teaching of rational numbers fractions, decimals and percents

Teaching of Rational NumbersFractions, Decimals and Percents

Why are Fractions Difficult to Learn?

Fractions

&

YOU


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


Learning the various fraction operations can be difficult for many children. It is not the concept of fractions that is difficult . . .


. . . It is the various operations that are done with fractions!


There are no less than 10 different procedures.


Add/Subtract Same Denominators

Add/Subtract Unlike Denominators

Writing Equivalent Fractions

Mixed Numbers to a Fractions

Simplifying Fractions


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.


Rules/Procedures

Vs

Visualization


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.


In the second circle each slice has been cut into two.

Before 1 slice

After 2 slices


These two circles are EQUIVALENT because the pictures show the same amount.


Each slice has been cut into two.

Before 3 colored slices

After 6 colored slices


These two circle are EQUIVALENT because the pictures show the same amount.


Write two equivalent fractions for the green sections in these circles.


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.

Fractions Are Difficult to Learn: Are Decimals Truly

Easier?

Many adults and children do not have a true understanding of decimals/percents?


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


Easier?

The most basic idea about decimals is that, like fractions, they enable us to describe parts of a unit quantity.


Easier?

They do this not by creating new "sub-units" but by creating new numbers.

Decimals and fractions are two solutions to one problem.


Easier?

Most students ( and even adults) do not make the decimal-fraction link correctly.


Easier?

The fundamental understanding of fractions, such as dealing with equivalent fractions, is critical to decimals as well.


Easier?

The most basic knowledge about decimals is to understand that both decimals and fractions are designed for the same purpose.


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


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


Whole Number Thinking


Zero

Makes

Small


Reverse Thinking


Shorter

is

Larger


Denominator

Focused

teaching of rational numbers fractions, decimals and percents

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