1 / 60

MAKING RATIONAL NUMBERS MORE MEANINGFUL

MAKING RATIONAL NUMBERS MORE MEANINGFUL. ATMIM WINTER CONFERENCE BOSTON COLLEGE JANUARY 9 2014. Margaret J. Kenney (kenney@bc.edu) Boston College, Chestnut Hill MA 02467. Factors Common Core Treatment Of the Rationals Pre-service teachers Bias about Number L ine Use.

delila
Download Presentation

MAKING RATIONAL NUMBERS MORE MEANINGFUL

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. MAKING RATIONAL NUMBERS MORE MEANINGFUL ATMIM WINTER CONFERENCE BOSTON COLLEGE JANUARY 9 2014 Margaret J. Kenney (kenney@bc.edu) Boston College, Chestnut Hill MA 02467

  2. Factors Common Core Treatment Of the Rationals Pre-service teachers Bias about Number Line Use

  3. Unit Fractions are key to the development of rational numbers in CCSSM What of unit fractions in math history?

  4. Solve: Divide L loaves Among P persons Equally using ‘largest unit fractions’ .

  5. OUR SOLUTION ?

  6. OUR SOLUTION ? 4 ÷ 7 4 / 7

  7. EGYPTIAN SOLUTION

  8. EGYPTIAN SOLUTION

  9. TRY Divide 3 loaves Among 7 persons

  10. EGYPTIAN SOLUTION

  11. EGYPTIAN SOLUTION

  12. EGYPTIAN SOLUTION

  13. EGYPTIAN SOLUTION

  14. Key relation for Rational numbers Equality Given: a /b=c /d if and only if ad = bc

  15. WHY ??

  16. a /b=c /d if and only if ad/bd = bc/bd implies ad = bc

  17. a /b=c /d if and only if ac/bc = ac/ad implies ad = bc

  18. WHY ?? SAME DENOMINATORS OR NUMERATORS

  19. A Ready-to-Use Fraction Tool

  20. Try Number tiles Useful in Problem Solving

  21. 2 1 3 6 3 9

  22. How Many like

  23. How many like

  24. CHALLENGE

  25. Points to Ponder: What is largest/smallest sum? Closest means? How many pairs ? Sums?

  26. a/b c/d The Power of the Number Line

  27. Find a Rational Number between two Rational Numbers

  28. Find a Rational Number between two Rational Numbers NAME THREE WAYS TO ACCOMPLISH THIS

  29. Averaging Halve the distance Add /Subtract

  30. Given: 1 /4and2 /3 Between: (1+ 2) / (4 +3) ? ?

  31. Given: 1 /4and2 /3 Is (1+ 2) / (4 +3) between them ? ? Try other examples

  32. What about 1 /5and3 /4 Between: (1+ 3) / (5 +4) ? ? 3 /8and5 /4 Between: (3+ 5) / (8 + 4) ? ?

  33. CONJECTURES With Rational Numbers

  34. CONJECTURE - Given: a /bandc /d then (a+ c) / (b + d) is between them

  35. Key relation to apply Less than

  36. Key relation to apply Less than Given: a /b<c /d if and only if ad < bc

  37. Given: a /b<c /d Show a /b < (a+ c) / (b + d) and (a+ c) / (b + d) < c /d

  38. Algorithms /Operations With Rational Numbers

  39. Addition a c ad bc b d bdbd ad + bc bd + + = =

  40. Multiplication a c a x c b d b x d x =

  41. Division Invert & Multiply a c a d b d b c ÷ =

  42. Division Is this valid? a c a ÷ c b d b ÷ d ÷ =

  43. Is this valid? a ÷ c a/c b ÷ d b/d (a/c )(d/b) (b/d)(d/b) ad bc = = =

More Related