Assessment Design and

Field 030: Middle Grades Mathematics

The assessment design below describes general assessment information. The framework that follows is a detailed outline that explains the knowledge and skills that this assessment measures.

Assessment Design

Format Computer-based test (CBT) and online-proctored test
Number of Questions 125 multiple-choice questions
Time* 255 minutes
Passing Score 220

*Does not include 15-minute tutorial or optional 15-minute break for online-proctored assessment


Pie chart of approximate test weighting outlined in the table below.

Domain Range of Competencies Approximate Percentage of Assessment Score
I Number Sense and Operations 0001–0002 19%
II Algebra and Functions 0003–0006 36%
III Measurement and Geometry 0007–0009 27%
IV Statistics and Probability 0010–0011 18%
Domain I–Number Sense and Operations

0001 Understand numbers. (9%)


  1. Analyze the relationships between the subsets of the real numbers.
  2. Analyze the role of place value in any number system.
  3. Analyze the use of estimation in a variety of situations.
  4. Translate between different representations of numbers.
  5. Apply number-theory concepts (e.g., divisibility rules, prime factorization, greatest common factors) in problem-solving situations.

0002 Understand operations. (10%)


  1. Analyze relational and operational properties, including order of operations.
  2. Analyze a variety of conventional and alternative algorithms.
  3. Solve a variety of mathematical and real-world problems involving integers, fractions, and decimals.
  4. Solve a variety of mathematical and real-world problems involving ratios, proportions, and percents.
Domain II–Algebra and Functions

0003 Understand patterns, relations, and functions. (10%)


  1. Analyze a variety of patterns.
  2. Analyze the properties of relations and functions in multiple representations (e.g., tables, graphs, equations, words).
  3. Analyze direct and inverse proportional relationships.
  4. Determine the effects of transformations on the graph of a function or relation.

0004 Understand algebraic techniques and applications. (10%)


  1. Manipulate algebraic expressions, equations, and inequalities (e.g., simplify, transform, factor).
  2. Solve linear and nonlinear equations and inequalities.
  3. Connect appropriate algebraic notation to phrases and sentences.

0005 Understand linear relations and applications. (10%)


  1. Analyze the relationship between a linear equation or inequality and its representations.
  2. Solve systems of linear inequalities or equations with a variety of methods.
  3. Interpret the meaning of the slope and the y-intercept in various contexts.
  4. Solve a variety of real-world problems by modeling them with linear equations, systems, and inequalities.

0006 Understand nonlinear relations. (6%)


  1. Analyze relationships between multiple representations of a nonlinear equation or inequality.
  2. Solve a variety of real-world problems by modeling them with nonlinear equations and inequalities.
Domain III–Measurement and Geometry

0007 Understand measurement principles, procedures, and applications. (9%)


  1. Analyze the use of various units and unit conversions within the customary and metric systems.
  2. Calculate or estimate measures of lengths, areas, and volumes.
  3. Apply the concepts of similarity, scale factors, and proportional reasoning to solve indirect measurement problems.
  4. Analyze precision, accuracy, and rounding in measurements and computed quantities.

0008 Understand Euclidean geometry in two and three dimensions. (9%)


  1. Analyze properties of points, lines, planes, and angles.
  2. Use the properties of triangles, quadrilaterals, and other polygons and circles to solve problems.
  3. Apply principles of similarity and congruence.
  4. Apply the Pythagorean theorem and its converse.
  5. Use nets, cross sections, and projections to analyze three-dimensional figures.
  6. Analyze geometric arguments using deductive reasoning.

0009 Understand coordinate and transformational geometry. (9%)


  1. Analyze two- and three-dimensional figures using coordinate systems.
  2. Connect algebra and geometry by applying concepts of distance, midpoint, and slope to classify figures and solve problems in the coordinate plane.
  3. Analyze transformations of figures in the coordinate plane.
  4. Analyze figures in terms of symmetry, and analyze tessellations of the plane.
Domain IV–Statistics and Probability

0010 Understand principles and techniques of statistics. (9%)


  1. Analyze the effects of bias and sampling techniques.
  2. Use appropriate formats for organizing and displaying data.
  3. Analyze univariate and bivariate data in a variety of representations.
  4. Make predictions from data presented in a variety of representations.
  5. Analyze the use of measures of central tendency and spread.

0011 Understand principles of probability and techniques for determining probability. (9%)


  1. Determine probabilities of simple and compound events.
  2. Use counting principles to calculate probabilities.
  3. Use a variety of visual representations to calculate probabilities.
  4. Demonstrate knowledge of methods for simulating probabilities.

0012 Understand principles of discrete mathematics. (0%)