2. Teaching of Rational Numbers Fractions, Decimals and Percents

3. Why are Fractions Difficult to Learn? Fractions&YOU

4. “Fractions are difficult to teach and learn, but they should not be viewed as a lost cause”

5. Why are Fractions Difficult to Learn? Learning the various fraction operations can be difficult for many children. It is not the concept of fractions that is difficult...

6. Why are Fractions Difficult to Learn?... It is the various operations that are done with fractions!

7. Why are Fractions Difficult to Learn? There are no less than 10 different procedures.

8. Why are Fractions Difficult to Learn? Add/Subtract Same Denominators Add/Subtract Same Denominators Add/Subtract Unlike Denominators Add/Subtract Unlike Denominators Writing Equivalent Fractions Writing Equivalent Fractions Mixed Numbers to a Fractions Mixed Numbers to a Fractions Simplifying Fractions Simplifying Fractions

9. Why are Fractions Difficult to Learn? Improper Fraction to a Mixed Number Improper Fraction to a Mixed Number Multiplication of Fractions Multiplication of Fractions Division of Fractions Division of Fractions Converting Fractions to Decimals Converting Fractions to Decimals Converting Decimals to Fractions Converting Decimals to Fractions

10. Making Sense of Fractions If children just memorize these procedures without understanding how they were derived, they will seem like a meaningless jumble of rules.

11. Making Sense of Fractions Rules/ProceduresVsVisualization

12. Before learning how to subtract or add fractions with unlike denominators, students MUST understand equivalent fractions.

13. Visualization Example#1 Equivalent Fractions These two circles are EQUIVALENT because the pictures show the same amount.

14. Visualization Example#1 Equivalent Fractions In the second circle each slice has been cut into two. Before 1 slice After 2 slices After 2 slices

15. Visualization Example#1 Equivalent Fractions These two circles are EQUIVALENT because the pictures show the same amount.

16. Visualization Example#1 Equivalent Fractions Each slice has been cut into two. Before 3 colored slices After 6 colored slices

17. Visualization Example#1 Equivalent Fractions These two circle are EQUIVALENT because the pictures show the same amount.

18. Visualization Example#1 Equivalent Fractions Write two equivalent fractions for the green sections in these circles.

19. Visualization Example#1 Equivalent Fractions Write two equivalent fractions for the green sections in these circles.

20. Visualization Example#1 Equivalent Fractions Write two equivalent fractions for the green sections in these circles. What is the multiplier?

21. Equivalent Fractions Practice #1 Write the name of each fraction beside it. Connect the fractions that show the same amount.

22. Equivalent Fractions Practice #2

23. Equivalent Fractions Practice #3

24. Equivalent Fractions Practice #4

25. Fractions Are Difficult to Learn: Are Decimals Truly Easier? Many adults and children do not have a true understanding of decimals/percents?

26. Fractions Are Difficult to Learn: Are Decimals Truly Easier? " We are now slightly less than one-fifth of the world's population, but we have slightly more than 20% of the world's wealth and income. This is not a matter requiring Einstein to calculate.” Bill Clinton, 1997

27. Fractions Are Difficult to Learn: Are Decimals Truly Easier? The most basic idea about decimals is that, like fractions, they enable us to describe parts of a unit quantity.

28. Fractions Are Difficult to Learn: Are Decimals Truly Easier? They do this not by creating new "sub-units" but by creating new numbers. Decimals and fractions are two solutions to one problem.

29. Fractions Are Difficult to Learn: Are Decimals Truly Easier? Most students ( and even adults) do not make the decimal-fraction link correctly.

30. Fractions Are Difficult to Learn: Are Decimals Truly Easier? The fundamental understanding of fractions, such as dealing with equivalent fractions, is critical to decimals as well.

31. Fractions Are Difficult to Learn: Are Decimals Truly Easier? The most basic knowledge about decimals is to understand that both decimals and fractions are designed for the same purpose.

32. Fractions Are Difficult to Learn: Are Decimals Truly Easier? Kids basically see the decimal point as a character separating two whole numbers. 4. 7

33. Those who have not completely made the decimal-fraction link think two different types of whole numbers make up a decimal. Fractions Are Difficult to Learn: Are Decimals Truly Easier?

34. What does the fraction tell you? What does this fraction, written as a decimal (0.4) tell you?

35. Examples of Incorrect Decimal-Fraction Associations Fractions with a numerator of 1 8.4 is the same as 4.6 is the same as

36. Fractions Are Difficult to Learn: Are Decimals Truly Easier? To understand a fraction, the numerator and the denominator must be considered simultaneously. denominator indicates the number of parts in the whole object numerator indicates the number of parts being used

37. Decimal Number Misconception #1 Longer is Larger

38. Decimal Number Misconception #2 Whole Number Thinking

39. Decimal Number Misconception #3 Zero Makes Small

40. Decimal Number Misconception #4 Reverse Thinking

41. Decimal Number Misconception #4 Shorter is Larger

42. Decimal Number Misconception #5 Denominator Focused