36 = 76 – 24 = 63 – 28 = • Stepwise (shopkeepers method), Splitting, Smart calculation

  30. Studies • Teaching-learning trajectory ‘stepwise addition and subtraction, • Teaching-learning trajectory splitting • Teaching-learning trajectory smart calculation

  31. Studies • How does it start? • Which steps for the learners to make in the learning trajectory? • Which teaching materials are usefull in the teaching trajectory? • Which notation schemes do the learners use? • What are the learning outcomes in this teaching learning trajectory?

  32. The 100-caterpillar 100 • Choose two different numbers between 0 en 100, • Put these numbers in order in the first and the second part of the caterpillar, • Make the number in the next part by adding the two previous numbers, • The number in the fifth part must be 100! Just for fun

  33. 75-game • Rules of the game: • Take a turn to a number, • Choosefrom the numbers 5, 10, 15, 20, 25, 30, 35, • 40, 45, • Each number can be chosen only once! • Do you have three numbers which together have 75? • You are the winner! Just for fun

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