1. FRACTIONS & DECIMALS WORKSHOP Erie 1 BOCES January 30, 2013 Presenters: Steve Graser & Andrea Tamarazio

10. FRACTIONS WARM-UP Compare & order the following fractions from greatest to least: 3/8, 6/10, 7/12 and 4/5

11. FRACTIONS WARM-UP Write a number that is half way between zero and one. Draw and show this on a number line.

12. FRACTIONS WARM-UP Write a number that is half way between zero and one-half. Draw and show this on a number line.

13. FRACTIONS WARM-UP Write other numbers that are the same as one-half. Draw and show this on a number line.

14. FRACTIONS WARM-UP Write a number that is one-fourth more than one-half? Write a number that is one-sixth more than one-half. Show this on a number line.

15. FRACTIONS WARM-UP What number is one-sixth less than one? Show this on a number line.

16. FRACTIONS WARM-UP What number is one-third more than one? Show this one a number line.

17. FRACTIONS WARM-UP What number is half-way between one-twelfth and three- twelfths? Show on a number line.

18. FRACTIONS WARM-UP Which number is closest to zero? A. one-third B. one-sixth C. one-half D. one-fourth E. one-twelfth Plot all numbers on a number line.

19. FRACTIONS WARM-UP What number is closest to one? A. three-eighths B. three-fourths C. one-half D. eleven-sixteenths Plot all numbers on a number line.

20. FRACTIONS WARM-UP What number is halfway between zero and one-twelfth? Solve using multiplication.

21. VIDEO: Skip Counting Skip Counting by Fractions Video

22. Cognition & Learning Background  Fractions are a major concept that students are first introduced to in 1 st grade as per CCLS. This concept continues throughout their mathematical education. The goal of fraction instruction is for students to visual fraction amounts accurately.

23. Fraction Proficiency and Success with Higher Level Math  There is a clear relationship between fraction proficiency and success in algebra. Inability to successfully manipulate and perform basic operations on common fractions has lead to negative performance in algebraic reasoning ( Brown & Quinn, 2007).

25. PROGRESSIONS OF FRACTIONS & DECIMALS WITH THE CCLS

36. What Percent of …. 8 th grade students can successfully arrange the following fractions in order from least to greatest? 2/7, 1/12, and 5/9 What percentage of 17 year olds can convert the following decimal to a fraction? 0.029 TABLE GROUP DISCUSSION

37. Causes for Low Performance in Fractions  Complexity of Fraction Concepts (Streefland, 1991)  Incorrect Wrote Procedures (Mac, 1990)  Difficulty with Identification of Units (Hunting, 1996)  Teaching Computation before Understand the Meaning of Fractions (Aksu, 1996)  More Emphasis on Teaching Procedures instead of Teaching Conceptual Meaning (Moss & Case, 1999)  Influence of Multiple Representations of Fraction Ideas (Cramer, Post, & delMas, 2002)

38. Develop Rational Number Concepts  Part Whole Comparison  Equal parts of the unit, with equivalent fractions found by thinking of the parts in terms of larger or smaller chunks  VIDEO – Sharing of CakesSharing of Cakes  Measure  A distance on a number line or a given area  Operator  Gives a rule that tells how to operate on a unit  VIDEO – Fractions as DivisionFractions as Division  Quotients  Amount that each person receives when it is being shared  VIDEO – Interpret Fraction as DivisionInterpret Fraction as Division  Ratios & Rates  Relationship in which there are items compared, in a multiplicative rather than an additive sense

39. PART WHOLE COMPARISON

42. MEASURE

43. OPERATOR

47. QUOTIENTS

50. RATES & RATIOS

51. MULTIPLE CATEGORIES

52. COMPARING & ORDERING DECIMALS

53. CONVERTING & COMPARING FRACTIONS AND DECIMALS