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What Is Number Sense and Why Don ’ t My Students Have It?

What Is Number Sense and Why Don ’ t My Students Have It?. Slight modification of the presentation at the NCTM Annual Conference by Dr. Eric Milou Rowan University Department of Mathematics milou@rowan.edu 856-256-4500 x3876. Content Overview. National Math Panel

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What Is Number Sense and Why Don ’ t My Students Have It?

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  1. What Is Number Sense and Why Don’t My Students Have It? Slight modification of the presentation at the NCTM Annual Conference by Dr. Eric Milou Rowan University Department of Mathematics milou@rowan.edu 856-256-4500 x3876

  2. Content Overview • National Math Panel • Number Sense & Computation Proficiency • Algebraic Symbolic Manipulation vs Algebraic Thinking • The role of Technology

  3. National Math Panel (NMP) • A focused, coherent progression of mathematics learning, with an emphasis on proficiency with key topics, should become the norm in elementary and middle school mathematics curricula. Any approach that continually revisits topics year after year without closure is to be avoided.

  4. NMP • A major goal for K–8 mathematics education should be proficiency with fractions (including decimals, percents, and negative fractions).

  5. Response by Peppermint Patty

  6. Your Test! 4 x 9 x 25 How many ounces are in a gallon? 50 ÷ 1/2

  7. Conceptual Understanding • 24 ÷ 4 = 6 • 24 ÷ 3 = 8 • 24 ÷ 2 =12 • 24 ÷ 1 = 24 • 24 ÷ 1/2 = ??

  8. Fractions - Conceptually More than 1 or Less than 1 Explain your reasoning

  9. Which is larger? • (2/3 + 3/4 + 4/5 + 5/6) or 4 • 12.5 x 45 or 4.5 x 125 • (1/3 + 2/4 + 2/4 + 5/11) or 2

  10. Where’s the Point? • 2.43 x 5.1 = 12393 • 4.85 x 4.954 = 240269 • 21.25 x 1.08 = 2295 • 1.25 x 64 = 80 • 4.688 x 1.355 = 635224 • 46.88 x 1.355 = 635224 • 4.688 x 135.5 = 635224 • 46.88 x 13.55 = 635224

  11. Conceptual Fraction task • Kim’s teacher asked her class to design a flag using four colors, dividing a square into parts, and to color the parts as follows: • 1/2 is colored red • 1/4 is colored blue • 1/8 is colored green • Any other part is to be left white

  12. Flags

  13. Harder Task • A chocolate bar is separated into several equal pieces. • If Laura eats 1/4 of the pieces; and • Paul eats 1/2 of the remaining pieces; • There are six pieces left over • Into how many pieces was the original bar divided?

  14. Chocolate Bar P A U L LAURA 16 pieces

  15. 1.49 1000 Decimals • 1000 ÷ 1.49 = 671.1409396 = Torture! • Big Macs Sell for $1.49, how many Big Macs can I buy for $10.00? • 1 is $1.50 • 2 are $3 • 4 are $6 • 6 are $9 Number Sense is a vital skill

  16. Computation

  17. Active Computation • Virtual Manipulatives • http://illuminations.nctm.org • nlvm.usu.edu/en/nav/vlibrary.html

  18. Conceptual & Contextual • 8 + 7 = ? • How do we teach this? x x x x x x x x x x x x x x x

  19. 8 + 7 = ? 8 + 7 = ? 5 2 10 + 5 = 15

  20. Number Line Addition 5 + 4 = nlvm.usu.edu/en/nav/vlibrary.html

  21. 1000 - 279 = ? 279 +1 = 280 + 20 = 300 +700 = 1000 1000 - 279 = 721

  22. Multiplication • 13 x 17 = ? 10 7 2 10 3 1 3 x 1 7 1 0 0 7 0 ------- 3 0 2 1 9 1 1 3 0 ------- 2 2 1 221

  23. Conceptual approach leads to ? • Algebra: (x + 3) (x + 7) = x 7 x 3 x2 7x 3x 21

  24. Example: Drug Steady State • 10 mg Zrytec daily • 50% of Zrytec is eliminated daily • What % is in the body • after 7 days • 10 days • n days?

  25. 10mg Daily of Zrytec 10 1 15 2 17.5 3 18.75 4 5 19.375 6 19.6875

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