College and Career Readiness Standards: High school
Skills available for Texas high school math standards
Section
Print skill plan
I
Numeric Reasoning
I.A Number representations and operations
I.A.1 Compare relative magnitudes of rational and irrational numbers, and understand that numbers can be represented in different ways.
Identify rational and irrational numbers
Compare rational and irrational numbers
I.A.1 Compare relative magnitudes of rational and irrational numbers, and understand that numbers can be represented in different ways.
Identify rational and irrational numbers
Compare rational and irrational numbers
I.A.2 Perform computations with rational and irrational numbers.
I.A.2 Perform computations with rational and irrational numbers.
I.B Number sense and number concepts
I.B.1 Use estimation to check for errors and reasonableness of solutions.
I.B.1 Use estimation to check for errors and reasonableness of solutions.
I.B.2 Interpret the relationships between the different representations of numbers.
Number classification
Decimals, fractions, and percents
Exponents
Radical expressions
I.B.2 Interpret the relationships between the different representations of numbers.
Number classification
Decimals, fractions, and percents
Exponents
Radical expressions
I.C Systems of measurement
I.C.1 Select or use the appropriate type of method, unit, and tool for the attribute being measured.
I.C.1 Select or use the appropriate type of method, unit, and tool for the attribute being measured.
I.C.2 Convert units within and between systems of measurement.
I.C.2 Convert units within and between systems of measurement.
II
Algebraic Reasoning
II.A Identifying expressions and equations
II.A.1 Explain the difference between expressions and equations.
II.A.1 Explain the difference between expressions and equations.
II.B Manipulating expressions
II.B.1 Recognize and use algebraic properties, concepts, and algorithms to combine, transform, and evaluate expressions (e.g., polynomials, radicals, rational expressions).
Powers of monomials
Add and subtract polynomials
Multiply polynomials
Algebraic properties
Quadratic expressions
Rational expressions
Radical expressions
II.B.1 Recognize and use algebraic properties, concepts, and algorithms to combine, transform, and evaluate expressions (e.g., polynomials, radicals, rational expressions).
Powers of monomials
Add and subtract polynomials
Multiply polynomials
Algebraic properties
Quadratic expressions
Rational expressions
Radical expressions
II.C Solving equations, inequalities, and systems of equations and inequalities
II.C.1 Describe and interpret solution sets of equalities and inequalities.
Equations
Systems of equations
Inequalities
II.C.1 Describe and interpret solution sets of equalities and inequalities.
Equations
Systems of equations
Inequalities
II.C.2 Explain the difference between the solution set of an equation and the solution set of an inequality.
II.C.2 Explain the difference between the solution set of an equation and the solution set of an inequality.
II.C.3 Recognize and use algebraic properties, concepts, and algorithms to solve equations, inequalities, and systems of linear equations and inequalities.
Solve equations
Applications
Linear inequalities
Systems of equations
Systems of inequalities
II.C.3 Recognize and use algebraic properties, concepts, and algorithms to solve equations, inequalities, and systems of linear equations and inequalities.
Solve equations
Applications
Linear inequalities
Systems of equations
Systems of inequalities
II.D Representing relationships
II.D.1 Interpret multiple representations of equations, inequalities, and relationships.
Sequences
Linear functions
Model equations
II.D.1 Interpret multiple representations of equations, inequalities, and relationships.
Sequences
Linear functions
Model equations
II.D.2 Convert among multiple representations of equations, inequalities, and relationships.
Relations
Rate of change
Tables, graphs, and equations
Inequalities
II.D.2 Convert among multiple representations of equations, inequalities, and relationships.
Relations
Rate of change
Tables, graphs, and equations
Inequalities
III
Geometric and Spatial Reasoning
III.A Figures and their properties
III.A.1 Recognize characteristics and dimensional changes of two- and three-dimensional figures.
Perimeter and area
Three-dimensional figures
Surface area and volume
Perimeter, area, and volume
III.A.1 Recognize characteristics and dimensional changes of two- and three-dimensional figures.
Perimeter and area
Three-dimensional figures
Surface area and volume
Perimeter, area, and volume
III.A.2 Form and validate conjectures about one-, two-, and three-dimensional figures and their properties.
Constructions with lines
Constructions with angles
Constructions with polygons
Line and angle bisectors
Angle relationships
Triangles
Triangle congruence
Congruent shapes
Quadrilaterals
Circles
III.A.2 Form and validate conjectures about one-, two-, and three-dimensional figures and their properties.
Constructions with lines
Constructions with angles
Constructions with polygons
Line and angle bisectors
Angle relationships
Triangles
Triangle congruence
Congruent shapes
Quadrilaterals
Circles
III.A.3 Recognize and apply right triangle relationships including basic trigonometry.
Pythagorean Theorem
Trigonometric ratios
III.A.3 Recognize and apply right triangle relationships including basic trigonometry.
Pythagorean Theorem
Trigonometric ratios
III.B Transformations and symmetry
III.B.1 Identify transformations and symmetries of figures.
Translations
Reflections
Rotations
Mixed transformations
Symmetry
III.B.1 Identify transformations and symmetries of figures.
Translations
Reflections
Rotations
Mixed transformations
Symmetry
III.B.2 Use transformations to investigate congruence, similarity, and symmetries of figures.
Transformations
Similar figures
Proofs
III.B.2 Use transformations to investigate congruence, similarity, and symmetries of figures.
Transformations
Similar figures
Proofs
III.C Connections between geometry and other mathematical content strands
III.C.1 Make connections between geometry and algebraic equations.
Slope
Linear equations
Linear systems
Parallel and perpendicular lines
Circles
Triangles and quadrilaterals
III.C.1 Make connections between geometry and algebraic equations.
Slope
Linear equations
Linear systems
Parallel and perpendicular lines
Circles
Triangles and quadrilaterals
III.C.2 Make connections between geometry, statistics, and probability.
III.C.2 Make connections between geometry, statistics, and probability.
III.D Measurements involving geometry and algebra
III.D.1 Find the perimeter and area of two-dimensional figures.
III.D.1 Find the perimeter and area of two-dimensional figures.
III.D.2 Determine the surface area and volume of three-dimensional figures.
Surface area and volume
Surface area
Volume
III.D.2 Determine the surface area and volume of three-dimensional figures.
Surface area and volume
Surface area
Volume
III.D.3 Determine indirect measurements of geometric figures using a variety of methods.
III.D.3 Determine indirect measurements of geometric figures using a variety of methods.
IV
Probabilistic Reasoning
IV.A Counting principles
IV.A.1 Determine the nature and the number of elements in a finite sample space.
IV.A.1 Determine the nature and the number of elements in a finite sample space.
IV.B Computation and interpretation of probabilities
IV.B.1 Compute and interpret the probability of an event and its complement.
IV.B.1 Compute and interpret the probability of an event and its complement.
IV.B.2 Compute and interpret the probability of compound events.
Independent and dependent events
Probability
IV.B.2 Compute and interpret the probability of compound events.
Independent and dependent events
Probability
IV.C Measurement involving probability
IV.C.1 Use probability to make informed decisions.
IV.C.1 Use probability to make informed decisions.
V
Statistical Reasoning
V.A Design a study
V.A.1 Formulate a statistical question, plan an investigation, and collect data.
V.A.1 Formulate a statistical question, plan an investigation, and collect data.
V.B Describe data
V.B.1 Classify types of data.
V.B.1 Classify types of data.
V.B.2 Construct appropriate visual representations of data.
V.B.2 Construct appropriate visual representations of data.
V.B.3 Compute and describe the study data with measures of center and basic notions of spread.
Measures of center
Measures of spread
Outliers
V.B.3 Compute and describe the study data with measures of center and basic notions of spread.
Measures of center
Measures of spread
Outliers
V.B.4 Describe patterns and departure from patterns in the study data.
V.B.4 Describe patterns and departure from patterns in the study data.
V.C Analyze, interpret, and draw conclusions from data
V.C.1 Analyze data sets using graphs and summary statistics.
V.C.1 Analyze data sets using graphs and summary statistics.
V.C.2 Analyze relationships between paired data using spreadsheets, graphing calculators, or statistical software.
V.C.2 Analyze relationships between paired data using spreadsheets, graphing calculators, or statistical software.
V.C.3 Make predictions using summary statistics.
Correlation coefficients
Best fit
Regression lines
V.C.3 Make predictions using summary statistics.
Correlation coefficients
Best fit
Regression lines
V.C.4 Identify and explain misleading uses of data.
V.C.4 Identify and explain misleading uses of data.
VI
Functions
VI.A Recognition and representation of functions
VI.A.1 Recognize if a relation is a function.
VI.A.1 Recognize if a relation is a function.
VI.A.2 Recognize and distinguish between different types of functions.
Linear functions
Quadratic functions
Exponential functions
Linear, quadratic, and exponential functions
VI.A.2 Recognize and distinguish between different types of functions.
Linear functions
Quadratic functions
Exponential functions
Linear, quadratic, and exponential functions
VI.B Analysis of functions
VI.B.1 Understand and analyze features of functions.
Domain and range
Function values
VI.B.1 Understand and analyze features of functions.
Domain and range
Function values
VI.B.2 Algebraically construct and analyze new functions.
Evaluate functions
Operations of functions
Inverse functions
Compositions of functions
VI.B.2 Algebraically construct and analyze new functions.
Evaluate functions
Operations of functions
Inverse functions
Compositions of functions
VI.C Model real-world situations with functions
VI.C.1 Apply known functions to model real-world situations.
VI.C.1 Apply known functions to model real-world situations.
VI.C.2 Develop a function to model a situation.
VI.C.2 Develop a function to model a situation.
VII
Problem Solving and Reasoning
VII.A Mathematical problem solving
VII.A.1 Analyze given information.
VII.A.1 Analyze given information.
VII.A.2 Formulate a plan or strategy.
VII.A.2 Formulate a plan or strategy.
VII.A.3 Determine a solution.
VII.A.3 Determine a solution.
VII.A.4 Justify the solution.
VII.A.4 Justify the solution.
VII.A.5 Evaluate the problem-solving process.
VII.A.5 Evaluate the problem-solving process.
VII.B Proportional reasoning
VII.B.1 Use proportional reasoning to solve problems that require fractions, ratios, percentages, decimals, and proportions in a variety of contexts using multiple representations.
Equivalent ratios
Proportions
Percents
Direct variation
VII.B.1 Use proportional reasoning to solve problems that require fractions, ratios, percentages, decimals, and proportions in a variety of contexts using multiple representations.
Equivalent ratios
Proportions
Percents
Direct variation
VII.C Logical reasoning
VII.C.1 Develop and evaluate convincing arguments.
Logical statements
Truth tables and truth values
VII.C.1 Develop and evaluate convincing arguments.
Logical statements
Truth tables and truth values
VII.C.2 Understand attributes and relationships with inductive and deductive reasoning.
VII.C.2 Understand attributes and relationships with inductive and deductive reasoning.
VII.D Real-world problem solving
VII.D.1 Interpret results of the mathematical problem in terms of the original real-world situation.
VII.D.1 Interpret results of the mathematical problem in terms of the original real-world situation.
VII.D.2 Evaluate the problem-solving process.
VII.D.2 Evaluate the problem-solving process.
VIII
Communication and Representation
VIII.A Language, terms, and symbols of mathematics
VIII.A.1 Use mathematical symbols, terminology, and notation to represent given and unknown information in a problem.
Variables
Applications
VIII.A.1 Use mathematical symbols, terminology, and notation to represent given and unknown information in a problem.
Variables
Applications
VIII.A.2 Use mathematical language to represent and communicate the mathematical concepts in a problem.
Independent and dependent variables
Number of solutions
Functions
Transformations
Probability
VIII.A.2 Use mathematical language to represent and communicate the mathematical concepts in a problem.
Independent and dependent variables
Number of solutions
Functions
Transformations
Probability
VIII.A.3 Use mathematical language for reasoning, problem solving, making connections, and generalizing.
VIII.A.3 Use mathematical language for reasoning, problem solving, making connections, and generalizing.
VIII.B Interpretation of mathematical work
VIII.B.1 Model and interpret mathematical ideas and concepts using multiple representations.
VIII.B.1 Model and interpret mathematical ideas and concepts using multiple representations.
VIII.B.2 Summarize and interpret mathematical information provided orally, visually, or in written form within the given context.
VIII.B.2 Summarize and interpret mathematical information provided orally, visually, or in written form within the given context.
VIII.C Presentation and representation of mathematical work
VIII.C.1 Communicate mathematical ideas, reasoning, and their implications using symbols, diagrams, models, graphs, and words.
VIII.C.1 Communicate mathematical ideas, reasoning, and their implications using symbols, diagrams, models, graphs, and words.
VIII.C.2 Create and use representations to organize, record, and communicate mathematical ideas.
VIII.C.2 Create and use representations to organize, record, and communicate mathematical ideas.
VIII.C.3 Explain, display, or justify mathematical ideas and arguments using precise mathematical language in written or oral communications.
Angles
Parallel lines
Congruence
Triangles
Quadrilaterals
Similarity
Pythagorean Theorem
VIII.C.3 Explain, display, or justify mathematical ideas and arguments using precise mathematical language in written or oral communications.
Angles
Parallel lines
Congruence
Triangles
Quadrilaterals
Similarity
Pythagorean Theorem
IX
Connections
IX.A Connections among the strands of mathematics
IX.A.1 Connect and use multiple key concepts of mathematics in situations and problems.
IX.A.1 Connect and use multiple key concepts of mathematics in situations and problems.
IX.A.2 Connect mathematics to the study of other disciplines.
IX.A.2 Connect mathematics to the study of other disciplines.
IX.B Connections of mathematics to nature, real-world situations, and everyday life
IX.B.1 Use multiple representations to demonstrate links between mathematical and real-world situations.
IX.B.1 Use multiple representations to demonstrate links between mathematical and real-world situations.
IX.B.2 Understand and use appropriate mathematical models in the natural, physical, and social sciences.
IX.B.2 Understand and use appropriate mathematical models in the natural, physical, and social sciences.
IX.B.3 Know and understand the use of mathematics in a variety of careers and professions.
IX.B.3 Know and understand the use of mathematics in a variety of careers and professions.