Elementary Education (Grades K–6) Subtest 2

Subarea 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 number sets (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 as measurable attributes of real-world and mathematical objects
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 measurement 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 interpreting 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, graphic organizers)
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 mathematics.

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, construct logical arguments informally and formally, and solve mathematical and nonmathematical problems
demonstrating knowledge of the connections among mathematical concepts and procedures and the relationships between mathematics and other fields (e.g., finance, population dynamics, optimal planning)
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 mathematical problems
demonstrating knowledge of the history of mathematics and the interactions between various cultures and mathematics
demonstrating knowledge of methods for integrating technological and nontechnological tools in mathematics
applying mathematical language to solve problems and communicate understanding