Mathematics: Performance-Level Results

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Mathematics Performance-level Descriptions

Reporting mathematics performance-level results

Long-term trend performance levels describe the range of mathematics skills demonstrated by students when responding to assessment questions. Results are reported in terms of the percentages of students attaining each performance level. Changes in the percentages at or above each performance level reflect changes in the proportion of students who demonstrated the knowledge and skills associated with that level.

The five performance levels are applicable at all three age groups (age 9, age 13, and age 17); however, the likelihood of attaining higher performance levels is related to a student's age. The performance-level results presented for each age are those that are most likely to show significant change across the assessment years. For this reason, only three performance levels are discussed for each age. For age 9, performance-level results are presented for at or above 150, 200, and 250. Read more about the setting of long-term trend performance levels.

See all NAEP LTT mathematics performance-level descriptions.

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Performance-level trends
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Item map

What 9-year-olds know and can do in mathematics

The item map below illustrates a range of mathematical skills associated with scores on the long-term trend mathematics scale. Cut scores for the three performance levels reported at age 9 are highlighted in boxes on the scale. The descriptions of selected assessment questions indicate what students need to do to receive credit for a correct answer. For example, 9-year-olds with a score of 225 were likely to be able to identify a symmetric shape. Nine-year-olds with a score of 259 were likely to be able to solve an application problem involving multiple operations.

Scale scoreQuestion description
297Multiply two fractions (MC)
281Divide a three-digit number by a two-digit number (CR)
280Add two fractions with like denominators (MC)
280Identify a relationship shown on a number line (MC)
271Use the transitive property (MC)
261Identify a figure based on relationship to other figures (MC)
259Multiply a three-digit number by a single-digit number (MC)
259Solve an application problem involving multiple operations (MC)
255Determine a simple probability from a context (MC)
254Compute the perimeter of a square (MC)
253Use and interpret number models (CR)
Level 250: Numerical Operations and Beginning Problem Solving
243Model a relationship using a number sentence (MC)
237Convert units of length (CR)
230Calculate elapsed time (MC)
229Solve a problem involving conversion between units of volume (MC)
225Divide a two-digit number by a one-digit number (CR)
225Identify a symmetric shape (MC)
223Subtract a two-digit number from a two-digit number (CR)
212Identify congruent triangles (MC)
212Solve a story problem involving subtraction (CR)
202Identify the true inequality (MC)
201Identify whole number place value (MC)
Level 200: Beginning Skills and Understandings
189Solve a story problem involving multiplication (MC)
185Read and interpret a circle graph (MC)
172Translate number words to numerals (MC)
Level 150: Simple Arithmetic Facts
149Find the value of an unknown quantity in a number sentence (CR)
132Identify a polygon (MC)
NOTE: CR denotes a constructed-response question. MC denotes a multiple-choice question. The position of a question on the scale represents the scale score attained by students who had a 65 percent probability of successfully answering a constructed-response question, a 77 percent probability of correctly answering a three-option multiple-choice question, a 74 percent probability of correctly answering a four-option multiple-choice question, a 72 percent probability of correctly answering a five-option multiple-choice question, or a 71 percent probability of correctly answering a six-option multiple-choice question. For constructed-response questions, the question description represents students' performance rated as completely correct.