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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 at grade 12 should be able to perform computations with real numbers and estimate the results of numerical calculations. These students should also be able to estimate, calculate, and compare measures and identify and compare properties of two- and three-dimensional figures, and solve simple problems using two-dimensional coordinate geometry. At this level, students should be able to identify the source of bias in a sample and make inferences from sample results; calculate, interpret, and use measures of central tendency; and compute simple probabilities. They should understand the use of variables, expressions, and equations to represent unknown quantities and relationships among unknown quantities. They should be able to solve problems involving linear relations using tables, graphics, or symbols, and solve linear equations involving one variable. |
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Proficient(176) |
These students should be able to interpret an argument, justify a mathematical process, and make comparisons dealing with a wide variety of mathematical tasks. They should also be able to perform calculations involving similar figures including right triangle trigonometry. They should understand and apply properties of geometric figures and relationships between figures in two and three dimensions. Students at this level should select and use appropriate units of measure as they apply formulas to solve problems. Students performing at this level should be able to use measures of central tendency and variability of distributions to make decisions and predictions, calculate combinations and permutations to solve problems, and understand the use of the normal distribution to describe real-world situations. Students performing at the |

Advanced(216) |
Students should be able to integrate knowledge to solve complex problems and justify and explain their thinking. These students should be able to analyze, make and justify mathematical arguments, and communicate their ideas clearly. |

Last updated 20 December 2006 (FW)