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## Investigation - Comparing and Ordering Fractions

### Subject

Math, Science & Technology

### 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.

2-3 lessons

### Procedure

DOING THE INVESTIGATION

1. 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.
2. Students order various unit fractions by comparing the size of the corresponding fraction strips.
3. 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:
1. determine which fractions are greater.
2. record their findings.
3. represent fractions which are equivalent to 1/2, 1/3, 1/4.
4. provide written explanations of their work.
4. 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.

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

• About The Core Curriculum Companion
• ### 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.