fraction interpretations. students should be given the opportunity to develop concepts as well as...

Fraction Interpretations

Students should be given the opportunity to develop concepts as well as number sense with fractions and decimals.

NCTM (2000)

Virginia Standards of Learning

KindergartenK.5 The student will identify the parts of a set and/or region that represent fractions for halves and fourths.

First Grade 1.3 The student will identify the parts of a set and/or

region that represent fractions for halves, thirds, and fourths and write the fractions.

Virginia Standards of Learning

Second Grade2.3 The student will

a) identify the parts of a set and/or region that represent fractions for halves, thirds, fourths, sixths, eighths, and tenths;

b) write the fractions; c) compare the unit fractions for halves, thirds,

fourths, sixths, eighths, and tenths

Virginia Standards of Learning

Third Grade3.3 The student will

a) name and write fractions (including mixed numbers) represented by a model;

b) model fractions (including mixed numbers) and write the fractions’ names; and

c) compare fractions having like and unlike denominators, using words and symbols(>, <, or =).

Virginia Standards of Learning

Third Grade3.7 The student will add and subtract proper fractions having like denominators of 12 or less.

Virginia Standards of Learning

Fourth Grade4.2 The student will

a) compare and order fractions and mixed numbers;

b) represent equivalent fractions; and

c) identify the division statement that represents a fraction.

Virginia Standards of Learning Fourth Grade 4.2 The student will

a) determine common multiples and factors, including least common multiple and greatest common factor;

b) add and subtract fractions having like and unlike denominators that are limited to 2, 3, 4, 5, 6, 8, 10, and 12, and simplify the resulting fractions, using common multiples and factors;

d) solve single-step and multistep practical problems involving addition and subtraction with fractions and with decimals.

Virginia Standards of Learning

Fifth Grade5.2 The student will

a) recognize and name fractions in their equivalent decimal form and vice versa; and

b) compare and order fractions and decimals in a given set from least to greatest and greatest to least.

5.6 The student will solve single-step and multistep practical problems involving addition and subtraction with fractions and mixed numbers and express answers in simplest form.

Five Meanings of Fractions

1. Part-Whole

2. Division 3. Ratio

•Set

•Region/Area

•Length

What fraction of the musical instruments have strings?

2

5

The Set Model

What fraction of the fish have stripes?

3

5

The Set Model

The Whole15 Marbles

Partitioned into 5 equal parts:

Each part is one-fifth.

Two parts are two-fifths.

Three parts are three-fifths.

Four parts are four-fifths.

Five parts are five-fifths or the whole.

The Area Modelmeans two parts out of three

2

3

The Area Model

What fraction of the rectangle is purple?

2

6

3

4

The Area Model

What fraction of the pie is purple?

The Area ModelHow many ways can you divide this rectangle into four equal pieces?

Which figures show the area model?

Division

means 2 ÷ 3

2 pizzas divided equally among 3 children

Ratio

means 2 : 3

Two boys compared to three girls

Measure

means

means a distance of from 0 on a

number line

Operator

of something

is a rule that tells how to operate on a unit (or on

the result of a previous operation): Multiple by 2 and divide the result by 3 or divide by 3 and multiply the result by 2. This results in multiple meanings for

: and