# Middle School Content Knowledge (0146/5146)

## Topics Covered

Representative descriptions of topics covered in each category are provided below. Within each content area, the approximate percentage of examination questions is shown for each topic.

Current section: II. Mathematics

### II. Mathematics

Focus is on the mathematical understandings that middle school teachers must have, the ability to communicate these understandings, and the ability to solve mathematical problems.

Because the emphasis is on assessing the examinee's ability to reason logically, to use mathematical techniques in problem solving, and to communicate mathematical ideas effectively, examinees are not required to do much computation. Examinees may use non-programmable calculators while taking the test; a basic four-function calculator will be adequate.

The test questions do not require knowledge of advanced-level mathematics vocabulary but may require examinees to relate mathematics to real-life situations. Mathematics is conceptualized as an integrated field; therefore, a single problem may test several mathematical content areas.

Although few technical words are used in the test questions, terms such as area, perimeter, ratio, integer, factor, and prime number are used because it is assumed that these are commonly encountered in the mathematics that all examinees have studied.

• Number sense and numeration (20%)
• understand the meaning/implication of number and number concepts as they relate to problem solving, using cardinal and ordinal numbers, place value, ordering of fractions, decimals, whole numbers
• Geometry (20%)
• knowledge of relationships in both two and three dimensions
• ability to draw inferences based on precepts/concepts of parallelism, perpendicularity, congruence and similarity, angle measures and polygons
• Measurement (5%)
• knowledge and application of standard units of both the English and metric systems, nonstandard units, estimation, perimeter, area, volume, mass, weight, angle measure, time, temperature
• Algebraic concepts (10%)
• recognize and apply algebraic concepts and properties
• describe patterns by writing or identifying a formula
• Number theory (10%)
• problem solving that demonstrates an understanding of prime and composite numbers, divisibility rules, least common multiple, greatest common divisor and set theory
• The real number system and its subsystems (20%)
• solve real-world situational problems
• work with both standard and alternate algorithms
• Probability and statistics (15%)
• understand the organization, presentation, and interpretation of data in various forms
• recognize valid and invalid inferences
• solve basic problems
• make predictions involving probability and statistics