Since 1973, the National Assessment of Educational Progress (NAEP) has gathered information about student achievement in mathematics. The NAEP assessment in mathematics has two components that differ in purpose. One assessment measures long-term trends in achievement among 9-, 13-, and 17-year-old students by using the same basic design each time. The main NAEP assessment is based on a framework (such as this one) that can be updated periodically. The "2019 Mathematics Framework" reflects changes from 2005 in grade 12 only; mathematics content objectives for grades 4 and 8 have not changed. Therefore, main NAEP trend lines from the early 1990s can continue at fourth and eighth grades for the 2019 assessment. Special analyses have also determined that main NAEP trend lines from 2005 can continue at 12th grade for the 2019 assessment. Taken together, the NAEP assessments provide a rich, broad, and deep picture of student mathematics achievement in the U.S. An assessment framework is like a blueprint. It lays out the basic design of the assessment by describing the mathematics content that should be tested and the types of assessment questions that should be included. It also describes how the various design factors should be balanced across the assessment. A companion document to this framework, "Assessment and Item Specifications for the NAEP Mathematics Assessment," gives more detail about development of the items and conditions for the 2019 NAEP Mathematics Assessment. This is an assessment framework, not a curriculum framework. In broad terms, this framework attempts to answer the question: What mathematics skills should be assessed on NAEP at grades 4, 8, and 12? The answer to this question must necessarily take into account the constraints of a large-scale assessment such as NAEP with its limitations on time and resources. Of critical importance is the fact that this document does not attempt to answer the question: What (or how) mathematics should be taught? The framework was developed with the understanding that some concepts, skills, and activities in school mathematics are not suitable to be assessed on NAEP, although they may well be important components of a school curriculum. This framework describes a design for the main NAEP assessments at the national, state, and district levels, but it is not the framework for the long-term trend NAEP Assessment. [The following individuals authored the introductions to the content areas: Roger Howe, Richard Scheaffer, and Mary Lindquist.]