Exhibit 3.11 provides the description of student achievement at the Intermediate International Benchmark. At this level, students could apply basic mathematical knowledge in a variety of situations.

Exhibit 3.11.1 presents an item from the number domain. As shown in this item, students reaching the Intermediate Benchmark demonstrated familiarity with negative numbers. The international average was 59 percent. The highest performance on the item was in Finland—85 percent of the students responded correctly.

Exhibit 3.11.2 presents a geometry item. Fifty-six percent of the eighth grade students, on average, were able to use the properties of angles to determine the size of a fourth angle in a quadrilateral when given the values of the other three angles. The Singaporean students had the highest achievement, with 90 percent correct.

Exhibit 3.11.3 shows a multi-part item from the data and probability domain. Eighty-three percent of the students in Singapore were able to compute and compare three unit prices based on advertisements. The international average was 56 percent.