1. 1 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 What Is Number Sense and Why Don’t My Students Have It?

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

3. 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. 4 NMP  A major goal for K–8 mathematics education should be proficiency with fractions (including decimals, percents, and negative fractions).

5. 5 Response by Peppermint Patty

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

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

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

9. 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. 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. 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. 12 Flags

13. 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. 14 Chocolate Bar LAURA P A U L 16 pieces

15. 15 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 1.491000

16. 16 Computation

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

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

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

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

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

22. 22 Multiplication  13 x 17 = ? 1 3 x 1 7 1 2 9 031 2 2 1 ------- 10 7 10 3 1 0 0 3 0 7 0 2 1 221

23. 23 Conceptual approach leads to ? x 7 x3x3 x2x2 3x 7x 21  Algebra: (x + 3) (x + 7) =

24. 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. 25 10mg Daily of Zrytec DayMg. of Zyrtec 1 2 3 4 5 6 10 15 17.5 18.75 19.375 19.6875