How many triangles of the shape and size of the shaded triangle can the trapezoid below be divided into?
A) Three B) Four C) Five D) Six
6 cm
2 cm
2 cm
4 cm
2 cm
The figure shows a shaded parallelogram inside a rectangle. What is the area of the parallelogram?
2 cm
3 cm
10 cm
How many of the shaded right triangles shown below are needed to exactly cover the surface of the rectangle?
A) Four B) Six C) Eight D) Ten
2 cm
3 cm
6 cm
4 cm

The figure shows a shaded rectangle inside a parallelogram. What is the area of the shaded rectangle?
3 cm
4 cm
8 cm

Comments
The problems above were taken from the Third International Mathematics and Science
Study (TIMSS, 1995, 1999) public item release. The first two problems were copyrighted in 1994; the last two were copyrighted in 1997.
The problems in this section were developed to incorporate multiple aspects of topics covered in geometry units. These problems were included to give the instructor a basis of comparison. Over ten thousand students were given these assessments. I have included in this section the percentage of students generating correct responses and the grading rubric for open-ended responses. Given the increased emphasis on standardized test results as primary measure of student achievement, I felt it only fair to include assessment items from that mold.
Problem 1:
Content Category (Geometry), Performance Expectation (Using Complex Procedures)
Correct Response: C (Five)
47% of 7 th
graders responded correctly, 52% of 8 th
graders responded correctly.
Problem 2:
Content Category (Measurement), Performance Expectation (Using Complex Procedures)
Correct Response: 24 square cm. [There is no distinction made between responses with and without units]
Incorrect Responses: 10, 18, 26, 30, & 60.
34% of 7 th
graders responded correctly & 40% of 8 th
graders responded correctly.
Problem 3:
Content Category (Geometry), Performance Expectation (Using Complex Procedures)
Correct Response: C (Eight)
46% of international 8 th
grade students responded correctly.
Problem 4:
Content Category (Measurement), Performance Expectation (Investigation & Solving
Problems)
43 percent of international 8 th
grade students responded correctly.
Correct Response: 20 square centimeters
Common incorrect responses: 32 (8*4), 18 (perimeter).
Note: There is no distinction made between responses with or without units.