| Standards Summary |
The standards describe a connected body of mathematical understandings and competencies and are a comprehensive foundation that all students should learn. They describe the mathematical understanding, knowledge, and skills that students should acquire from Kindergarten through high school.
Kindergarten through Grade 8 Standards
Number Sense
Number sense allows students to combine or decompose numbers naturally and solve problems using knowledge of the base-ten system and the relationships among operations.
Computation
Students should become fluent at performing computations in different ways, including mental calculations, estimation, and paper-and-pencil calculations using mathematically sound algorithms.
Algebra and Functions
Algebra involves the understanding of patterns, relations, and functions, as well as the representation and analysis of mathematical situations and structures using algebraic symbols.
Geometry
Geometry involves relationships among shapes and their properties and offers ways to interpret our physical environment. Geometry allows the development of students’ reasoning skills.
Measurement
Students should understand measurable attributes of objects and the units, systems, and processes of measurement, as well as be able to apply appropriate techniques and formulas to determine measurements.
Data Analysis and Probability
Through the collection and analysis of data, students can learn to make sense of and interpret information. This will enable them to make and critically examine statistical arguments.
Problem Solving
Problem solving means engaging in a task for which the solution process is not known in advance. Good problem solvers develop a range of strategies for finding solutions to problems and learn to monitor and adjust the strategies they choose in the process of solving a problem.
High School Standards
Mathematical Reasoning and Problem Solving
Students need a strong set of problem solving skills in order to increase their understanding of mathematics. By proving mathematical laws, using counterexamples, and learning about inductive and deductive reasoning, students can increase their problem solving abilities.
Equations and Inequalities
This knowledge area teaches students to graph and solve equations and inequalities in order to solve word problems. They learn to solve systems of equations and inequalities to model data and make predictions. Students derive the quadratic formula and use it and other methods to solve equations. They learn how to deal with radical expressions and complex numbers that appear in equations as well as how to graph quadratic functions.
Relations and Functions
By learning to draw and interpret relations, as well as polynomial, rational, algebraic, and absolute value functions, students learn to simplify and manipulate functions. They are able to explain important functional concepts such as domain, range, intercept, and pole. They gain an understanding of the relationships between the solutions of an equation, the zeros of a function, the x-intercepts of a graph, and the factors of a polynomial.
Logarithmic and Exponential Functions
Students use logarithmic and exponential functions to solve problems involving rate of decay and population change. They also learn how to convert logarithms between bases and to find inverse relationships between exponents and logarithms.
Sequences and Series
Arithmetic and geometric sequences are used to solve word problems and to determine if sequences converge or diverge.
Geometry
Using their knowledge of shapes and the coordinate system, students learn to construct proofs to prove mathematical theorems. Students determine the measure of sides and angles using proofs to justify their methods.
Trigonometry
Central to this knowledge area is an understanding of trigonometric functions and their relationship to right triangles. Students use the trigonometric functions and their identities to solve advanced word problems.
Calculus
Students learn differential and integral calculus and their applications to real-world situations. These skills can be used to solve rate of change and area problems as well as word problems in biology, physics, and economics.
Probability and Statistics
Through experiences with the collection and analysis of data, students can learn to interpret information and determine probabilities that will enable them to make and critically examine statistical arguments.
Discrete Mathematics
Students apply discrete mathematics to word problems in order to determine outcomes and probabilities. Students learn how matrices can be used to solve systems of equations and how graph theory can be used to model problem situations. |
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