teaching of rational numbers
DESCRIPTION
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?. - PowerPoint PPT PresentationTRANSCRIPT
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Teaching of Rational NumbersFractions, Decimals and Percents
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Why are Fractions Difficult to Learn?
Fractions&
YOU
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Why are Fractions Difficult to Learn?
“Fractions are difficult to teach and learn, but they should not be viewed as a lost cause”
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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 . . .
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Why are Fractions Difficult to Learn?
. . . It is the various operations that are done with fractions!
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Why are Fractions Difficult to Learn?
There are no less than 10 different procedures.
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Why are Fractions Difficult to Learn?
Add/Subtract Same DenominatorsAdd/Subtract Unlike
DenominatorsWriting Equivalent FractionsMixed Numbers to a FractionsSimplifying Fractions
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Why are Fractions Difficult to Learn?
Improper Fraction to a Mixed NumberMultiplication of FractionsDivision of FractionsConverting Fractions to DecimalsConverting Decimals to Fractions
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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.
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Making Sense of Fractions
Rules/ProceduresVs
Visualization
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Making Sense of Fractions
Before learning how to subtract or add fractions with unlike denominators, students MUST understand equivalent fractions.
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Visualization Example#1Equivalent Fractions
These two circles are EQUIVALENT because the pictures show the same amount.
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Visualization Example#1Equivalent Fractions
In the second circle each slice has been cut into two.
Before 1 slice
After 2 slices
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Visualization Example#1Equivalent Fractions
These two circles are EQUIVALENT because the pictures show the same amount.
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Visualization Example#1Equivalent Fractions
Each slice has been cut into two.
Before 3 colored slices
After 6 colored slices
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Visualization Example#1Equivalent Fractions
These two circle are EQUIVALENT because the pictures show the same amount.
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Visualization Example#1Equivalent Fractions
Write two equivalent fractions for the green sections in these circles.
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Visualization Example#1Equivalent Fractions
Write two equivalent fractions for the green sections in these circles.
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Visualization Example#1Equivalent Fractions
Write two equivalent fractions for the green sections in these circles.
What is the multiplier?
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Equivalent FractionsPractice #1
Write the name of each fraction beside it. Connect the fractions that show the same amount.
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Equivalent FractionsPractice #2
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Equivalent FractionsPractice #3
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Equivalent FractionsPractice #4
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Fractions Are Difficult to Learn: Are Decimals Truly Easier?
Many adults and children do not have a true understanding of decimals and percents?
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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
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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.
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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.
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Fractions Are Difficult to Learn: Are Decimals Truly Easier?
Most students ( and even adults) do not make the decimal-fraction link correctly.
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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.
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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.
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Fractions Are Difficult to Learn: Are Decimals Truly Easier?
Kids basically see the decimal point as a character separating two whole numbers.
4 . 7
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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?
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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?
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Examples of Incorrect Decimal-Fraction Associations
Fractions with a numerator of 1
8.4 is the same as
4.6 is the same as
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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 objectnumerator indicates the number of parts being used
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Decimal Number Misconception #1
Longer is
Larger
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Decimal Number Misconception #2
Whole Number Thinking
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Decimal Number Misconception #3
ZeroMakes Small
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Decimal Number Misconception #4
Reverse Thinking
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Decimal Number Misconception #4
Shorter is
Larger
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Decimal Number Misconception #5
DenominatorFocused