### Lesson Plan

## Investigation - Comparing and Ordering Fractions

### Subject

Math, Science & Technology

### Grade Levels

Elementary, 4th Grade

### Materials

Fraction strips (made from construction paper) or fraction bars

### Authors

The Core Curriculum Companion For The New York State Mathematics Resource Guide Writing Team.

### Duration

2-3 lessons

### Procedure

**DOING THE INVESTIGATION **

- Have the class use construction paper to make strips representing fractions with the denominators 2, 3, 4, 5, 6, 8, 10 and 12 and 1 whole. Write the proper fraction on each strip.
- Students order various unit fractions by comparing the size of the corresponding fraction strips.
- Students work in pairs to represent various other fractions (i.e., 2/3, 3/4, 6/12). By comparing the size of the strips, they will:
- determine which fractions are greater.
- record their findings.
- represent fractions which are equivalent to 1/2, 1/3, 1/4.
- provide written explanations of their work.

- Students will discuss their findings.

**POSSIBLE SOLUTIONS **

### Vocabulary

Fraction, proper fraction, rational number, equivalent fraction, numerator, denominator

### Description

The students will use fraction strips to compare and order fractions.

**WHAT'S THE MATHEMATICS? **

- identify various ways a figure can be divided
- order unit fractions and decimals
- find equivalent fractions
- recognize and order fractions with the denominators 2, 3, 4, 5, 6, 8, 10, 12

### Extending the Activity

Students will develop a rule for finding equivalent fractions by looking for patterns.

i.e.,

1/2 = 2/4, 3/6, 4/8, 5/10, 6/12

1/3 = 2/6, 4/12

1/4 = 2/8, 3/12

### Assessment 1

One half of Sam's scarf is striped. Which scarf is Sam's?

Ans. A, B has 3/4 striped; C has 2/6 or 1/3 striped; D has 1/4 striped.

### Assessment 2

Write 2 fractions that are equivalent to 1/5. Explain how you arrived at your answer.

Ans. 2/10, 3/15, 4/20, . . . 100/500, . . .

Equivalent fractions can be found by multiplying both the numerator and the denominator of the fraction by the same number.

### Additional Notes

For additional information and activities, see pages 44 and 53-54
in the New York State Core Curriculum/Mathematics Resource Guide.

### Source

The Core Curriculum Companion For The New York State Mathematics Resource Guide Writing Team. “NUMBER AND NUMERATION”. In * The Core Curriculum Companion For The New York State Mathematics Resource Guide*, 113-115.

### Related New York City Performance Standards

- M1d Describe and compare quantities by using simple fractions.
- M7a Use appropriate mathematical terms, vocabulary and language.
- M7c Explain solutions to problems clearly and logically.