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NAEP Assessment Item, Grade 4: Justify two correct interpretations
3, 4, 5
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Professional Commentary

Students must explain with words or pictures the equivalence of two different representations for a fractional part of a set of discrete objects. This multiple-choice question is a sample test item used in grade 4 in the 2003 National Assessment of Educational Progress (see About NAEP). The URL link (above) takes the user directly to the NAEP test item, with access to performance data by various subgroups of students, a scoring key, and discussion of the content on which the item is based. The NAEP website allows users to build their own printable database of test items by clicking on Add Question in the upper right hand corner of the screen. NAEP Reference Number: 2003-4M7, No. 15. (sw)

Ohio Mathematics Academic Content Standards (2001)
Number, Number Sense and Operations Standard
Benchmarks (3–4)
Recognize and generate equivalent representations for whole numbers, fractions and decimals.
Represent commonly used fractions and mixed numbers using words and physical models.
Grade Level Indicators (Grade 3)
Represent fractions and mixed numbers using words, numerals and physical models.
Recognize and use decimal and fraction concepts and notations as related ways of representing parts of a whole or a set; e.g., 3 of 10 marbles are red can also be described as 3/10 and 3 tenths are red.
Principles and Standards for School Mathematics
Number and Operations Standard
Understand numbers, ways of representing numbers, relationships among numbers, and number systems
Expectations (3–5)
recognize equivalent representations for the same number and generate them by decomposing and composing numbers;
develop understanding of fractions as parts of unit wholes, as parts of a collection, as locations on number lines, and as divisions of whole numbers;