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## Fraction Operations Testing Package

#### ASFMN – Addition and Subtraction of Fractions and Mixed Numbers

Test Details
• Subject: Intermediate Mathematics
• Category: Fraction Operations
• Suggested Grade Level: 4 thru 8

This diagnostic test explores the following:

• Student’s understanding of the concept of Lowest Common Multiple (LCM)
• Student’s understanding of how to convert a whole number into the appropriate fraction representation
• Student’s understanding of the procedural steps to convert a fraction
Sample Question • If the student answered A, there is a mixed number operation error. Student regroups in correct area, but does not decrease the whole number portion by one.
• If the student answered B, there is a failure to properly perform the operation of subtraction because student will ignore which fraction is to be subtracted and instead chooses the more convenient fraction to subtract. Nor is renaming properly in place.
• If the student answered C, the student answered correctly.
• If the student answered D, there is a failure to properly perform the operation. Ignoring the fraction part and is only considering the whole numbers.
• If the student answered E, the student is confused by the question and results in an error pattern unable to be diagnosed.

#### MXFWN – Multiplication of Fractions and Whole Numbers

Test Details
• Subject: Intermediate Mathematics
• Category: Fraction Operations
• Suggested Grade Level: 4 thru 8

This diagnostic test explores the following:

• Skills needed to simplify fractions and mixed numbers
• Rules of which parts of the fractions to multiply together
• Student’s understanding of how to convert a whole number into the appropriate fraction representation
Sample Question • If the student answered A, the student answered correctly.
• If the student answered B, the student incorrectly added the numerators and multiplied the denominators.
• If the student answered C, the student incorrectly cross multiplied to arrive at their answer.
• If the student answered D, the student incorrectly multiplied just the numerators.
• If the student answered E, the student is confused by the question and results in an error pattern unable to be diagnosed.

#### DVFWN – Division of Fractions and Whole Numbers

Test Details
• Subject: Intermediate Mathematics
• Category: Fraction Operations
• Suggested Grade Level: 4 thru 8

This diagnostic test explores the following:

• Proper use of the Invert-and-multiply method
• Student’s understanding of how to convert a whole number into the appropriate fraction representation
• Skills needed to simplify fractions and mixed numbers
Sample Question • If the student answered A, the student answered correctly.
• If the student answered B, when dividing a fraction by a whole number, the student incorrectly divided the denominator by the whole number, instead of multiplying them.
• If the student answered C, when dividing a fraction by a whole number, the student incorrectly multiplied the numerator by the whole number, instead of the denominator.
• If the student answered D, the student misused the invert-and-multiply method by inverting both fractions instead of just the second value.
• If the student answered E, the student is confused by the question and results in an error pattern unable to be diagnosed.

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