# NAEP Long-Term Trend Assessment Results:Reading and Mathematics

## Performance-Level Results

### Performance-Level Summary

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. That is, younger students are more likely to successfully respond to questions that reflect the lower performance level descriptions. 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. While some assessment questions are administered at more than one age group, cross-age comparisons in student performance results are not supported by the data and are discouraged. Read more about  the setting of long-term trend performance levels

#### Performance Levels for Age 9

##### Level 150Simple Arithmetic Facts
of students performed at or above 150 in 2022
##### Level 200Beginning Skills and Understandings
of students performed at or above 200 in 2022
##### Level 250Numerical Operations and Beginning Problem Solving
of students performed at or above 250 in 2022

### Skills Associated With Each Performance Level

Each performance level is associated with a cut score on the long-term trend mathematics scale. The cut scores for each of the three reported performance levels for age 9 students are indicated in the item map below, which presents a range of mathematical skills demonstrated by 9-year-old students in 2022. 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 227 were likely to be able to subtract a two-digit number from a two-digit number. Nine-year-olds with a score of 255 were likely to be able to compute the perimeter of a square.

Skills associated with each performance level
LevelScale scoreStudents with a score of......were likely to have this knowledge or skill
Top end of scale300 to 500
Level 250:
Numerical Operations and Beginning Problem Solving
250 to 300297Multiply two fractions (MC)
280Divide a three-digit number by a two-digit number (CR)
279Add two fractions with like denominators (MC)
275Identify a relationship shown on a number line (MC)
271Use the transitive property (MC)
261Identify a figure based on relationship to other figures (MC)
260Multiply a three-digit number by a single-digit number (MC)
257Solve an application problem involving multiple operations (MC)
257Determine a simple probability from a context (MC)
255Compute the perimeter of a square (MC)
253Use and interpret number models (CR)
Level 200:
Beginning Skills and Understandings
200 to 250243Model a relationship using a number sentence (MC)
236Identify a symmetric shape (MC)
234Convert units of length (CR)
229Solve a problem involving conversion between units of volume (MC)
227Subtract a two-digit number from a two-digit number (CR)
226Divide a two-digit number by a one-digit number (CR)
223Calculate elapsed time (MC)
218Identify congruent triangles (MC)
208Solve a story problem involving subtraction (CR)
203Identify the true inequality (MC)
202Identify whole number place value (MC)
Level 150:
Simple Arithmetic Facts
150 to 200195Solve a story problem involving multiplication (MC)
187Read and interpret a circle graph (MC)
178Translate number words to numerals (MC)
151Identify a polygon (MC)
Below Level 1500 to 150

Legend: MC: multiple-choice question. CR: constructed-response question.

Note: 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.

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