The first goal in the development of fractions is to develop the idea of fractional parts of the whole, or, dividing one whole into equal size portions or fair shares. Many children understand the idea of sharing a quantity into two or more parts to be shared fairly among friends. Making the connection between fair shares and fractional parts is a next step for students. An example of a sharing word problem:

Four children are sharing ten brownies so that each one will get the same amount. How much can each child have?

Development of fractional concepts also includes the understanding that fractions can be parts of a whole or parts of a set. Students begin to learn that fractional parts have special names that tell how many of that size are needed to make the whole. For example, thirds requires three parts to make one whole.

As students continue their learning they begin to develop benchmark fractions. Some important benchmark fractions are 0, 1/2 and 1 whole. For example : 5/6 is closer to 1 whole (6/6) . The understanding that the size of the fractional part is dependent on the size of the whole is also developed; e.g. Eating 1/2 of a large pizza is different than eating 1/2 of a small pizza because of the size of the whole pizza.

Early on in their fraction learning, students will also learn that the denominator of the fraction indicates by what number the whole has been divided, while the numerator counts or tells how many of the fractional parts. As conceptual understanding develops, students will learn that the denominator is the divisor.

One way to help students create an understanding of equivalent fractions is to have them use models to find different names for a fraction. Through the use of models, students develop the understanding that two equivalent fractions are two ways of describing the same amount using different fractional parts. For example:

It is important that students have many opportunities to develop fractional number sense before moving onto computation with fractions. Focusing on “rules” to solve fraction equations means students will be unable to judge the reasonableness of their answer and the variety of rules for different operations quickly become mixed up in a students’ mind. As students begin to develop fluency with computation using fractions, an emphasis is placed on estimation. Here are some word problems involving fractions:

Paul and his brother were each eating the same kind of candy bar. Paul had 3/4 of his candy bar. His brother still had 7/8 of his candy bar. How much candy did the two boys have together?

Jack and Jill ordered two identical sized pizzas, one cheese and one pepperoni. Jack ate 5/6 of a pizza and Jill ate 1/2 of a pizza. How much pizza did they eat together?

There are 15 cars in Michael’s toy collection. Two-thirds of the cars are red. How many red cars does Michael have?

Cassie has 5 1/4 yards of ribbon to make three bows for birthday packages. How much ribbon should she use for each bow if she wants to use the same length of ribbon for each?

Developing Decimal Concepts

Linking the ideas of fractions and decimals is important. Developing the understanding that decimals numbers are another way of writing fractions is an early concept that students encounter. When students are learning about decimals, it is helpful to clarify the way they are commonly read and what they mean. For example, it is natural to read decimals such as 2.7 as “two point seven.” However, students should learn that this decimal can also be read on “two and seven-tenths” which will allow students to relate decimals to fractions. 2.7 = 2 7/10. Students also develop the understanding that the base-ten place value system extends to the left and right of the decimal point; e.g. between the tenths and the hundredths place is still x10, just as between the tens and the hundreds place.

Addition and subtraction with decimals are based on the concept of adding and subtracting numbers in the same position, which is similar to whole numbers. As with whole numbers, students use estimation throughout their work with decimals to judge the reasonableness of their answer.

## Fractions and Decimals

The first goal in the development of fractions is to develop the idea of fractional parts of the whole, or, dividing one whole into equal size portions or fair shares. Many children understand the idea of sharing a quantity into two or more parts to be shared fairly among friends. Making the connection between fair shares and fractional parts is a next step for students.

An example of a sharing word problem:

Four children are sharing ten brownies so that each one will get the same amount. How much can each child have?

Development of fractional concepts also includes the understanding that fractions can be parts of a whole or parts of a set. Students begin to learn that fractional parts have special names that tell how many of that size are needed to make the whole. For example,

thirdsrequires three parts to make one whole.As students continue their learning they begin to develop benchmark fractions. Some important benchmark fractions are 0, 1/2 and 1 whole. For example : 5/6 is closer to 1 whole (6/6) . The understanding that the size of the fractional part is dependent on the size of the whole is also developed; e.g. Eating 1/2 of a large pizza is different than eating 1/2 of a small pizza because of the size of the whole pizza.

Early on in their fraction learning, students will also learn that the denominator of the fraction indicates by what number the whole has been divided, while the numerator counts or tells how many of the fractional parts. As conceptual understanding develops, students will learn that the denominator is the divisor.

One way to help students create an understanding of equivalent fractions is to have them use models to find different names for a fraction. Through the use of models, students develop the understanding that two equivalent fractions are two ways of describing the same amount using different fractional parts. For example:

It is important that students have many opportunities to develop fractional number sense before moving onto computation with fractions. Focusing on “rules” to solve fraction equations means students will be unable to judge the reasonableness of their answer and the variety of rules for different operations quickly become mixed up in a students’ mind. As students begin to develop fluency with computation using fractions, an emphasis is placed on estimation.

Here are some word problems involving fractions:

Developing Decimal Concepts

Linking the ideas of fractions and decimals is important. Developing the understanding that decimals numbers are another way of writing fractions is an early concept that students encounter. When students are learning about decimals, it is helpful to clarify the way they are commonly read and what they mean. For example, it is natural to read decimals such as 2.7 as “two point seven.” However, students should learn that this decimal can also be read on “two and seven-tenths” which will allow students to relate decimals to fractions. 2.7 = 2 7/10.

Students also develop the understanding that the base-ten place value system extends to the left and right of the decimal point; e.g. between the tenths and the hundredths place is still x10, just as between the tens and the hundreds place.

Addition and subtraction with decimals are based on the concept of adding and subtracting numbers in the same position, which is similar to whole numbers. As with whole numbers, students use estimation throughout their work with decimals to judge the reasonableness of their answer.

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