# NAEP Report Card: Mathematics

## Sample Questions

The NAEP mathematics assessment measures students' knowledge and skills in five broad content areas of mathematics (Number properties and operations; Measurement; Geometry; Data analysis, statistics, and probability; and Algebra) and their ability to apply their content area knowledge to problem-solving situations. The NAEP mathematics framework guides the content and development of the mathematics assessment at grades 4, 8, and 12. The assessments at grades 4 and 8 measure all five content areas. The grade 12 assessment measures four content areas; because most measurement topics suitable for twelfth-grade students are geometric in nature, geometry and measurement are combined into one content area.

As specified in the framework, questions are classified by mathematical subtopic which is used to determine the key concept or skill that should be measured within each content area. Questions are also classified by mathematical complexity which deals with what students are asked to do in a question. Each of the three levels of complexity―low, moderate, and high―describes the demands a question might make on a student's thinking. Read more about the NAEP mathematics assessment.

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### Student Performance on Mathematics Assessment Questions

To better understand students’ mathematics knowledge and skills across the content areas, student performance on samples of publicly released questions from the 2022 mathematics assessments at grades 4 and 8 are presented below. Each example contains a brief description of the item, the mathematics content area, and mathematics subtopic.

Student performance results are expressed as the average percent correct for each question in 2022 compared to performance on the same set of questions that were administered as part of the 2019 assessments. The declines in average overall mathematics scores at grades 4 and 8 in 2022 are reflected in average percent correct performance on the released sample assessment questions.

Number Properties and Operations
Question
Subtopic
Percentage correct
2019
2022
Change
Find total in a representation of money
Number sense
92%
89%
-2
Subtract decimal numbers
Number operations
89%
88%
-1
Decompose a 4-digit number based on place value
Number sense
83%
81%
-2
Interpret value of a point on a number line
Number sense
75%
71%
-4
Classify whole numbers as even or odd
Properties of number and operations
67%
59%
-7
Identify inverse relationship between addition and subtraction
Number operations
55%
51%
-4
Determine whether a conclusion about a situation is valid and explain
Estimation
52%
51%
-1
Determine the validity of statements about comparing fractions
Number sense
43%
42%
-1
Solve a story problem involving decimal numbers
Number operations
31%
29%
-2
Find and describe how to create the largest result in a given expression
Number operations
24%
23%
-1
Identify representations that show a number is a factor of another
Mathematical reasoning using number
23%
20%
-3
Select factors of a given number
Properties of number and operations
14%
11%
-3
Significantly different from 2019
Not significantly different from 2019
On-screen calculator was available with this question

### Additional NAEP Sample Question Resources

See the NAEP Questions Tool to learn more about the full set of released mathematics questions from the 2022 assessment (grades 4 and 8) and previous assessment years (grades 4, 8, and 12). The tool presents examples of students’ answers to constructed-response questions along with scorer comments; the percentage of students who answered each question correctly, and how students’ performance on a given question corresponds to their overall scores on the mathematics assessment.

NAEP Questions Tool

#### Experience the mathematics digitally based assessment as students did

You can try test questions that were administered to students as part of the 2022 mathematics assessment. After completing the questions, you can see the correct answers, scoring rubrics, and student performance results. ##### Try grade 4 mathematics questions
Questions with an onscreen calculator availableQuestions with an onscreen calculator not available

Some sections of the mathematics assessment provided students with access to a calculator and some did not. The use of an onscreen calculator was available to students on approximately 30 percent of the test questions. To view these questions, you will need to use Chrome (48 or higher). The questions are best viewed at a zoom of 67 percent.

#### Review NAEP item maps

One way to understand the NAEP mathematics scale is by seeing the types of questions that students performing at different points on the scale are likely to answer correctly. See the 2022 item map with a range of comprehension skills demonstrated on the mathematics scale and within the score range for each NAEP achievement level.

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