## Fraction Concepts Testing Package

#### FRCON – Basic Fraction Concepts

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

This test will identify misunderstandings in number sense by exploring the following:

• Basic fractions terminology such as numerator and denominator
Sample Question • If the student answered A, in identifying the name of a fraction, student misread of directions, reversed the word shaded and unshaded.
• If the student answered B, in identifying the name of a fraction, student wrote shaded to unshaded rather than shaded to whole.
• If the student answered D, in identifying the name of a fraction, student interchanged numerator with denominator and reversed the word shaded and unshaded.
• If the student answered E, in identifying the name of a fraction, student simply counted the number of parts that are unshaded, no fraction identified.

#### FRCIR – Fractions – Shaded Circles

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

This diagnostic test explores the following:

• Student’s understanding of number sense referring to fractions and mixed numbers
• Basic understanding of fractions – Numerators vs denominators, Shaded vs Unshaded
• Ability to express a value in terms of a fraction
Sample Question • If the student answered A, in identifying the name of a fraction, the student wrote shaded to unshaded rather than shaded to whole.
• If the student answered B, in identifying the name of a fraction, the student wrote unshaded to shaded rather than shaded to whole.
• If the student answered D, in identifying the name of a fraction, the student simply counted the number of parts that are shaded, no fraction identified.
• If the student answered E, the student is confused by the question and results in an error pattern unable to be diagnosed.

#### FRRECT – Fractions – Shaded Rectangles

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

This diagnostic test explores the following:

• Student’s understanding of number sense referring to fractions and mixed numbers
• Basic understanding of fractions – Numerators vs denominators, Shaded vs Unshaded
• Ability to express a value in terms of a fraction
Sample Question • If the student answered A, in identifying the name of a fraction, the student wrote unshaded to shaded rather than unshaded to whole.
• If the student answered B, when identifying the fraction, the student interchanges numerator with denominator, with or without mixed number.
• If the student answered D, in identifying the name of a fraction, the student simply counted the number of parts that are unshaded, no fraction identified.
• If the student answered E, the student is confused by the question and results in an error pattern unable to be diagnosed.

#### FRPIE – Fractions – Shaded Pies

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

This diagnostic test explores the following:

• Student’s understanding of number sense referring to fractions and mixed numbers
• Basic understanding of fractions – Numerators vs denominators, Shaded vs Unshaded
• Ability to express a value in terms of a fraction
Sample Question • If the student answered B, in identifying the name of a fraction, the student wrote shaded to unshaded rather than shaded to whole.
• If the student answered C, when identifying the fraction, the student interchanges numerator with denominator, with or without mixed number.
• If the student answered D, when identifying the fraction, the student misread the directions. The fraction shaded will be written in terms of the unshaded pieces.
• If the student answered E, the student is confused by the question and results in an error pattern unable to be diagnosed.

#### FRNL – Fractions – Number Lines

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

This diagnostic test explores the following:

• Student’s ability to gauge proportionality within the number line
• Student’s ability to recognize the overall unit values of the number line marks in relation to the entire line
• Spatial understanding is weak. Student cannot estimate equal parts when no hash marks are included
Sample Question • If the student answered B, in identifying the name of a fraction, the student interchanged numerator with denominator, with or without mixed number.
• If the student answered C, when identifying the fraction on number line, the student noted only numerator and not a denominator. Expressed as a whole number only. No fraction ID.
• If the student answered D, the student’s spatial understanding weak. The student cannot estimate equal parts when no hash marks are included.
• If the student answered E, the student is confused by the question and results in an error pattern unable to be diagnosed.

#### FRCC – Fractions – Comparison and Conversion

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

This diagnostic test explores the following:

• Student’s understanding of number sense referring to fractions relative to other fractions
• Procedural steps to convert a fraction
• Skill of how to use reasoning to compare rather than computing
Sample Question • If the student answered A, in Numeracy of Fractions, the student fails to recognize mixed fractions within a number model.
• If the student answered B, in Numeracy of Fractions, the student fails to recognize mixed fractions within a number model.
• If the student answered C, in Numeracy of Fractions, the student fails to recognize mixed fractions within a number model.
• If the student answered D, the student is confused by the question and results in an error pattern unable to be diagnosed.

#### FREQ – Fractions – Equivalents

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

This diagnostic test explores the following:

• Student’s understanding of number sense referring to fractions relative to other fractions
• Basic understanding of fractions – Numerators vs denominators
• Procedural steps to convert a fraction
• Skill of how to use reasoning to compare rather than computing
Sample Question • If the student answered B, these are not equivalent, the student just inverted the Numerator and Denominator.
• If the student answered C, the student failed to find equivalent but created equivalent to one by placing Numerator from the example as both the Numerator and Denominator.
• If the student answered D, the student failed to find equivalent. Instead squaring numerator rather than setting a whole number.
• If the student answered E, the student is confused by the question and results in an error pattern unable to be diagnosed.

#### FRPN – Fractions – Prime Numbers

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

This diagnostic test explores the following:

• Numeracy of Fractions-Student does not know that 1 is neither prime nor composite.
• Numeracy of Fractions-Minimal understanding of mathematical meaning of prime.
• Numeracy of Fractions-Student does not know that 0 cannot be prime.
Sample Question • If the student answered A, in Numeracy of Fractions, the student does not know that 1 is neither prime nor composite.
• If the student answered C, in Numeracy of Fractions, the student has a minimal understanding of mathematical meaning of prime.
• If the student answered D, in Numeracy of Fractions, the student has a minimal understanding of mathematical meaning of prime.
• If the student answered E, the student is confused by the question and results in an error pattern unable to be diagnosed.

#### FRPF – Fractions – Prime Factorizations

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

This diagnostic test explores the following:

• Understanding of factoring out fractions and mixed numbers.
• What is a factor?
Sample Question • If the student answered A, in Numeracy of Fractions, the student does not know how to find the Prime Factorization of the number or does not know which numbers are prime.
• If the student answered B, in Numeracy of Fractions, the student does not know how to find the Prime Factorization of the number or does not know which numbers are prime.
• If the student answered C, in Numeracy of Fractions, the student does not know how to find the Prime Factorization of the number or does not know which numbers are prime.
• If the student answered E, the student is confused by the question and results in an error pattern unable to be diagnosed.

#### FRMULT – Fractions – Multiples

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

This diagnostic test explores the following:

• Understanding the multiples of a number
• Skill needed to simplify or rename fractions and mixed numbers of factoring out fractions and mixed numbers
Sample Question • If the student answered B, the student made a careless error – directions stated to choose the non-multiple, but student chose a multiple.
• If the student answered C, the student made a careless error – directions stated to choose the non-multiple, but student chose a multiple.
• If the student answered D, the student made a careless error – directions stated to choose the non-multiple, but student chose a multiple.
• If the student answered E, the student is confused by the question and results in an error pattern unable to be diagnosed.

#### FRGCF – Fractions – Greatest Common Factor (GCF)

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

This diagnostic test explores the following:

• Student’s understanding the greatest common factor of number
• Skills needed to simplify fractions and mixed numbers
• GCF must be common factor of both numbers
• Confusion of factor vs multiple
Sample Question • If the student answered A, in Numeracy of Fractions, the student fails to recognize-GCF is the largest common factor for consideration.
• If the student answered C, in Numeracy of Fractions, the student fails to recognize-GCF must be common factor of both numbers.
• If the student answered D, in Numeracy of Fractions, the student confuses factor and multiple.
• If the student answered E, the student is confused by the question and results in an error pattern unable to be diagnosed.

#### FRLCM – Fractions – Lowest Common Multiple (LCM)

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

This diagnostic test explores the following:

• Student’s understanding the lowest common multiples of a number
• Skills needed to rename fractions and mixed numbers in order to add or subtract them
• LCM must be a common multiple that is the least of the numbers
• Confusion of factor vs multiple
Sample Question • If the student answered A, in Numeracy of Fractions, the student fails to recognize the LCM, confuses GCF for LCM.
• If the student answered B, the student chose lesser of two numbers rather than the LCM.