## 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 150 Simple Arithmetic Facts

##### Level 200 Beginning Skills and Understandings

##### Level 250 Numerical Operations and Beginning Problem Solving

### Performance-Level Trends

#### Higher percentages of 9-year-old students at or above 200 and 250 performance levels compared to 1978

Compared to 1978, higher percentages of 9-year-old students performed at or above two of the three performance levels reported for that age. The percentage performing at or above level 200 has increased by 10 percentage points, and the percentage of 9-year-olds performing at or above level 250 has increased by 18 percentage points since 1978. There was no statistically significant change in the percentage of 9-year-olds at or above 150 compared to 1978. Compared to the previous assessment in 2020, however, the percentages of students performing at or above each of the three performance levels were lower. Click on the performance level in the figure below to see the percentages of students at or above the selected baseline performance level.

##### Figure Trend in NAEP long-term trend mathematics performance-level results for 9‑year‑old students

### 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.

Level | Scale score | Students with a score of... | ...were likely to have this knowledge or skill |
---|---|---|---|

Top end of scale | 300 to 500 | ||

Level 250:Numerical Operations and Beginning Problem Solving | 250 to 300 | 297 | Multiply two fractions (MC) |

280 | Divide a three-digit number by a two-digit number (CR) | ||

279 | Add two fractions with like denominators (MC) | ||

275 | Identify a relationship shown on a number line (MC) | ||

271 | Use the transitive property (MC) | ||

261 | Identify a figure based on relationship to other figures (MC) | ||

260 | Multiply a three-digit number by a single-digit number (MC) | ||

257 | Solve an application problem involving multiple operations (MC) | ||

257 | Determine a simple probability from a context (MC) | ||

255 | Compute the perimeter of a square (MC) | ||

253 | Use and interpret number models (CR) | ||

Level 200:Beginning Skills and Understandings | 200 to 250 | 243 | Model a relationship using a number sentence (MC) |

236 | Identify a symmetric shape (MC) | ||

234 | Convert units of length (CR) | ||

229 | Solve a problem involving conversion between units of volume (MC) | ||

227 | Subtract a two-digit number from a two-digit number (CR) | ||

226 | Divide a two-digit number by a one-digit number (CR) | ||

223 | Calculate elapsed time (MC) | ||

218 | Identify congruent triangles (MC) | ||

208 | Solve a story problem involving subtraction (CR) | ||

203 | Identify the true inequality (MC) | ||

202 | Identify whole number place value (MC) | ||

Level 150:Simple Arithmetic Facts | 150 to 200 | 195 | Solve a story problem involving multiplication (MC) |

187 | Read and interpret a circle graph (MC) | ||

178 | Translate number words to numerals (MC) | ||

151 | Identify a polygon (MC) | ||

Below Level 150 | 0 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.