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Sample Questions
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2005 NAEP Mathematics Sample Questions

Try These Questions Yourself

The sample questions below give a brief introduction to the materials that assess the mathematical ability of students in grades 4 and 8. All questions are based on the NAEP mathematics framework, which defines the test design and content. The framework was developed through an extensive national consensus process and adopted by the National Assessment Governing Board (NAGB). Visit the NAGB website to download the full text of the mathematics framework.

Several other tools are available to help students, parents, and teachers look more closely at NAEP questions. View the item maps that provide concrete examples of what students at various achievement levels likely know and can do. Visit the NAEP Questions Tool to see over 1,600 items in all NAEP subject areas.

Sample Grade 4 Short Constructed-Response Question

Sample Question 1 is a short constructed-response question in the number properties and operations content area. This question asked students to identify the point indicated on a number line.

A number line with six points marked. The first point is marked 5.6, the fourth is marked 6.2, and the fifth is marked 6.4. The third point is marked P.

1. On the number line above, what number would be located at
        point P?

Answer: 6.0    


56 percent of fourth-graders wrote responses rated as "Correct."


Sample Grade 4 Multiple-Choice Question

Sample Question 2 is a multiple-choice question in the algebra content area. This question asked students to represent a given situation with an algebraic expression.

2. N stands for the number of hours of sleep Ken gets each night.
        Which of the following represents the number of hours of sleep
        Ken get in 1 week?

  A)  N + 7
  B)  N - 7
Correct Answer C)  N x 7
  D)  N ÷ 7

61 percent of fourth-graders answered this question correctly.


Sample Grade 8 Short Constructed-Response Question

Sample Question 3 is a short constructed-response question in the geometry content area. This question asked students to shade 5 additional squares in a grid that has 3 shaded squares to create a symmetric pattern. Students were given paper squares for this question.

3. Shade five more squares on the grid below so that if your
        completed figure were folded along the fold line both sides
        would match.

A grid six squares wide by five squares high, with shaded squares at row 2, column 3; at row 3, column 2; and at row 3, column 4, and a fold line separating the third and fourth columns. The suggested answer provides additional squares shaded at row 2, column 4; row 3, column 3; row 3, column 4; row 4, column 3; and rows 4, column 4.

58 percent of eighth-graders wrote responses rated as "Correct."


Sample Grade 8 Multiple-Choice Question

Sample question 4 is a multiple-choice question in the algebra content area. This question asked students to infer a rule and find the next term in a sequence. The terms in this sequence are the squares of consecutive odd numbers.

1, 9, 25, 49, 81,...

4. The same rule is applied to each number in the pattern above. 
        What is the 6th number in the pattern?

  A)    40
  B)  100
Correct Answer C)  121
  D)  144
  E)  169

60 percent of eighth-graders answered this question correctly.



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