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# The NAEP Mathematics Achievement Levels by Grade

## Grade 4

## Grade 8

## Grade 12

# NAEP Mathematics Achievement Levels for Grade 12, 1990–2003

Last updated 21 October 2015 (FW)

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Grade 4

Grade 8

Grade 12

Grade 12 (1990—2003)

Specific definitions of the *Basic*, *Proficient*, and *Advanced* achievement levels for grades 4, 8, and 12 are presented in the tables that follow. Because of changes made to the NAEP mathematics framework in 2005, the achievement-level descriptions and cut points indicated below for grade 12 have been updated. To maintain trend, results for grades 4 and 8 are reported on a 0–500 scale while results for grade 12, beginning with the 2005 assessment, are reported on a 0–300 scale. View the grade 12 achievement-level descriptions and cut scores used prior to 2005.

The achievement levels are cumulative; therefore, students performing at the *Proficient* level also display the competencies associated with the *Basic* level, and students at the *Advanced* level also demonstrate the skills and knowledge associated with both the *Basic* and the *Proficient* levels. The cut score indicating the lower end of the score range for each level is noted in parentheses.

Basic(214) |
Fourth-graders performing at the |
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Proficient(249) |
Fourth-graders performing at the |

Advanced(282) |
Fourth-graders performing at the |

Basic(262) |
Eighth-graders performing at the As they approach the |
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Proficient(299) |
Eighth-graders performing at the Quantity and spatial relationships in problem solving and reasoning should be familiar to them, and they should be able to convey underlying reasoning skills beyond the level of arithmetic. They should be able to compare and contrast mathematical ideas and generate their own examples. These students should make inferences from data and graphs, apply properties of informal geometry, and accurately use the tools of technology. Students at this level should understand the process of gathering and organizing data and be able to calculate, evaluate, and communicate results within the domain of statistics and probability. |

Advanced(333) |
Eighth-graders performing at the |

Basic(141) |
Students performing at the At this level, students should be able to interpret information about functions presented in various forms, including verbal, graphical, tabular, and symbolic. They should be able to evaluate polynomial functions and recognize the graphs of linear functions. Twelfth-grade students should also understand key aspects of linear functions, such as slope and intercepts. These students should be able to extrapolate from sample results; calculate, interpret, and use measures of center; and compute simple probabilities. Students at this level should be able to solve problems involving area and perimeter of plane figures, including regular and irregular polygons, and involving surface area and volume of solid figures. They should also be able to solve problems using the Pythagorean theorem and using scale drawings. Twelfth-graders performing at the |
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Proficient(176) |
Twelfth-grade students performing at the
Students performing at this level should be able to use technology to calculate summary statistics for distributions of data. They should be able to recognize and determine a method to select a simple random sample, identify a source of bias in a sample, use measures of center and spread of distributions to make decisions and predictions, describe the impact of linear transformations and outliers on measures of center, calculate combinations and permutations to solve problems, and understand the use of the normal distribution to describe real-world situations. Twelfth-grade students should be able to use theoretical probability to predict experimental outcomes involving multiple events. These students should be able to solve problems involving right triangle trigonometry, use visualization in three dimensions, and perform successive transformations of a geometric figure in a plane. They should be able to understand the effects of transformations, including changes in scale, on corresponding measures and to apply slope, distance, and midpoint formulas to solve problems. |

Advanced(216) |
Students at this level should be able to reason about functions as mathematical objects. They should be able to evaluate logarithmic and trigonometric functions and recognize the properties and graphs of these functions. They should be able to use properties of functions to analyze relationships and to determine and construct appropriate representations for solving problems, including the use of advanced features of graphing calculators and spreadsheets. These students should be able to describe the impact of linear transformations and outliers on measures of spread (including standard deviation), analyze predictions based on multiple data sets, and apply probability and statistical reasoning to solve problems involving conditional probability and compound probability. Twelfth-grade students performing at the |

Basic(288) |
Twelfth-grade students performing at the They should be able to apply statistical reasoning in the organization and display of data and in reading tables and graphs. They also should be able to generalize from patterns and examples in the areas of algebra, geometry, and statistics. At this level, they should use correct mathematical language and symbols to communicate mathematical relationships and reasoning processes, and use calculators appropriately to solve problems. |
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Proficient(336) |
Twelfth-graders performing at the |

Advanced(367) |
Twelfth-grade students performing at the They should be able to formulate generalizations and create models through probing examples and counterexamples. They should be able to communicate their mathematical reasoning through the clear, concise, and correct use of mathematical symbolism and logical thinking. |

Last updated 21 October 2015 (FW)