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Basic Facts

Basic Facts. The many faces of Basic Facts. Basic Facts. Times tables (and thence division) Addition facts (and thence subtraction) Other whole number facts Fractional facts Other mathematical facts (includes theorems) Definition : (a tentative go)

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Basic Facts

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  1. Basic Facts The many faces of Basic Facts

  2. Basic Facts • Times tables (and thence division) • Addition facts (and thence subtraction) • Other whole number facts • Fractional facts • Other mathematical facts (includes theorems) Definition:(a tentative go) Any number or mathematical fact (or idea) that can be instantly recalled without having to resort to a strategy to derive it. 6 + 3, 14 - 8, 7 × 8, 82 r2 = x2 + y2

  3. Memory Model from research

  4. How the brain learns mathematicsDavid A. Sousa (2008)ISBN 978-1-4129-5306-1

  5. Start with Strategies There is no point in a student learning a number fact until: • They have some understanding of the domain in which the fact resides. • They have at least one strategy which they could use to construct the answer. Example: 8 × 6 = 48 • Is the student a multiplicative thinker (or at least advanced additive)? • Can they get 6 × 8 = 6 + 6 + 6 + 6 + 6 + 6 = 48 or 6× 8 = 5× 8 + 8 = 48 or some other way

  6. Plenty of practice As a student does more and more examplesusing a variety of strategies, they gradually come to instantly recall some of them. Practice with strategies Strategies are in procedural memory

  7. Move on to memorisation • Practicing strategies alone is not enough to getinstant recall of basic facts. • Which is harder to do? 8 × 6 = 8 + 6 = Practice for memorisation Basic facts are in declarative memory

  8. Memory has RANDOM ACCESS You don’t have to repeat a memorised sequence to obtain the result you want • What is 8 × 6? Level II 8 × 1 = 8; 8 × 2 = 16 ….. Level III48 • What is the fifteenth letter of the alphabet?

  9. Who wants to be a millionaire? Put these cities in order from North to South A Palmerston North B New Plymouth C Napier D Tauranga D B C A

  10. Who wants to be a millionaire? Put these lines in the order of the Sound of Music Song A A name I call myself B A drink with jam and bread C A drop of golden sun D A needle pulling thread C A D B

  11. Second Number Addition facts up to 10 • Facts to 5 – Counting strategies • Second Number

  12. Subtraction • Count back by (8 – 3, 14 – 6) • Count back until ( 8 – 6, 14 – 8)Count on from … until … • Properties of 0 (identity) • Properties of 1 (predessor) • Inverse of addition5+3=8<=>8-3=5 <=>8-5=3

  13. Multiplication - strategies • Count all • Repeated addition • Skip count

  14. Multiplication 1x,2x,10x,5x

  15. Multiplication 3x & 4x

  16. Other times tables to know • 25 times • 125 times • 11 times • 11.1 times • 45 times • 21 times

  17. Fractions – Decimals - Percentages • Halves, tenths, and fifths 1/2 0.5 50% 1/10 0.1 10% 1/5 0.2 20% 1/2 x table 0.5 1.0 1.5 2.0 2.5 3.0 … 5x table 1/10 x table 0.1 0.2 0.3 0.4 0.5 0.6 … 10x table 1/5 x table 0.2 0.4 0.6 0.8 1.0 1.2 … 2x table

  18. Fractions – Decimals - Percentages • Halves, quarters, and eighths 1/2 0.5 50% 1/4 0.25 25% 1/8 0.125 12.5% 1/2 x table 0.5 1.0 1.5 2.0 2.5 … 5x table 1/4 x table 0.25 0.50 0.75 1.00 1.25 … 25x table 1/8 x table 0.125 0.250 0.375 0.500 0.625 … 125x table

  19. Fractions – Decimals - Percentages • Thirds, ninths, and sixths times table 1/3 0.333 33.3% 1/9 0.111 11.1% 1/6 0.166 16.6% 1/3 x table 0.333 0.666 0.999 (=1!) … 1/9 x table 0.111 0.222 0.333 0.444 …0.999 (=1) 11.1x table 1/6 x table0.166 0.333, 0.500, 0.666, 0.833, 1.000

  20. Basic facts Basic facts are in declarative memory Strategies are in non-declarative memory

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