# Elementary Education (Grades K–6) Subtest 2

## Subarea I.1. Mathematics

0010
Understand concepts of numerical literacy.

- demonstrating knowledge of number sense (e.g., place value, rounding, comparing and ordering numbers, estimation, equality)
- translating among equivalent representations of numbers and using them to solve problems
- demonstrating knowledge of concepts of number theory (e.g., divisibility rules, factors, multiples, perfect numbers, prime numbers) and of models, methods, and tools for exploring number relationships
- demonstrating the ability to apply a variety of computational procedures to model and solve problems and to examine the reasonableness of solutions
- demonstrating knowledge of the properties of numerical operations (e.g., associative, distributive) and the relationship of integers to other numbers (e.g., real, rational)

0011
Understand concepts of mathematical patterns, relations, and functions.

- identifying and extending number and geometric patterns
- using patterns, tables, graphs, and function rules to solve real-world and mathematical problems
- recognizing relationships between varying quantities using different representations (e.g., function rules, graphs, tables) and translating between any two of these representations
- interpreting and solving equations and inequalities involving variables and rational numbers
- recognizing types and properties of functions

0012
Understand concepts of space and shape.

- recognizing properties of planes, lines, and angles
- applying knowledge of the properties of and relationships between geometric figures
- applying knowledge of symmetry and transformations to geometric shapes and figures
- demonstrating knowledge of the concepts of direct and indirect measurement (e.g., volume, surface area, scale, similarity, Pythagorean theorem) of two- and three-dimensional figures and of real-world applications of these concepts
- selecting appropriate units of measurement, converting measurements within measurement systems, and solving real-world problems
- applying knowledge of the characteristics and uses of geometric learning tools (e.g., geoboard, protractor, ruler)

0013
Understand concepts and techniques of data investigations and the concepts of randomness and uncertainty.

- demonstrating knowledge of conceptual and procedural tools for collecting, organizing, and reasoning about data
- applying knowledge of statistical measures (e.g., mean, median, mode) for analyzing data
- applying knowledge of techniques for representing and summarizing data graphically (e.g., histogram, frequency distribution, stem-and-leaf plot, Venn diagram)
- interpreting and drawing inferences from data and making decisions in applied problem situations
- using principles of probability (e.g., counting, sample space, independence) to solve real-world and mathematical problems involving simple and compound events
- demonstrating knowledge of randomness and sampling in surveys and experimental studies

0014
Understand concepts and applications of discrete math.

- applying knowledge of set theory (e.g., Venn diagrams, union) and its real-world applications
- applying knowledge of permutations and combinations and their real-world applications
- demonstrating knowledge of graph theory and its real-world applications
- applying knowledge of sequences, series, and iterative processes to solve problems

0015
Understand mathematical processes and perspectives.

- demonstrating the ability to apply reasoning to make conjectures, justify ideas or arguments, and solve mathematical and nonmathematical problems
- demonstrating knowledge of the connections among mathematical concepts and procedures and the relationships between mathematics and other fields
- demonstrating the ability to communicate mathematically by translating between different representations (e.g., verbal, tabular, graphic, symbolic) of mathematical concepts and at different levels of formality
- selecting appropriate strategies to solve a variety of problems
- demonstrating knowledge of the history of mathematics and the interaction between different cultures and mathematics
- demonstrating knowledge of methods for integrating technological and nontechnological tools in mathematics
- applying mathematical language to solve problems and communicate understanding