Exhibit 3.13 presents the description of eighth grade performance at the Advanced International Benchmark. Students could apply and reason to solve a variety of problems as well as solve linear equations and make generalizations.

Exhibit 3.13.1 shows a multistep problem involving fractions from the number domain. This problem was relatively difficult for eighth grade students, with an international average of 18 percent. The top performances were in Chinese Taipei and Korea, where just over half the students answered correctly (52–53%).

Exhibit 3.13.2 involved students constructing a linear equation to solve a problem about perimeter. The international average was 26 percent. Almost three-fourths (74%) of the Singaporean students successfully completed this task.

Exhibit 3.13.3 shows a reasoning item from the geometry domain, which was based on properties of supplementary angles. Seventy-seven percent of eighth grade students answered correctly in both Japan and Korea. The international average was 26 percent.

Exhibit 3.13.4 presents an item from the data and probability domain that required students to interpret the change in a mean, using decimals and rounding. The international average was 36 percent. The highest percentage correct—71 percent—was in Korea.