Sample Questions

Mathematics Sample Questions

The mathematics assessment measures students' knowledge and skills in mathematics and their ability to apply their mathematical knowledge in problem-solving situations. As specified in the NAEP mathematics framework, questions are classified by content area and mathematical complexity. Each question assesses one of the five broad content areas: number properties and operations; measurement; geometry; data analysis, statistics, and probability; and algebra. Mathematical complexity deals with what students are asked to do in a question and each of the three levels of complexity―low, medium, and high―describes the demands a question might make on a student's thinking. Read more about the mathematical content areas and levels of complexity.

The NAEP mathematics digitally based assessment (DBA) was administered on a touchscreen tablet with an attached keyboard. Some DBA questions included interactive, onscreen tools (such as a ruler or scratchwork tool). The use of an onscreen calculator was available to students on approximately 30 percent of the test questions at both grades 4 and 8. At the beginning of the assessment, students viewed an interactive tutorial demonstrating how to effectively use the onscreen tools when answering questions.

In addition to reporting students' answers to assessment questions, the DBA system enables NAEP to report on actions students took when using the keyboard, touchscreen, or mouse to answer questions. These actions include how students used onscreen tools to solve math problems.

Grade 4 Sample Mathematics Questions

Questions from the 2019 NAEP mathematics assessment were not released to the public. However, samples of released mathematics questions from the 2017 NAEP assessment, including how students performed on them, are presented below as examples of the types of questions given to students in the 2019 assessment. Each example contains a brief description of the item, the format type (selected response or constructed response), and the content area (number properties and operations; measurement; geometry; data analysis, statistics, and probability; and algebra). The percentage of students who answered a selected-response question correctly or who received full credit for their answer to a constructed-response question is also displayed. Learn more about the NAEP mathematics assessment.

Connect decimal numbers to area models
Selected response
Number Properties and Operations
58% Correct
show
Compare fractions to a given fraction
Selected response
Number Properties and Operations
32% Correct
show
Extend a numerical pattern to solve a problem in context
Short constructed response
Algebra
22% Correct
show

A complete list of questions released from the 2017 mathematics assessment is available in the NAEP Questions Tool. Read more about the framework that guided the development of the assessment questions.

Experience the Mathematics Assessment

Experience the mathematics digitally based assessment as students did and try sample test questions administered in 2017.

Try grade 4 mathematics questions (onscreen calculator available) Try grade 4 mathematics questions (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.

Item Maps

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