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