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Teaching of Rational Numbers

Teaching of Rational Numbers. Fractions, Decimals and Percents. Why are Fractions Difficult to Learn?. Fractions & YOU. Why are Fractions Difficult to Learn?. “Fractions are difficult to teach and learn, but they should not be viewed as a lost cause” . Why are Fractions Difficult to Learn?.

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Teaching of Rational Numbers

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  1. Teaching of Rational Numbers Fractions, Decimals and Percents

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

  3. Why are Fractions Difficult to Learn? “Fractions are difficult to teach and learn, but they should not be viewed as a lost cause”

  4. 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 . . .

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

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

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

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

  9. 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.

  10. Making Sense of Fractions Rules/Procedures Vs Visualization

  11. Making Sense of Fractions Before learning how to subtract or add fractions with unlike denominators, students MUST understand equivalent fractions.

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

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

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

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

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

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

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

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

  20. Equivalent FractionsPractice #1 Write the name of each fraction beside it. Connect the fractions that show the same amount.

  21. Equivalent FractionsPractice #2

  22. Equivalent FractionsPractice #3

  23. Equivalent FractionsPractice #4

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

  25. 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

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

  27. 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.

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

  29. 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.

  30. 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.

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

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

  33. Fractions Are Difficult to Learn: Are Decimals Truly Easier? What does the fraction tell you? What does this fraction, written as a decimal (0.4) tell you?

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

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

  36. Decimal Number Misconception #1 Longer is Larger

  37. Decimal Number Misconception #2 Whole Number Thinking

  38. Decimal Number Misconception #3 Zero Makes Small

  39. Decimal Number Misconception #4 Reverse Thinking

  40. Decimal Number Misconception #4 Shorter is Larger

  41. Decimal Number Misconception #5 Denominator Focused

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