The 2011 NAEP-TIMSS linking study conducted by the National Center for Education Statistics (NCES) was designed to predict Trends in International Mathematics and Science Study (TIMSS) scores for the U.S. states that participated in 2011 National Assessment of Educational Progress (NAEP) mathematics and science assessment of eighth-grade students. The study design involved four samples of students: (1) Students assessed in NAEP mathematics or science during the winter (January-March) 2011 NAEP administration (NAEP operational/national sample); (2) Students in the United States assessed in TIMSS (mathematics and science) during the spring (April-June) 2011 TIMSS administration (TIMSS U.S. operational/national sample); (3) Students assessed during the 2011 NAEP testing window with booklets, referred to as braided booklets, containing one block of NAEP and one block of TIMSS items (which followed NAEP administration procedures); and (4) Students assessed during the spring 2011 TIMSS testing window with booklets, also referred to as braided booklets, containing one block of NAEP and three blocks of TIMSS items (which followed TIMSS administration procedures). The braided-booklet sample under the NAEP administration window (i.e., sample 3) was given the NAEP-like booklets, which were designed to appear as similar as possible to a regular NAEP assessment booklet and were administered under the same conditions as NAEP. Similarly, the braided-booklet sample under the TIMSS administration window (i.e., sample 4) was given the TIMSS-like booklets. Those booklets were designed to appear as similar as possible to a regular TIMSS assessment booklet and were administered under nearly the same conditions as TIMSS. In addition, the braided booklets in the 2011 TIMSS window were administered in the same schools in which TIMSS was administered, with one intact classroom randomly assigned to the U.S. TIMSS national sample and another to the braided-booklet sample. In addition to these linking study samples, nine states--Alabama, California, Colorado, Connecticut, Indiana, Florida, Massachusetts, Minnesota, and North Carolina--participated in 2011 TIMSS directly as separate jurisdictions and, therefore, received actual TIMSS scores. These nine states provided a "validation sample" upon which the NAEP-TIMSS link was evaluated. The validation states were selected based on their state enrollment and willingness to participate, and also on whether they as a whole represented a substantial range of performances relative to the national NAEP average, had previous experience as benchmarking participants in TIMSS, and were geographically diverse. [This 2011 NAEP-TIMSS linking methodology paper was prepared to supplement the "Linking Methodologies" section presented in "U.S. States in a Global Context: Results from the 2011 NAEP-TIMSS Linking Study. NCES 2013-460" (ED544218). This report was prepared with support from American Institutes for Research (AIR), Educational Testing Service (ETS), and the Human Resources Research Organization (HumRRO) for the contract No. ED-07-CO-0107.]