California Content Standards
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CA.AI.Algebra I
Algebra I
A-APR. Algebra: Arithmetic with Polynomials and Rational Expressions
Perform arithmetic operations on polynomials. [Linear and quadratic]
A-APR.1. Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials.
Quiz, Flash Cards, Worksheet, Game & Study Guide Polynomials and Exponents
A-CED. Algebra: Creating Equations
Create equations that describe numbers or relationships. [Linear, quadratic, and exponential (integer inputs only); for A.CED.3 linear only]
A-CED.1. Create equations and inequalities in one variable including ones with absolute value and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. CA
Quiz, Flash Cards, Worksheet, Game & Study Guide Equations and inequalities
A-CED.2. Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.
Quiz, Flash Cards, Worksheet, Game & Study Guide Linear equations
Quiz, Flash Cards, Worksheet, Game & Study Guide Solving linear equations
A-CED.3. Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context. For example, represent inequalities describing nutritional and cost constra
Quiz, Flash Cards, Worksheet, Game & Study Guide Equations and inequalities
Quiz, Flash Cards, Worksheet, Game & Study Guide Solving linear equations
A-CED.4. Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. For example, rearrange Ohm’s law V = IR to highlight resistance R.
Quiz, Flash Cards, Worksheet, Game & Study Guide Solving equations and inequalities
A-REI. Algebra: Reasoning with Equations and Inequalities
Solve systems of equations. [Linear-linear and linear-quadratic]
A-REI.5. Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions.
Flip Charts Introduction to Functions
Flip Charts Math Grade 8
Flip Charts Systems of Equations
Flip Charts Systems of Equations
A-REI.6. Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.
Flip Charts Introduction to Functions
Flip Charts Math Grade 8
Flip Charts Systems of Equations
Flip Charts Systems of Equations
Understand solving equations as a process of reasoning and explain the reasoning. [Master linear; learn as general principle.]
A-REI.1. Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method.
Flip Charts Math Grade 8
Flip Charts Ratios, Rates & Proportions
Quiz, Flash Cards, Worksheet, Game & Study Guide Equations and inequalities
Quiz, Flash Cards, Worksheet, Game & Study Guide Integer operations
Quiz, Flash Cards, Worksheet, Game & Study Guide Rational numbers and operations
Quiz, Flash Cards, Worksheet, Game & Study Guide Solving equations and inequalities
Quiz, Flash Cards, Worksheet, Game & Study Guide Solving linear equations
Represent and solve equations and inequalities graphically. [Linear and exponential; learn as general principle.]
A-REI.11. Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of va
Flip Charts Introduction to Functions
Flip Charts Math Grade 8
Flip Charts Systems of Equations
Flip Charts Systems of Equations
A-REI.12. Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the correspondin
Quiz, Flash Cards, Worksheet, Game & Study Guide Linear relationships
Solve equations and inequalities in one variable. [Linear inequalities; literal equations that are linear in the variables being solved for; quadratics with real solutions]
A-REI.3. Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.
Flip Charts Math Grade 8
Flip Charts Ratios, Rates & Proportions
Quiz, Flash Cards, Worksheet, Game & Study Guide Equations and inequalities
Quiz, Flash Cards, Worksheet, Game & Study Guide Integer operations
Quiz, Flash Cards, Worksheet, Game & Study Guide Rational numbers and operations
Quiz, Flash Cards, Worksheet, Game & Study Guide Solving equations and inequalities
Quiz, Flash Cards, Worksheet, Game & Study Guide Solving linear equations
A-SSE. Algebra: Seeing Structure in Expressions
Write expressions in equivalent forms to solve problems. [Quadratic and exponential]
A-SSE.3. Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.
A-SSE.3.c. Use the properties of exponents to transform expressions for exponential functions. For example, the expression 1.15^t can be rewritten as (1.15^(1/12))^12t ≈ 1.012^12t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%.
Quiz, Flash Cards, Worksheet, Game & Study Guide Functions
F-BF. Functions: Building Functions
Build a function that models a relationship between two quantities. [For F.BF.1, 2, linear, exponential, and quadratic]
F-BF.1. Write a function that describes a relationship between two quantities.
F-BF.1.a. Determine an explicit expression, a recursive process, or steps for calculation from a context.
Quiz, Flash Cards, Worksheet, Game & Study Guide Solving linear equations
F-IF. Functions: Interpreting Functions
Analyze functions using different representations. [Linear, exponential, quadratic, absolute value, step, piecewise-defined]
F-IF.7. Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.
F-IF.7.a. Graph linear and quadratic functions and show intercepts, maxima, and minima.
Quiz, Flash Cards, Worksheet, Game & Study Guide Linear equations
F-IF.8. Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.
F-IF.8.b. Use the properties of exponents to interpret expressions for exponential functions. For example, identify percent rate of change in functions such as y = (1.02)^t, y = (0.97)^t, y = (1.01)^(12t), and y = (1.2)^(t/10), and classify them as representing exp
Quiz, Flash Cards, Worksheet, Game & Study Guide Functions
Understand the concept of a function and use function notation. [Learn as general principle; focus on linear and exponential and on arithmetic and geometric sequences.]
F-IF.1. Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f c
Quiz, Flash Cards, Worksheet, Game & Study Guide Functions
F-IF.3. Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. For example, the Fibonacci sequence is defined recursively by f(0) = f(1) = 1, f(n + 1) = f(n) + f(n − 1) for n ≥ 1.
Flip Charts Arithmetic & Sequences
Flip Charts Math Grade 8
Quiz, Flash Cards, Worksheet, Game & Study Guide Sequences
Interpret functions that arise in applications in terms of the context. [Linear, exponential, and quadratic]
F-IF.4. For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercep
Quiz, Flash Cards, Worksheet, Game & Study Guide Linear equations
F-IF.6. Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.
Quiz, Flash Cards, Worksheet, Game & Study Guide Linear equations
F-LE. Functions: Linear, Quadratic, and Exponential Models
Construct and compare linear, quadratic, and exponential models and solve problems.
F-LE.1. Distinguish between situations that can be modeled with linear functions and with exponential functions.
F-LE.1.a. Prove that linear functions grow by equal differences over equal intervals, and that exponential functions grow by equal factors over equal intervals.
Quiz, Flash Cards, Worksheet, Game & Study Guide Functions
Quiz, Flash Cards, Worksheet, Game & Study Guide Linear equations
N-RN. Number and Quantity: The Real Number System
Extend the properties of exponents to rational exponents.
N-RN.2. Rewrite expressions involving radicals and rational exponents using the properties of exponents.
Quiz, Flash Cards, Worksheet, Game & Study Guide Polynomials and Exponents
Use properties of rational and irrational numbers.
N-RN.3. Explain why the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational.
Flip Charts Math Grade 8
Flip Charts The Real Numbers
S-ID. Statistics and Probability: Interpreting Categorical and Quantitative Data
Summarize, represent, and interpret data on two categorical and quantitative variables. [Linear focus; discuss general principle.]
S-ID.5. Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal, and conditional relative frequencies). Recognize possible associations and trends in the data.
Quiz, Flash Cards, Worksheet, Game & Study Guide Using graphs to analyze data
S-ID.6. Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.
S-ID.6.b. Informally assess the fit of a function by plotting and analyzing residuals.
Flip Charts Math Grade 8
Flip Charts Organizing & Displaying Data
S-ID.6.c. Fit a linear function for a scatter plot that suggests a linear association.
Quiz, Flash Cards, Worksheet, Game & Study Guide Linear relationships
CA.AII.Algebra II
Algebra II
A-APR. Algebra: Arithmetic with Polynomials and Rational Expressions
Perform arithmetic operations on polynomials. [Beyond quadratic]
A-APR.1. Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials.
Quiz, Flash Cards, Worksheet, Game & Study Guide Polynomials and Exponents
A-CED. Algebra: Creating Equations
Create equations that describe numbers or relationships. [Equations using all available types of expressions, including simple root functions]
A-CED.1. Create equations and inequalities in one variable including ones with absolute value and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. CA
Quiz, Flash Cards, Worksheet, Game & Study Guide Equations and inequalities
A-CED.2. Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.
Quiz, Flash Cards, Worksheet, Game & Study Guide Linear equations
Quiz, Flash Cards, Worksheet, Game & Study Guide Solving linear equations
A-CED.3. Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context.
Quiz, Flash Cards, Worksheet, Game & Study Guide Equations and inequalities
Quiz, Flash Cards, Worksheet, Game & Study Guide Solving linear equations
A-CED.4. Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations.
Quiz, Flash Cards, Worksheet, Game & Study Guide Solving equations and inequalities
A-REI. Algebra: Reasoning with Equations and Inequalities
Represent and solve equations and inequalities graphically. [Combine polynomial, rational, radical, absolute value, and exponential functions.]
A-REI.11. Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of va
Flip Charts Introduction to Functions
Flip Charts Math Grade 8
Flip Charts Systems of Equations
Flip Charts Systems of Equations
F-IF. Functions: Interpreting Functions
Interpret functions that arise in applications in terms of the context. [Emphasize selection of appropriate models.]
F-IF.4. For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercep
Quiz, Flash Cards, Worksheet, Game & Study Guide Linear equations
F-IF.6. Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.
Quiz, Flash Cards, Worksheet, Game & Study Guide Linear equations
CA.CC.MP.Mathematical Practices
Mathematical Practices
MP.1. Make sense of problems and persevere in solving them.
Quiz, Flash Cards, Worksheet, Game & Study Guide Mathematical processes
MP.2. Reason abstractly and quantitatively.
Quiz, Flash Cards, Worksheet, Game & Study Guide Mathematical processes
CA.G.Geometry
Geometry
G-CO. Geometry: Congruence
Prove geometric theorems. [Focus on validity of underlying reasoning while using variety of ways of writing proofs.]
G-CO.9. Prove theorems about lines and angles. Theorems include: vertical angles are congruent; when a transversal crosses parallel lines, alternate interior angles are congruent and corresponding angles are congruent; points on a perpendicular bisector of a line
Flip Charts Math Grade 8
Flip Charts Plane Geometry
Experiment with transformations in the plane.
G-CO.1. Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc.
Flip Charts Math Grade 8
Flip Charts Perimeter & Area
Flip Charts Plane Geometry
Flip Charts Ratios, Rates & Proportions
Quiz, Flash Cards, Worksheet, Game & Study Guide Patterns in geometry
Quiz, Flash Cards, Worksheet, Game & Study Guide Perimeter and area
Quiz, Flash Cards, Worksheet, Game & Study Guide Plane figures
Quiz, Flash Cards, Worksheet, Game & Study Guide Similarity and scale
Quiz, Flash Cards, Worksheet, Game & Study Guide Three dimensional geometry/Measurement
G-CO.2. Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and an
Quiz, Flash Cards, Worksheet, Game & Study Guide Patterns in geometry
Quiz, Flash Cards, Worksheet, Game & Study Guide Similarity and scale
G-CO.3. Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself.
Quiz, Flash Cards, Worksheet, Game & Study Guide Patterns in geometry
G-CO.4. Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments.
Quiz, Flash Cards, Worksheet, Game & Study Guide Patterns in geometry
G-CO.5. Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, e.g., graph paper, tracing paper, or geometry software. Specify a sequence of transformations that will carry a given figure onto another.
Quiz, Flash Cards, Worksheet, Game & Study Guide Patterns in geometry
Understand congruence in terms of rigid motions. [Build on rigid motions as a familiar starting point for development of concept of geometric proof.]
G-CO.6. Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure; given two figures, use the definition of congruence in terms of rigid motions to decide if they are congruent.
Quiz, Flash Cards, Worksheet, Game & Study Guide Patterns in geometry
G-GMD. Geometry: Geometric Measurement and Dimension
Explain volume formulas and use them to solve problems.
G-GMD.1. Give an informal argument for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone. Use dissection arguments, Cavalieri’s principle, and informal limit arguments.
Flip Charts Math Grade 8
Flip Charts Perimeter & Area
Quiz, Flash Cards, Worksheet, Game & Study Guide Perimeter and area
G-GMD.3. Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.
Quiz, Flash Cards, Worksheet, Game & Study Guide Three dimensional geometry/Measurement
G-GPE. Geometry: Expressing Geometric Properties with Equations
Use coordinates to prove simple geometric theorems algebraically. [Include distance formula; relate to Pythagorean Theorem.]
G-GPE.5. Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point).
Quiz, Flash Cards, Worksheet, Game & Study Guide Plane figures
G-GPE.7. Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula.
Quiz, Flash Cards, Worksheet, Game & Study Guide Plane figures
G-SRT. Geometry: Similarity, Right Triangles, and Trigonometry
Understand similarity in terms of similarity transformations.
G-SRT.1. Verify experimentally the properties of dilations given by a center and a scale factor:
G-SRT.1.a. A dilation takes a line not passing through the center of the dilation to a parallel line, and leaves a line passing through the center unchanged.
Quiz, Flash Cards, Worksheet, Game & Study Guide Similarity and scale
G-SRT.1.b. The dilation of a line segment is longer or shorter in the ratio given by the scale factor.
Quiz, Flash Cards, Worksheet, Game & Study Guide Similarity and scale
G-SRT.2. Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles
Flip Charts Math Grade 8
Flip Charts Ratios, Rates & Proportions
Quiz, Flash Cards, Worksheet, Game & Study Guide Ratios, proportions and percents
Quiz, Flash Cards, Worksheet, Game & Study Guide Similarity and scale
Prove theorems involving similarity.
G-SRT.5. Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.
Flip Charts Math Grade 8
Flip Charts Ratios, Rates & Proportions
S-CP. Statistics and Probability: Conditional Probability and the Rules of Probability
Understand independence and conditional probability and use them to interpret data. [Link to data from simulations or experiments.]
S-CP.2. Understand that two events A and B are independent if the probability of A and B occurring together is the product of their probabilities, and use this characterization to determine if they are independent.
Quiz, Flash Cards, Worksheet, Game & Study Guide Theoretical probability and counting
CA.MI.Mathematics I
Mathematics I
A-CED. Algebra: Creating Equations
Create equations that describe numbers or relationships. [Linear and exponential (integer inputs only); for A.CED.3, linear only]
A-CED.1. Create equations and inequalities in one variable including ones with absolute value and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. CA
Quiz, Flash Cards, Worksheet, Game & Study Guide Equations and inequalities
A-CED.2. Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.
Quiz, Flash Cards, Worksheet, Game & Study Guide Linear equations
Quiz, Flash Cards, Worksheet, Game & Study Guide Solving linear equations
A-CED.3. Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context. For example, represent inequalities describing nutritional and cost constra
Quiz, Flash Cards, Worksheet, Game & Study Guide Equations and inequalities
Quiz, Flash Cards, Worksheet, Game & Study Guide Solving linear equations
A-CED.4. Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. For example, rearrange Ohm’s law V = IR to highlight resistance R.
Quiz, Flash Cards, Worksheet, Game & Study Guide Solving equations and inequalities
A-REI. Algebra: Reasoning with Equations and Inequalities
Solve systems of equations. [Linear systems]
A-REI.5. Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions.
Flip Charts Introduction to Functions
Flip Charts Math Grade 8
Flip Charts Systems of Equations
Flip Charts Systems of Equations
A-REI.6. Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.
Flip Charts Introduction to Functions
Flip Charts Math Grade 8
Flip Charts Systems of Equations
Flip Charts Systems of Equations
Understand solving equations as a process of reasoning and explain the reasoning. [Master linear; learn as general principle.]
A-REI.1. Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method.
Flip Charts Math Grade 8
Flip Charts Ratios, Rates & Proportions
Quiz, Flash Cards, Worksheet, Game & Study Guide Equations and inequalities
Quiz, Flash Cards, Worksheet, Game & Study Guide Integer operations
Quiz, Flash Cards, Worksheet, Game & Study Guide Rational numbers and operations
Quiz, Flash Cards, Worksheet, Game & Study Guide Solving equations and inequalities
Quiz, Flash Cards, Worksheet, Game & Study Guide Solving linear equations
Represent and solve equations and inequalities graphically. [Linear and exponential; learn as general principle.]
A-REI.11. Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of va
Flip Charts Introduction to Functions
Flip Charts Math Grade 8
Flip Charts Systems of Equations
Flip Charts Systems of Equations
A-REI.12. Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the correspondin
Quiz, Flash Cards, Worksheet, Game & Study Guide Linear relationships
Solve equations and inequalities in one variable.
A-REI.3. Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. [Linear inequalities; literal equations that are linear in the variables being solved for; exponential of a form, such as 2^x = 1/16.]
Flip Charts Math Grade 8
Flip Charts Ratios, Rates & Proportions
Quiz, Flash Cards, Worksheet, Game & Study Guide Equations and inequalities
Quiz, Flash Cards, Worksheet, Game & Study Guide Integer operations
Quiz, Flash Cards, Worksheet, Game & Study Guide Rational numbers and operations
Quiz, Flash Cards, Worksheet, Game & Study Guide Solving equations and inequalities
Quiz, Flash Cards, Worksheet, Game & Study Guide Solving linear equations
F-BF. Functions: Building Functions
Build a function that models a relationship between two quantities. [For F.BF.1, 2, linear and exponential (integer inputs)]
F-BF.1. Write a function that describes a relationship between two quantities.
F-BF.1.a. Determine an explicit expression, a recursive process, or steps for calculation from a context.
Quiz, Flash Cards, Worksheet, Game & Study Guide Solving linear equations
F-IF. Functions: Interpreting Functions
Analyze functions using different representations. [Linear and exponential]
F-IF.7. Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.
F-IF.7.a. Graph linear and quadratic functions and show intercepts, maxima, and minima.
Quiz, Flash Cards, Worksheet, Game & Study Guide Linear equations
Understand the concept of a function and use function notation. [Learn as general principle. Focus on linear and exponential (integer domains) and on arithmetic and geometric sequences.]
F-IF.1. Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f c
Quiz, Flash Cards, Worksheet, Game & Study Guide Functions
F-IF.3. Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. For example, the Fibonacci sequence is defined recursively by f(0) = f(1) = 1, f(n + 1) = f(n) + f(n − 1) for n ≥ 1.
Flip Charts Arithmetic & Sequences
Flip Charts Math Grade 8
Quiz, Flash Cards, Worksheet, Game & Study Guide Sequences
Interpret functions that arise in applications in terms of the context. [Linear and exponential (linear domain)]
F-IF.4. For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercep
Quiz, Flash Cards, Worksheet, Game & Study Guide Linear equations
F-IF.6. Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.
Quiz, Flash Cards, Worksheet, Game & Study Guide Linear equations
F-LE. Functions: Linear, Quadratic, and Exponential Models
Construct and compare linear, quadratic, and exponential models and solve problems. [Linear and exponential]
F-LE.1. Distinguish between situations that can be modeled with linear functions and with exponential functions.
F-LE.1.a. Prove that linear functions grow by equal differences over equal intervals, and that exponential functions grow by equal factors over equal intervals.
Quiz, Flash Cards, Worksheet, Game & Study Guide Functions
Quiz, Flash Cards, Worksheet, Game & Study Guide Linear equations
G-CO. Geometry: Congruence
Experiment with transformations in the plane.
G-CO.1. Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc.
Flip Charts Math Grade 8
Flip Charts Perimeter & Area
Flip Charts Plane Geometry
Flip Charts Ratios, Rates & Proportions
Quiz, Flash Cards, Worksheet, Game & Study Guide Patterns in geometry
Quiz, Flash Cards, Worksheet, Game & Study Guide Perimeter and area
Quiz, Flash Cards, Worksheet, Game & Study Guide Plane figures
Quiz, Flash Cards, Worksheet, Game & Study Guide Similarity and scale
Quiz, Flash Cards, Worksheet, Game & Study Guide Three dimensional geometry/Measurement
G-CO.2. Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and an
Quiz, Flash Cards, Worksheet, Game & Study Guide Patterns in geometry
Quiz, Flash Cards, Worksheet, Game & Study Guide Similarity and scale
G-CO.3. Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself.
Quiz, Flash Cards, Worksheet, Game & Study Guide Patterns in geometry
G-CO.4. Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments.
Quiz, Flash Cards, Worksheet, Game & Study Guide Patterns in geometry
G-CO.5. Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, e.g., graph paper, tracing paper, or geometry software. Specify a sequence of transformations that will carry a given figure onto another.
Quiz, Flash Cards, Worksheet, Game & Study Guide Patterns in geometry
Understand congruence in terms of rigid motions. [Build on rigid motions as a familiar starting point for development of concept of geometric proof.]
G-CO.6. Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure; given two figures, use the definition of congruence in terms of rigid motions to decide if they are congruent.
Quiz, Flash Cards, Worksheet, Game & Study Guide Patterns in geometry
G-GPE. Geometry: Expressing Geometric Properties with Equations
Use coordinates to prove simple geometric theorems algebraically. [Include distance formula; relate to Pythagorean Theorem.]
G-GPE.5. Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point).
Quiz, Flash Cards, Worksheet, Game & Study Guide Plane figures
G-GPE.7. Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula.
Quiz, Flash Cards, Worksheet, Game & Study Guide Plane figures
S-ID. Statistics and Probability: Interpreting Categorical and Quantitative Data
Summarize, represent, and interpret data on two categorical and quantitative variables. [Linear focus; discuss general principle.]
S-ID.5. Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal, and conditional relative frequencies). Recognize possible associations and trends in the data.
Quiz, Flash Cards, Worksheet, Game & Study Guide Using graphs to analyze data
S-ID.6. Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.
S-ID.6.b. Informally assess the fit of a function by plotting and analyzing residuals.
Flip Charts Math Grade 8
Flip Charts Organizing & Displaying Data
S-ID.6.c. Fit a linear function for a scatter plot that suggests a linear association.
Quiz, Flash Cards, Worksheet, Game & Study Guide Linear relationships
CA.MII.Mathematics II
Mathematics II
A-APR. Algebra: Arithmetic with Polynomials and Rational Expressions
Perform arithmetic operations on polynomials. [Polynomials that simplify to quadratics]
A-APR.1. Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials.
Quiz, Flash Cards, Worksheet, Game & Study Guide Polynomials and Exponents
A-CED. Algebra: Creating Equations
Create equations that describe numbers or relationships.
A-CED.1. Create equations and inequalities in one variable including ones with absolute value and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. CA
Quiz, Flash Cards, Worksheet, Game & Study Guide Equations and inequalities
A-CED.2. Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.
Quiz, Flash Cards, Worksheet, Game & Study Guide Linear equations
Quiz, Flash Cards, Worksheet, Game & Study Guide Solving linear equations
A-CED.4. Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. [Include formulas involving quadratic terms.]
Quiz, Flash Cards, Worksheet, Game & Study Guide Solving equations and inequalities
A-SSE. Algebra: Seeing Structure in Expressions
Write expressions in equivalent forms to solve problems. [Quadratic and exponential]
A-SSE.3. Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.
A-SSE.3.c. Use the properties of exponents to transform expressions for exponential functions. For example, the expression 1.15^t can be rewritten as (1.15^(1/12))^(12t) ≈ 1.012^(12t) to reveal the approximate equivalent monthly interest rate if the annual rate is 1
Quiz, Flash Cards, Worksheet, Game & Study Guide Functions
F-BF. Functions: Building Functions
Build a function that models a relationship between two quantities. [Quadratic and exponential]
F-BF.1. Write a function that describes a relationship between two quantities.
F-BF.1.a. Determine an explicit expression, a recursive process, or steps for calculation from a context.
Quiz, Flash Cards, Worksheet, Game & Study Guide Solving linear equations
F-IF. Functions: Interpreting Functions
Interpret functions that arise in applications in terms of the context. [Quadratic]
F-IF.4. For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercep
Quiz, Flash Cards, Worksheet, Game & Study Guide Linear equations
F-IF.6. Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.
Quiz, Flash Cards, Worksheet, Game & Study Guide Linear equations
Analyze functions using different representations. [Linear, exponential, quadratic, absolute value, step, piecewise-defined]
F-IF.7. Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.
F-IF.7.a. Graph linear and quadratic functions and show intercepts, maxima, and minima.
Quiz, Flash Cards, Worksheet, Game & Study Guide Linear equations
F-IF.8. Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.
F-IF.8.b. Use the properties of exponents to interpret expressions for exponential functions. For example, identify percent rate of change in functions such as y = (1.02)^t, y = (0.97)^t, y = (1.01)^(12t), and y = (1.2)^(t/10), and classify them as representing exp
Quiz, Flash Cards, Worksheet, Game & Study Guide Functions
G-CO. Geometry: Congruence
Prove geometric theorems. [Focus on validity of underlying reasoning while using variety of ways of writing proofs.]
G-CO.9. Prove theorems about lines and angles. Theorems include: vertical angles are congruent; when a transversal crosses parallel lines, alternate interior angles are congruent and corresponding angles are congruent; points on a perpendicular bisector of a line
Flip Charts Math Grade 8
Flip Charts Plane Geometry
G-GMD. Geometry: Geometric Measurement and Dimension
Explain volume formulas and use them to solve problems.
G-GMD.1. Give an informal argument for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone. Use dissection arguments, Cavalieri’s principle, and informal limit arguments.
Flip Charts Math Grade 8
Flip Charts Perimeter & Area
Quiz, Flash Cards, Worksheet, Game & Study Guide Perimeter and area
G-GMD.3. Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.
Quiz, Flash Cards, Worksheet, Game & Study Guide Three dimensional geometry/Measurement
G-SRT. Geometry: Similarity, Right Triangles, and Trigonometry
Understand similarity in terms of similarity transformations.
G-SRT.1. Verify experimentally the properties of dilations given by a center and a scale factor:
G-SRT.1.a. A dilation takes a line not passing through the center of the dilation to a parallel line, and leaves a line passing through the center unchanged.
Quiz, Flash Cards, Worksheet, Game & Study Guide Similarity and scale
G-SRT.1.b. The dilation of a line segment is longer or shorter in the ratio given by the scale factor.
Quiz, Flash Cards, Worksheet, Game & Study Guide Similarity and scale
G-SRT.2. Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles
Flip Charts Math Grade 8
Flip Charts Ratios, Rates & Proportions
Quiz, Flash Cards, Worksheet, Game & Study Guide Ratios, proportions and percents
Quiz, Flash Cards, Worksheet, Game & Study Guide Similarity and scale
Prove theorems involving similarity. [Focus on validity of underlying reasoning while using variety of formats.]
G-SRT.5. Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.
Flip Charts Math Grade 8
Flip Charts Ratios, Rates & Proportions
N-RN. Number and Quantity: The Real Number System
Extend the properties of exponents to rational exponents.
N-RN.2. Rewrite expressions involving radicals and rational exponents using the properties of exponents.
Quiz, Flash Cards, Worksheet, Game & Study Guide Polynomials and Exponents
Use properties of rational and irrational numbers.
N-RN.3. Explain why the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational.
Flip Charts Math Grade 8
Flip Charts The Real Numbers
S-CP. Statistics and Probability: Conditional Probability and the Rules of Probability
Understand independence and conditional probability and use them to interpret data. [Link to data from simulations or experiments.]
S-CP.2. Understand that two events A and B are independent if the probability of A and B occurring together is the product of their probabilities, and use this characterization to determine if they are independent.
Quiz, Flash Cards, Worksheet, Game & Study Guide Theoretical probability and counting
CA.MIII.Mathematics III
Mathematics III
A-APR. Algebra: Arithmetic with Polynomials and Rational Expressions
Perform arithmetic operations on polynomials. [Beyond quadratic]
A-APR.1. Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials.
Quiz, Flash Cards, Worksheet, Game & Study Guide Polynomials and Exponents
A-CED. Algebra: Creating Equations
Create equations that describe numbers or relationships. [Equations using all available types of expressions, including simple root functions]
A-CED.1. Create equations and inequalities in one variable including ones with absolute value and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. CA
Quiz, Flash Cards, Worksheet, Game & Study Guide Equations and inequalities
A-CED.2. Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.
Quiz, Flash Cards, Worksheet, Game & Study Guide Linear equations
Quiz, Flash Cards, Worksheet, Game & Study Guide Solving linear equations
A-CED.3. Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context. For example, represent inequalities describing nutritional and cost constra
Quiz, Flash Cards, Worksheet, Game & Study Guide Equations and inequalities
Quiz, Flash Cards, Worksheet, Game & Study Guide Solving linear equations
A-CED.4. Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations.
Quiz, Flash Cards, Worksheet, Game & Study Guide Solving equations and inequalities
A-REI. Algebra: Reasoning with Equations and Inequalities
Represent and solve equations and inequalities graphically. [Combine polynomial, rational, radical, absolute value, and exponential functions.]
A-REI.11. Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of va
Flip Charts Introduction to Functions
Flip Charts Math Grade 8
Flip Charts Systems of Equations
Flip Charts Systems of Equations
F-IF. Functions: Interpreting Functions
Interpret functions that arise in applications in terms of the context. [Include rational, square root and cube root; emphasize selection of appropriate models.]
F-IF.4. For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercep
Quiz, Flash Cards, Worksheet, Game & Study Guide Linear equations
F-IF.6. Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.
Quiz, Flash Cards, Worksheet, Game & Study Guide Linear equations
CA.PC.Precalculus
Precalculus
A-CED. Algebra: Creating Equations
Create equations that describe numbers or relationships.
A-CED.1. Create equations and inequalities in one variable including ones with absolute value and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. CA
Quiz, Flash Cards, Worksheet, Game & Study Guide Equations and inequalities
A-CED.2. Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.
Quiz, Flash Cards, Worksheet, Game & Study Guide Linear equations
Quiz, Flash Cards, Worksheet, Game & Study Guide Solving linear equations
A-CED.3. Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context. For example, represent inequalities describing nutritional and cost constra
Quiz, Flash Cards, Worksheet, Game & Study Guide Equations and inequalities
Quiz, Flash Cards, Worksheet, Game & Study Guide Solving linear equations
A-CED.4. Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. For example, rearrange Ohm’s law V = IR to highlight resistance R.
Quiz, Flash Cards, Worksheet, Game & Study Guide Solving equations and inequalities
F-IF. Functions: Interpreting Functions
Interpret functions that arise in applications in terms of the context.
F-IF.4. For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercep
Quiz, Flash Cards, Worksheet, Game & Study Guide Linear equations
CA.PS.Advanced Placement Probability and Statistics Standards
Advanced Placement Probability and Statistics Standards
PS.1.0. Students solve probability problems with finite sample spaces by using the rules for addition, multiplication, and complementation for probability distributions and understand the simplifications that arise with independent events.
Quiz, Flash Cards, Worksheet, Game & Study Guide Theoretical probability and counting
PS.12.0. Students find the line of best fit to a given distribution of data by using least squares regression.
Quiz, Flash Cards, Worksheet, Game & Study Guide Linear relationships
PS.15.0. Students are familiar with the notions of a statistic of a distribution of values, of the sampling distribution of a statistic, and of the variability of a statistic.
Quiz, Flash Cards, Worksheet, Game & Study Guide Collecting and describing data
PS.3.0. Students demonstrate an understanding of the notion of discrete random variables by using this concept to solve for the probabilities of outcomes, such as the probability of the occurrence of five or fewer heads in 14 coin tosses.
Quiz, Flash Cards, Worksheet, Game & Study Guide Theoretical probability and counting
PS.5.0. Students know the definition of the mean of a discrete random variable and can determine the mean for a particular discrete random variable.
Flip Charts Math Grade 8
Flip Charts Organizing & Displaying Data
Quiz, Flash Cards, Worksheet, Game & Study Guide Collecting and describing data
Quiz, Flash Cards, Worksheet, Game & Study Guide Using graphs to analyze data
PS.6.0. Students know the definition of the variance of a discrete random variable and can determine the variance for a particular discrete random variable.
Quiz, Flash Cards, Worksheet, Game & Study Guide Collecting and describing data
CA.SP.Statistics and Probability
Statistics and Probability
S-CP. Conditional Probability and the Rules of Probability
Understand independence and conditional probability and use them to interpret data.
S-CP.2. Understand that two events A and B are independent if the probability of A and B occurring together is the product of their probabilities, and use this characterization to determine if they are independent.
Quiz, Flash Cards, Worksheet, Game & Study Guide Theoretical probability and counting
S-CP.5. Recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations. For example, compare the chance of having lung cancer if you are a smoker with the chance of being a smoker if you have lung cance
Quiz, Flash Cards, Worksheet, Game & Study Guide Theoretical probability and counting
S-ID. Interpreting Categorical and Quantitative Data
Summarize, represent, and interpret data on two categorical and quantitative variables.
S-ID.5. Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal, and conditional relative frequencies). Recognize possible associations and trends in the data.
Quiz, Flash Cards, Worksheet, Game & Study Guide Using graphs to analyze data
S-ID.6. Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.
S-ID.6.b. Informally assess the fit of a function by plotting and analyzing residuals.
Flip Charts Math Grade 8
Flip Charts Organizing & Displaying Data
S-ID.6.c. Fit a linear function for a scatter plot that suggests a linear association.
Quiz, Flash Cards, Worksheet, Game & Study Guide Linear relationships
S-MD. Using Probability to Make Decisions
Calculate expected values and use them to solve problems.
S-MD.3. (+) Develop a probability distribution for a random variable defined for a sample space in which theoretical probabilities can be calculated; find the expected value. For example, find the theoretical probability distribution for the number of correct ans
Quiz, Flash Cards, Worksheet, Game & Study Guide Theoretical probability and counting
S-MD.4. (+) Develop a probability distribution for a random variable defined for a sample space in which probabilities are assigned empirically; find the expected value. For example, find a current data distribution on the number of TV sets per household in the U
Quiz, Flash Cards, Worksheet, Game & Study Guide Experimental Probability
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