APEC Summer Workshop Session 3 Fractions, Decimals, Percents.
Teaching of Rational Numbers Fractions, Decimals and Percents.
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Transcript of Teaching of Rational Numbers Fractions, Decimals and Percents.
Teaching of Rational NumbersFractions, 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?
Learning the various fraction operations can be difficult for many children. It is not the concept of fractions that is difficult . . .
Why are Fractions Difficult to Learn?
. . . It is the various operations that are done with fractions!
Why are Fractions Difficult to Learn?
There are no less than 10 different procedures.
Why are Fractions Difficult to Learn?
Add/Subtract Same Denominators
Add/Subtract Unlike Denominators
Writing Equivalent Fractions
Mixed Numbers to a Fractions
Simplifying Fractions
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
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.
Making Sense of Fractions
Rules/Procedures
Vs
Visualization
Making Sense of Fractions
Before learning how to subtract or add fractions with unlike denominators, students MUST understand equivalent fractions.
Visualization Example#1Equivalent Fractions
These two circles are EQUIVALENT because the pictures show the same amount.
Visualization Example#1Equivalent Fractions
In the second circle each slice has been cut into two.
Before 1 slice
After 2 slices
Visualization Example#1Equivalent Fractions
These two circles are EQUIVALENT because the pictures show the same amount.
Visualization Example#1Equivalent Fractions
Each slice has been cut into two.
Before 3 colored slices
After 6 colored slices
Visualization Example#1Equivalent Fractions
These two circle are EQUIVALENT because the pictures show the same amount.
Visualization Example#1Equivalent Fractions
Write two equivalent fractions for the green sections in these circles.
Visualization Example#1Equivalent Fractions
Write two equivalent fractions for the green sections in these circles.
Visualization Example#1Equivalent Fractions
Write two equivalent fractions for the green sections in these circles.
What is the multiplier?
Equivalent FractionsPractice #1
Write the name of each fraction beside it. Connect the fractions that show the same amount.
Equivalent FractionsPractice #2
Equivalent FractionsPractice #3
Equivalent FractionsPractice #4
Fractions Are Difficult to Learn: Are Decimals Truly
Easier?
Many adults and children do not have a true understanding of decimals/percents?
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
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.
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.
Fractions Are Difficult to Learn: Are Decimals Truly
Easier?
Most students ( and even adults) do not make the decimal-fraction link correctly.
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.
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.
Fractions Are Difficult to Learn: Are Decimals Truly
Easier?
Kids basically see the decimal point as a character separating two whole numbers.
4 . 7
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?
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?
Examples of Incorrect Decimal-Fraction Associations
Fractions with a numerator of 1
8.4 is the same as
4.6 is the same as
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
Decimal Number Misconception #1
Longer
is
Larger
Decimal Number Misconception #2
Whole Number Thinking
Decimal Number Misconception #3
Zero
Makes
Small
Decimal Number Misconception #4
Reverse Thinking
Decimal Number Misconception #4
Shorter
is
Larger
Decimal Number Misconception #5
Denominator
Focused