1. 2015 The Institute for the Professional Development of Adult Educators Using Fraction Tiles www.floridaipdae.org

2. 2015 The Institute for the Professional Development of Adult Educators A linear model gives an overview and shows relationships. Fraction Tiles

3. 2015 The Institute for the Professional Development of Adult Educators How many fourths in a whole? How many sixths? Fraction Tiles

4. 2015 The Institute for the Professional Development of Adult Educators What is more, 1/4 or 1/3? What is more, 1/9 or 1/10? Fraction Tiles

5. 2015 The Institute for the Professional Development of Adult Educators What is more, 1/4 or 1/3? What is more, 1/9 or 1/10? Fraction Tiles

6. 2015 The Institute for the Professional Development of Adult Educators Which is more, 3/4 or 4/5? Fraction Tiles

7. 2015 The Institute for the Professional Development of Adult Educators Which is more, 3/4 or 4/5? Which is more, 7/8 or 8/9? Fraction Tiles

8. 2015 The Institute for the Professional Development of Adult Educators The pattern of 1/2, 3/4, 4/5, 5/6, 6/7, 7/8, 8/9, 9/10. Fraction Tiles

9. 2015 The Institute for the Professional Development of Adult Educators How many fourths equal a half? Eighths? Sevenths? Fraction Tiles

10. 2015 The Institute for the Professional Development of Adult Educators How many fourths equal a half? Eighths? Sevenths? Fraction Tiles

11. 2015 The Institute for the Professional Development of Adult Educators What is half of a half? That’s multiplying fractions. Fraction Tiles

12. 2015 The Institute for the Professional Development of Adult Educators A fraction is part of a set or part of a whole. textbook definition What about ? Another common meaning of fraction is fragment or a small part. What is a fraction? 3 2

13. 2015 The Institute for the Professional Development of Adult Educators 1 1 1 or 3 ÷ 2. 1 1 1 2 1 2 1 2 1 2 3 2 means three s 1 2 What is a fraction?

14. 2015 The Institute for the Professional Development of Adult Educators * 9/8 is 1 plus 1/8 Fraction Tiles

15. 2015 The Institute for the Professional Development of Adult Educators 2 4 two 4s 3 + 3 11 = 11 Each row of connected rectangles represents 1. Write each quantity as a mixed number and as an improper fraction. How did you find the 11? Mixed to Improper Fractions

16. 2015 The Institute for the Professional Development of Adult Educators 2 4 two 4s 113 four 3s + 2 = 14 + 3 = 11 Mixed to Improper Fractions Each row of connected rectangles represents 1. Write each quantity as a mixed number and as an improper fraction.

17. 2015 The Institute for the Professional Development of Adult Educators 2 4 two 4s 113 four 5s + 3 = 23 four 3s + 2 = 14 + 3 = 11 Mixed to Improper Fractions Each row of connected rectangles represents 1. Write each quantity as a mixed number and as an improper fraction.

18. 2015 The Institute for the Professional Development of Adult Educators Improper to Mixed Fractions Circle the wholes and write each quantity as an improper fraction and as a mixed number.

19. 2015 The Institute for the Professional Development of Adult Educators Improper to Mixed Fractions The correlation to division becomes obvious here. Circle the wholes and write each quantity as an improper fraction and as a mixed number.

20. 2015 The Institute for the Professional Development of Adult Educators The correlation to division becomes obvious here. Improper to Mixed Fractions Circle the wholes and write each quantity as an improper fraction and as a mixed number.

21. 2015 The Institute for the Professional Development of Adult Educators 1 2 2 3 1 4 Fractional Parts of Geometric Figures

22. 2015 The Institute for the Professional Development of Adult Educators 1 2 2 3 1 4 Fractional Parts of Geometric Figures

23. 2015 The Institute for the Professional Development of Adult Educators 1 2 2 3 1 4 Fractional Parts of Geometric Figures

24. 2015 The Institute for the Professional Development of Adult Educators 1 2 2 3 1 4 A study showed that many students and adults thought this was impossible. Fractional Parts of Geometric Figures

25. 2015 The Institute for the Professional Development of Adult Educators 100 50 25 10 33 1313 1313 1313 * 12 1212 1212 1212 1212 1212 1212 1212 1212 Dividing 100

26. 2015 The Institute for the Professional Development of Adult Educators 1 2 Simplifying Fractions

27. 2015 The Institute for the Professional Development of Adult Educators 3 6 = 1 2 Simplifying Fractions

28. 2015 The Institute for the Professional Development of Adult Educators 4 8 = 1 2 Simplifying Fractions

29. 2015 The Institute for the Professional Development of Adult Educators Simplifying Fractions 8 12 = 2 3 4 Writing the common multiple in a circle, for example, the 4, helps students remember what they’re dividing by. Simplifying Fractions

30. 2015 The Institute for the Professional Development of Adult Educators 9 12 = 3 4 3 Writing the common multiple in a circle, in this example, 3, helps students remember what they’re dividing by. Simplifying Fractions

31. 2015 The Institute for the Professional Development of Adult Educators The fraction 4/8 can be reduced on the multiplication table as 1/2. 2128 4572 Simplifying Fractions

32. 2015 The Institute for the Professional Development of Adult Educators *1216 Simplifying Fractions

33. 2015 The Institute for the Professional Development of Adult Educators 3 5 4–4– 3 2 5 3 – 4 7 2 3 7 5 7 5 – 2 1 7 * Subtracting Fractions

34. 2015 The Institute for the Professional Development of Adult Educators 1 2 x = 1 2 The square represents 1. Multiplying Fractions

35. 2015 The Institute for the Professional Development of Adult Educators 1 2 x = 1 2 We are thinking 1/2 of 1/2. First find 1/2 of it vertically. Multiplying Fractions

36. 2015 The Institute for the Professional Development of Adult Educators 1 2 x = 1 2 1 4 Now find 1/2 of it horizontally. The solution is the double crosshatched area. Multiplying Fractions

37. 2015 The Institute for the Professional Development of Adult Educators 2 3 x = 3 4 Another example. Multiplying Fractions

38. 2015 The Institute for the Professional Development of Adult Educators 2 3 x = 3 4 Multiplying Fractions

39. 2015 The Institute for the Professional Development of Adult Educators 2 3 x = 3 4 Multiplying Fractions

40. 2015 The Institute for the Professional Development of Adult Educators 2 3 x = = 3 4 6 12 1 2 Multiplying Fractions

41. 2015 The Institute for the Professional Development of Adult Educators 2 3 x = 3 4 The total number of of rectangles is 3 x 4. Multiplying Fractions

42. 2015 The Institute for the Professional Development of Adult Educators 2 3 x = 3 4 The number of double crosshatched rectangles is 2 x 3. The total number of rectangles is 3 x 4. That’s why to multiply fractions, we multiply the numerators and the denominators. Multiplying Fractions

43. 2015 The Institute for the Professional Development of Adult Educators ÷ = 1 2 12 1 3 1 3 The third problem can be thought of as how many 2/3s are in 1 or half of 1 ÷ 1/3. ÷ = 2 3 1 3 2 2 sets of ½ = 1 3 sets of 1/3 = 1 1 set of 2/3 plus 1/2 of another set of 2/3 = 1 Dividing Fractions

44. 2015 The Institute for the Professional Development of Adult Educators ÷ = 1 2 12 1 3 13 1 3 1 4 13 14 3 4 1 4 3 2 3 1 3 2 1 ÷ 3 is simply the definition of a fraction. Notice the pattern. 1313 Dividing Fractions

45. 2015 The Institute for the Professional Development of Adult Educators ÷ = __ 3 4 2 11 1 4 1 4 1 4 1 4 1 4 1 4 1 4 1 4 2 sets of ¾ plus 2 of the 3 needed for the next set = 2 2/3 Dividing Fractions Find

46. 2015 The Institute for the Professional Development of Adult Educators 2 3 ÷ = __To find 3 4 (Is the answer more or less than 1?) Another example: How many 3/4s are in 2/3? Dividing Fractions

47. 2015 The Institute for the Professional Development of Adult Educators IPDAE