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Tapes Toilet Doors and Tables

Tapes Toilet Doors and Tables. Paul Swan Edith Cowan University. Yr 3, 1967. Yr 4, 1968. Yr 5, 1969. Yr 6, 1970. 100 Facts - Why so hard to learn?. Multiplication property of zero, that is, anything multiplied by zero is zero accounts for 21 basic multiplication facts.

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Tapes Toilet Doors and Tables

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  1. Tapes Toilet Doors and Tables Paul Swan Edith Cowan University

  2. Yr 3, 1967 Yr 4, 1968 Yr 5, 1969 Yr 6, 1970

  3. 100 Facts - Why so hard to learn? • Multiplication property of zero, that is, anything multiplied by zero is zero accounts for 21 basic multiplication facts. • Confusion with addition where adding zero does not make a difference

  4. Start from the known • 1, 2, 5, 10 • Can children count in …? • Multiples, skip counting • However, need to move on. • Watch for children who have to count multiples to get to a fact eg 7 x 2 • Watch for answer one multiple out eg 12, 16

  5. X 0, 1, 2, 5 and 10 • Robust understanding required • Look for links eg 5 x and 10 x

  6. Key propertySee Tackling Tables, p. 10 - 11 • Commutative property of multiplication • Muffin tray principle 3 rows of 4 4 rows of 3

  7. An interludeAn array split into parts 3 x 16 3 x 16 = (3 x 10) + (3 x 6)

  8. Power of commutative property • Virtually halves the number of facts to be learned. • Relies on Understanding the multiplication operation as more than simply repeated addition • Lots of, groups of … • Multiplicative thinking (key idea)

  9. 1 x 2 = 2 2 x 2 = 4 3 x 2 = 6 4 x 2 = 8 5 x 2 = 10 6 x 2 = 12 7 x 2 = 14 8 x 2 = 16 9 x 2 = 18 10 x 2 = 20 11 x 2 = 22 12 x 2 = 24 1 x 3 = 3 2 x 3 = 6 3 x 3 = 9 4 x 3 = 12 5 x 3 = 15 6 x 3 = 18 7 x 3 = 21 8 x 3 = 24 9 x 3 = 27 10 x 3 = 30 11 x 3 = 33 12 x 3 = 36 Standard tables charts

  10. Std Tables Chart • Help or Hindrance?

  11. Twenty-one hard facts • 3 x 3, 3x 4, 3x 6, 3 x 7, 3 x 8, 3 x 9 • 4 x 4, 4 x 6, 4 x 7, 4 x 8, 4 x 9 • 6 x 6, 6 x 7, 6 x 8, 6 x 9 • 7 x 7, 7 x 8, 7 x 9 • 8 x 8, 8 x 9, 9 x 9

  12. Why are tables so hard to learn? • Timed tests • Testing different to teaching • Classroom Atmosphere • Boring repetitive exercises • Premature Drill • Lack of mental strategies • Poor understanding of properties of number; commutative property( MLAO # 7 • Linguistic patterns (6 x 6 = 36) • Lack of a coherent whole school approach

  13. Classroom Atmosphere • Danny Champion of the world

  14. Boring Repetitive • Beat the tape

  15. Even more boring!

  16. Three x table • 3 x 3, 3 x 4, 3 x 6, 3 x 7, 3 x 8, 3 x 9 • Note the three x table is related to to the six • 6 x 6, 6 x 7, 6 x 8, 6 x 9 • And the nine x table • 3 x 9, 4 x 9, 6 x 9, 7 x 9, 9 x 9 • Consider teaching as a cluster (See FSiM: Number Calculate, p. 189 - 193)

  17. Relate to a known fact • A very powerful strategy. • Askew (1998). Explains it this way. • Askew, M. (1998). Teaching primary mathematics: A guide for newly qualified and student teachers. London: Hodder & Stoughton. KNOWN NUMBER FACTS HELP BUILD MORE ARE USED TO KNOWN NUMBER FACTS

  18. Mental Strategies • Known - derived facts • Doubling • Along with the commutative property

  19. Assessment - Find out what students know • See Tackling Tables p. 20 - 27. • The chocolate problem.

  20. Array Game • See Tackling tables p. 32 - 33

  21. From Known to Unknown • 3 x 2 = 6 • Double: 3 x 4 = 12 • Double again: 3 x 8 = 24 • Double again: 6 x 8 = 48 • Once the fact 6 eights is established (known) it may be used as the basis to derive a new fact

  22. From known to derived • 7 x 8 hardest fact to learn • 25 % of adults experience difficulty with it • Response rate slows • Linguistic pattern difficult • 6 x 8 (linguistic pattern flows) • Use 6 x 8 to derive 7 x 8

  23. From Known to Unknown 6 x 8 and Another 8

  24. 7 x 8 7 x 8 = 56 Or 56 = 7 x 8

  25. Make the links • Celebrity Heads

  26. Flashcards 7 56 8

  27. Alternate Flash Card 56 7 8

  28. Make the links explicit! • 7 x 8 = 56 • 8 x 7 = 56 • 56 = 7 x 8 … • 56 ÷ 7 = 8 • 56 ÷ 8 = 7 • 1/7 of 56 … • Remember factors

  29. Three times table • Digit Pattern • Link to divisibility • Sum of the digits add to 3, 6 or 9.

  30. Consider Patterns • 3x, 9x , 5x table

  31. 72 (7 + 2 = 9) 81 (8 + 1 = 9) 90 (9 + 0 = 9) 99 (9 + 9 = 18 … Use Patterns • 9 • 18 (1 + 8 = 9) • 27 (2 + 7 = 9) • 36 (3 + 6 = 9) • 45 (4 + 5 = 9) • 54 (5 + 4 = 9) • 63 (6 + 3 = 9)

  32. Relate to a known fact • 1 x 9 = 1 x 10 - 1 • 2 x 9 = 2 x 10 - 2 • 3 x 9 = 3 x 10 - 3 • 4 x 9 = 4 x 10 - 4 • 5 x 9 = 5 x 10 - 5 • 6 x 9 = 6 x 10 - 6 • 7 x 9 = 7 x 10 - 7

  33. Finger methods • 9 x table on fingers • Gloves of calculation

  34. Square numbers??? Note special type of array. Consider the factors.

  35. Develop Computational Fluency • Drill will make you faster at what you know • Jeremy’s story • Premature drill leads to the adoption of inefficient strategies. • Three second or less response time.

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