Secondary Math Standards

6th Grade (Expressions & Equations)

*Apply and extend previous understandings of arithmetic to algebraic expressions. *Reason about and solve one-variable equations. *Reason about one variable inequalities. *Represent and analyze quantitative relationships between dependent and independent variables.

Math 4 (Number and Quantity)

*Apply properties and operations with complex numbers. *Apply properties and operations with matrices and vectors. (including scalar multiplication on vectors)

Precalculus (Number & Quantity)

*Apply properties of complex numbers and the complex number system. *Apply properties and operations with matrices. *Understand properties and operations with vectors. (sum and differences only)

Math 4 (Algebra & Functions)

*Apply properties of function composition to build new functions from existing functions. *Apply properties of trigonometry to solve problems. *Apply the properties and key features of logarithmic functions. *Understand the properties and key features of piecewise functions. *Understand how to model functions with regression.

Precalculus (Algebra)

*Apply properties of solving inequalities that include rational and polynomial expressions in one variable. *Apply properties of solving equations involving exponential, logarithmic, and trigonometric functions.

Math 4 (Statistics and Probability)

*Create statistical investigations to make sense of real-world phenomena. *Apply informal and formal statistical inference to make sense of, and make decisions in, meaningful real-world contexts. *Apply probability distributions in making decisions in uncertainty.

8th Grade (Functions)

*Define, evaluate, and compare functions. *Use functions to model relationships between quantities.

6th Grade (Statistics & Probability)

*Develop understanding of statistical variability. *Summarize and describe distributions

7th Grade (Geometry)

*Draw, construct, and describe geometrical figures and describe the relationships between them. *Solve real-world and mathematical problems involving angle measure, area, surface area, and volume.

8th Grade (Geometry)

*Understand congruence and similarity using physical models, transparencies, or geometry software. *Analyze angle relationships. *Understand and apply the Pythagorean Theorem. *Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres.

Precalculus (Functions)

*Understand key features of sine, cosine, tangent, cotangent, secant and cosecant functions. *Apply properties of a unit circle with center (0,0) to determine the values of sine, cosine, tangent, cotangent, secant, and cosecant. *Apply properties of trigonometry to solve problems involving all types of triangles. *Understand the relationship of algebraic and graphical representations of exponential, logarithmic, rational, power functions, and conic sections to their key features. *Apply properties of function composition to build new functions from existing functions. *Apply mathematical reasoning to build recursive functions and solve problems. *Apply mathematical reasoning to build parametric functions and solve problems.

7th Grade (Expressions & Equations)

*Use properties of operations to generate equivalent expressions. *Solve real-world and mathematical problems using numerical and algebraic expressions, equations, and inequalities.

7th Grade (Statistics & Probability)

*Use random sampling to draw inferences about a population. *Make informal inferences to compare two populations. *Investigate chance processes and develop, use, and evaluate probability models.

8th Grade (Expressions & Equations)

*Work with radicals and integer exponents. *Analyze and solve linear equations and inequalities. *Analyze and solve pairs of simultaneous linear equations.

(4) Model with mathematics.

-Apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. -Comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later. -Identify important quantities in a practical situation and map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts and formulas. -Analyze those relationships mathematically to draw conclusions. -Interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose.

(6) Attend to precision.

-Communicate precisely to others. -Use clear definitions in discussion with others and in their own reasoning. -State the meaning of the symbols they choose, including using the equal sign consistently and appropriately. -Careful about specifying units of measure, and labeling axes to clarify the correspondence with quantities in a problem. -Calculate accurately and efficiently, express numerical answers with a degree of precision appropriate for the problem context. -Give carefully formulated explanations to each other. -Examine claims and make explicit use of definitions.

(5) Use appropriate tools strategically.

-Consider the available tools when solving a mathematical problem. -Familiar with tools appropriate for their grade or course to make sound decisions about when each of these tools might be helpful, recognizing both the insight to be gained and their limitations. -Detect possible errors by strategically using estimation and other mathematical knowledge. -Know that technology can enable them to visualize the results of varying assumptions, explore consequences, and compare predictions with data. -Identify relevant external mathematical resources, such as digital content located on a website, and use them to pose or solve problems. -Use technological tools to explore and deepen their understanding of concepts. Tools include: pencil and paper, concrete models, a ruler, a protractor, a calculator, a spreadsheet, a computer algebra system, a statistical package, or dynamic geometry software.

(1) Make sense of problems and persevere in solving them.

-Explaining to themselves the meaning of a problem and looking for entry points to its solution. -Analyze givens, constraints, relationships, and goals. ---Make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. -Consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution. -Monitor and evaluate their progress and change course if necessary. Transform algebraic expressions or change the viewing window on their graphing calculator to get the information they need. -Explain correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for regularity or trends. -Use concrete objects or pictures to help conceptualize and solve a problem. -Check their answers to problems using a different method, and they continually ask themselves, "Does this make sense?" -Understand the approaches of others to solving complex problems and identify correspondences between different approaches.

(7) Look for and make use of structure.

-Look closely to discern a pattern or structure. -Recognize the significance of an existing line in a geometric figure and can use the strategy of drawing an auxiliary line for solving problems. -Step back for an overview and shift perspective. -See complicated things, such as some algebraic expressions, as single objects or as being composed of several objects.

(2) Reason abstractly and quantitatively.

-Make sense of quantities and their relationships in problem situations. -Decontextualize—to abstract a given situation and represent it symbolically and manipulate the representing symbols as if they have a life of their own, without necessarily attending to their referents. -Contextualize, to pause as needed during the manipulation process in order to probe into the referents for the symbols involved. -Quantitative reasoning ---creating a coherent representation of the problem at hand; considering the units involved; ---attending to the meaning of quantities, not just how to compute them; ---knowing and flexibly using different properties of operations and objects.

(8) Look for and express regularity in repeated reasoning.

-Notice if calculations are repeated, and look both for general methods and for shortcuts. -Maintain oversight of the process, while attending to the details. -Continually evaluate the reasonableness of their intermediate results.

(3) Construct viable arguments and critique the reasoning of others.

-Understand and use stated assumptions, definitions, and previously established results in constructing arguments. -Make conjectures and build a logical progression of statements to explore the truth of their conjectures. -Analyze situations by breaking them into cases, and can recognize and use counterexamples. -Justify their conclusions, communicate them to others, and respond to the arguments of others. -Reason inductively about data, making plausible arguments that take into account the context from which the data arose. -Compare the effectiveness of two plausible arguments, distinguish correct logic or reasoning from that which is flawed, and—if there is a flaw in an argument—explain what it is. -Determine domains to which an argument applies. -Listen or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments.

The high school conceptual category A stands for...

Algebra

7th Grade (Ratio and Proportional Relationships)

Analyze proportional relationships and use them to solve real-world and mathematical problems.

6th Grade (The Number System)

Apply and extend previous understandings of multiplication and division to divide fractions by fractions.

6th Grade (The Number System)

Apply and extend previous understandings of numbers to the system of rational numbers.

7th Grade (The Number System)

Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers.

The high school domain code APR stands for...

Arithmetic with Polynomials and Rational Expressions

The high school domain code BF stands for...

Building Functions

The high school domain code C stands for...

Circles

6th Grade (The Number System)

Compute fluently with multi-digit numbers and find common factors and multiples.

The high school domain code CP stands for...

Conditional Probability and the Rules of Probability

The high school domain code CO stands for...

Congruence

Math 2 (Geometry)

Congruence: *Experiment with transformations in the plane. *Understand congruence in terms of rigid motions. *Prove geometric theorems. Similarity, Right Triangles, and Trigonometry: *Understand similarity in terms of similarity transformations. *Prove theorems involving similarity. *Define trigonometric ratios and solve problems involving right triangles.

Math 3 (Geometry)

Congruence: Prove geometric theorems. Circles: Understand and apply theorems about circles.

The high school domain code CED stands for...

Creating Equations

The high school domain code PE stands for...

Expressing Geometric Properties with Equations

Math 1 (Geometry)

Expressing Geometric Properties with Equations: Use coordinates to prove simple geometric theorems algebraically.

The middle grades domain code EE stands for...

Expressions and Equations

The domain code F, in middle grades, stands for... The conceptual category F, in high school, stands for...

Functions

The high school domain code MGD stands for...

Geometric Measurement and Dimension

The domain code G, in middle grades, stands for... The conceptual category G, in high school, stands for...

Geometry

The high school domain code ID stands for...

Interpreting Categorical and Quantitative Data

Math 1 (Statistics & Probability)

Interpreting Categorical and Quantitative Data: *Summarize, represent, and interpret data on a single count or measurement variable. *Summarize, represent, and interpret data on two categorical and quantitative variables. *Interpret linear models.

The high school domain code IF stands for...

Interpreting Functions

Math 1 (Functions)

Interpreting Functions: *Understand the concept of a function and use function notation. *Interpret functions that arise in applications in terms of a context. *Analyze functions using different representations. Building Functions: Build a function that models a relationship between two quantities. Linear, Quadratics, and Exponential Models: *Construct and compare linear and exponential models to solve problems. *Interpret expressions for functions in terms of the situations they model.

Math 2 (Functions)

Interpreting Functions: *Understand the concept of a function and use function notation. *Interpret functions that arise in applications in terms of a context. *Analyze functions using different representations. Building Functions: *Build a function that models a relationship between two quantities. *Build new functions from existing functions.

Math 3 (Functions)

Interpreting Functions: *Understand the concept of a function and use function notation. *Interpret functions that arise in applications in terms of a context. *Analyze functions using different representations. Building Functions: *Build a function that models a relationship between two quantities. *Build new functions from existing functions. Linear, Quadratics, and Exponential Models: Construct and compare linear and exponential models to solve problems Trigonometric Functions: *Extend the domain of trigonometric functions using the unit circle. *Model periodic phenomena with trigonometric functions.

8th Grade (Statistics & Probability)

Investigate patterns of association in bivariate data.

8th Grade (The Number System)

Know that there are numbers that are not rational and approximate them by rational numbers.

The high school domain code LE stands for...

Linear, Quadratic, and Exponential Models

Math 3 (Statistics & Probability)

Making Inference and Justifying Conclusions: *Understand and evaluate random processes underlying statistical experiments. *Making inferences and justify conclusions from sample surveys, experiments and observational studies.

Math 2 (Statistics & Probability)

Making Inference and Justifying Conclusions: Understand and evaluate random processes underlying statistical experiments. Conditional probability and the rules for probability: *Understand independence and conditional probability and use them to interpret data. *Use the rules of probability to compute probabilities of compound events in a uniform probability model.

The high school domain code IC stands for...

Making Inferences and Justifying Conclusions

The high school domain code MG stands for...

Modeling with Geometry

The high school conceptual category NQ stands for...

Number and Quantity

The high school domain code Q stands for...

Quantities

The middle grades domain code RP stands for...

Ratios and Proportional Relationships

The high school domain code REI stands for...

Reasoning with Equations and Inequalities

The high school domain code SSE stands for...

Seeing Structure in Expressions

Math 3 (Algebra)

Seeing Structure in Expressions: *Interpret the structure of expressions. *Write expressions in equivalent form to solve problems. Perform Arithmetic Operations on Polynomials: *Understand the relationship between zeros and the factors of polynomials. *Rewrite rational expressions. Creating Equations: Create equations that describe numbers or relationships. Reasoning with Equations and Inequalities: *Understand solving equations as a process of reasoning and explain the reasoning. *Represent and solve equations and inequalities graphically.

Math 1 (Algebra)

Seeing Structure in Expressions: *Interpret the structure of expressions. *Write expressions in equivalent forms to solve problems Perform Arithmetic Operations on Polynomials: *Perform arithmetic operations on polynomials. *Understand the relationship between zeros and factors of polynomials. Creating Equations: Create equations that describe numbers or relationships. Reasoning with Equations and Inequalities: *Understand solving equations as a process of reasoning and explain the reasoning. *Solve equations and inequalities in one variable. *Solve systems of equations. *Represent and solve equations and inequalities graphically.

Math 2 (Algebra)

Seeing Structure in Expressions: Interpret the structure of expressions. Perform Arithmetic Operations on Polynomials: Perform arithmetic operations on polynomials. Creating Equations: Create equations that describe numbers or relationships. Reasoning with Equations and Inequalities: *Understand solving equations as a process of reasoning and explain the reasoning. *Solve equations and inequalities in one variable. *Solve systems of equations. *Represent and solve equations and inequalities graphically.

The high school domain code SRT stands for...

Similarity, Right Triangles, and Trigonometry

6th Grade (Geometry)

Solve real-world and mathematical problems involving area, surface area, and volume.

The domain code SP, in middle grades, stands for... The conceptual category SP, in high school, stands for...

Statistics and Probability

The high school domain code CN stands for...

The Complex Number System

Math 3 (Number)

The Complex Number System: Use complex numbers in polynomial identities and equations.

The middle grades domain code NS stands for...

The Number System

The high school domain code RN stands for...

The Real Number System

Math 2 (Number)

The Real Number System: *Extend the properties of exponents to rational exponents. *Use properties of rational and irrational numbers. The Complex Number System: Define complex numbers.

Math 1 (Number)

The Real Number System: *Extend the properties of exponents.

The high school domain code TF stands for...

Trigonometric Functions

6th Grade (Ratio and Proportional Relationships)

Understand ratio concepts and use ratio reasoning to solve problems.

The high school domain code MD stands for...

Using Probability to Make Decisions

The high school domain code VM stands for...

Vector and Matrix Quantities