How do you describe the categories for the Math Screener assessment?

Math	A broad array of mathematical concepts and skills across various domains, tailored to grade levels from kindergarten through high school. This includes foundational number concepts, operations, and algebraic thinking for younger students, progressing to more advanced topics such as statistics, probability, and calculus for older students. The focus is on critical thinking and analytical skills through engaging with complex mathematical situations.
Number and Operations in Base Ten	Understanding the decimal numeral system, which is a way of representing numbers using ten digits (0-9) and employing place value to determine the value of each digit in a number. This system is fundamental to various mathematical operations, including addition, subtraction, multiplication, and division. Mastery of base ten concepts allows students to comprehend larger numbers, perform efficient calculations, and understand the relationships between units such as ones, tens, hundreds, and beyond. The base ten system also forms the foundation for understanding decimals and the metric system.
Counting and Cardinality	Focuses on Kindergarten and is essential for developing number sense. It includes learning to count in sequence, understanding the relationship between numbers and quantities, and comparing numbers to identify if one is greater than, less than, or equal to another. These standards aim to establish a foundation for young learners to understand "how many" through counting and to prepare them for more complex mathematical concepts in subsequent grades.
Data Analysis	Involves the collection, analysis, and interpretation of information including how to gather data through observation or experiments, organize it in meaningful ways using charts, graphs, and tables, and analyze it to draw conclusions. Key concepts include understanding different types of data (categorical and numerical), using measures of central tendency and variability, and applying probability to make predictions based on data.
Expressions and Equations	Primarily focused in middle and high school levels and deals with the understanding and solving of various types of equations and inequalities. This includes simple one-step equations in the earlier grades, advancing to multi-step equations, systems of equations, and quadratic equations in later grades. The domain emphasizes both the procedural fluency in algebraic manipulations and the conceptual understanding necessary to solve equations and inequalities, interpret their solutions, and apply them to real-world problems.
Number and Operations—Fractions	Involves understanding how to represent, interpret, and operate with parts of a whole. It includes recognizing and generating equivalent fractions, comparing and ordering fractions, and performing arithmetic operations such as addition, subtraction, multiplication, and division with fractions. This domain also extends to the understanding of mixed numbers and complex fractions and their applications in various contexts like measurement, geometry, and data.
Functions	Primarily targets middle and high school students, focusing on the concept of functions as a fundamental building block for higher mathematics and includes the definition, evaluation, and comparison of functions, and progresses to more complex topics such as linear, quadratic, polynomial, exponential, and trigonometric functions. Also included is the interpreting of functions represented in different forms — graphs, tables, and equations — and understanding the concept of a function as a rule that assigns exactly one output for each input. The domain also covers the analysis of functional relationships to solve real-world modeling problems and emphasizes the use of appropriate tools, such as graphing calculators and software, to visualize and analyze these relationships.
Geometry	Covers a progression from elementary shapes and properties to advanced concepts like congruence, similarity, and geometric proofs in later grades. Also includes understanding two-dimensional and three-dimensional spaces, using tools and technology to enhance understanding and solve real-world problems. The emphasis is on reasoning, constructing, and applying geometric principles to diverse scenarios.
The Number System	Encompasses a comprehensive understanding of different types of numbers, including whole numbers, integers, fractions, and decimals. It focuses on the properties and operations of these numbers, emphasizing their interactions through arithmetic operations and the relationships between them. This domain extends to include concepts such as divisibility, factors, multiples, and the rules for operations with negative numbers.
Measurement and Data	Encompasses the methods and processes used to assign numerical values to physical quantities such as length, area, volume, and weight. It involves understanding and using units of measurement, converting between different measurement systems (like metric and imperial), and applying these measures to calculate other properties, such as perimeter, surface area, and density.
Operations and Algebraic Thinking	Focuses on understanding and applying arithmetic operations within algebraic contexts. It begins with basic arithmetic strategies and progresses towards the exploration of algebraic expressions, equations, and functions. Key concepts include the use of variables, understanding the properties of operations to manipulate expressions, solving equations, and analyzing patterns and relationships.
Ratios and Proportional Relationships	Involves understanding and working with ratios, rates, and proportions. This includes identifying and using ratios to describe quantitative relationships, solving problems involving proportional relationships, and understanding unit rates in various contexts such as speed, density, or cost per item. This domain also covers the concepts of scaling and resizing, which are essential for interpreting maps, creating models, and converting measurements.
Statistics and Probability	Focuses on the ability to collect, organize, analyze, interpret, and present data. It encompasses various topics such as data representation (including tables, graphs, and charts), measures of central tendency (mean, median, mode), measures of variability (range, interquartile range), probability, and statistical inference. Students must critically evaluate data and make informed decisions based on statistical analysis.