These two examples required the students to work with algebraic expressions and equations. It is not surprising that students had even more difficulty identifying the correct expression to represent the number of Clarissa's hats in the next example. International performance on this item averaged 47 percent at the eighth-grade level. Note that the U.S. student scores did not reflect the international ranking for these questions. More U.S. students answered the hat question correctly than the question about equivalent expressions.
Arrow symbol indicates correct answer.
Juan has 5 fewer hats than Maria, and Clarissa has 3 times as many hats as Juan. Arrow symbol indicates correct answer. For the second part of the problem, only 10 percent of students internationally provided a correct ratio between the newly drawn and given rectangles. In the space below, draw a new rectangle whose length is one and one half times the length of the rectangle above, and whose width is half the width of the rectangle above. Show the length and width of the new rectangle in centimeters on the figure.