# Assessment Design and

Framework

## 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

### Framework

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%)**

Includes:

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

**0002 Understand operations. (10%)**

Includes:

- Analyze relational and operational properties, including order of operations.
- Analyze a variety of conventional and alternative algorithms.
- Solve a variety of mathematical and real-world problems involving integers, fractions, and decimals.
- 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%)**

Includes:

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

**0004 Understand algebraic techniques and applications. (10%)**

Includes:

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

**0005 Understand linear relations and applications. (10%)**

Includes:

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

**0006 Understand nonlinear relations. (6%)**

Includes:

- Analyze relationships between multiple representations of a nonlinear equation or inequality.
- 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%)**

Includes:

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

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

Includes:

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

**0009 Understand coordinate and transformational geometry. (9%)**

Includes:

- Analyze two- and three-dimensional figures using coordinate systems.
- Connect algebra and geometry by applying concepts of distance, midpoint, and slope to classify figures and solve problems in the coordinate plane.
- Analyze transformations of figures in the coordinate plane.
- 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%)**

Includes:

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

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

Includes:

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

**0012 Understand principles of discrete mathematics. (0%)**