Standards for Teaching and Learning
AI.N.3: Calculate and apply ratios, proportions, rates, and percentages to solve a range of consumer and practical problems.
Beam to Moon (Ratios and Proportions)
Estimating Population Size
Part:Part and Part:Whole Ratios
Percent of Change
Polling: Neighborhood
Simple and Compound Interest
AI.N.4: Use estimation to judge the reasonableness of results of computations and of solutions to problems involving real numbers, including approximate error in measurement and the approximate value of square roots. (Reminder: This is without the use of calculators.)
AI.P.1: Recognize, describe, and extend patterns governed by a linear, quadratic, or exponential functional relationship or by a simple iterative process (e.g., the Fibonacci sequence).
Arithmetic Sequences
Arithmetic and Geometric Sequences
Exponential Functions - Activity A
Finding Patterns
Geometric Sequences
Linear Functions
Quadratic and Absolute Value Functions
Quadratics in Factored Form
Quadratics in Polynomial Form - Activity A
Roots of a Quadratic
AI.P.3: Demonstrate an understanding of relations and functions. Identify the domain, range, and dependent and independent variables of functions.
Cosine Function
Functions Involving Square Roots
General Form of a Rational Function
Introduction to Functions
Logarithmic Functions - Activity A
Logarithmic Functions: Translating and Scaling
Radical Functions
Rational Functions
Sine Function
Tangent Function
AI.P.4: Translate between different representations of functions and relations: graphs, equations, sets of ordered pairs (scatter plots), verbal, and tabular.
Introduction to Functions
Linear Functions
Polynomials and Linear Factors
Scatter Plots - Activity A
Using Algebraic Equations
Using Algebraic Expressions
AI.P.5: Demonstrate an understanding of the relationship between various representations of a line. Determine a line’s slope and x- and y-intercepts from its graph or from a linear equation that represents the line.
Defining a Line with Two Points
Modeling Linear Systems - Activity A
Point-Slope Form of a Line - Activity A
Slope - Activity B
Slope-Intercept Form of a Line - Activity A
Solving Equations By Graphing Each Side
Standard Form of a Line
AI.P.6: Find a linear function describing a line from a graph or a geometric description of the line (e.g., by using the point-slope or slope y-intercept formulas). Explain the significance of a positive, negative, zero, or undefined slope.
Defining a Line with Two Points
Linear Functions
Modeling Linear Systems - Activity A
Point-Slope Form of a Line - Activity A
Slope - Activity B
Slope-Intercept Form of a Line - Activity A
Using Tables, Rules and Graphs
AI.P.7: Find linear functions that represent lines either perpendicular or parallel to a given line and through a point (e.g., by using the point-slope form of the equation).
Linear Functions
Point-Slope Form of a Line - Activity A
Slope-Intercept Form of a Line - Activity A
Using Tables, Rules and Graphs
AI.P.8: Add, subtract, and multiply polynomials with emphasis on 1st- and 2nd-degree polynomials.
Addition of Polynomials - Activity A
AI.P.9: Demonstrate facility in symbolic manipulation of polynomial and rational expressions by rearranging and collecting terms, factoring [e.g., a² – b² = (a + b)(a – b), x² + 10x + 21 = (x + 3) (x + 7), 5x the the 4th power + 10x³ – 5x² = 5x² (x² + 2x – 1)], identifying and canceling common factors in rational expressions, and applying the properties of positive integer exponents.
Dividing Exponential Expressions
Exponents and Power Rules
Factoring Special Products
Modeling the Factorization of x2+bx+c
AI.P.10: Divide polynomials by monomials with emphasis on 1st- and 2nd-degree polynomials.
Dividing Exponential Expressions
Dividing Polynomials Using Synthetic Division
AI.P.11: Perform basic arithmetic operations with rational expressions and functions.
General Form of a Rational Function
Rational Functions
AI.P.12: Find solutions to quadratic equations (with real roots) by factoring, completing the square, or using the quadratic formula. Demonstrate an understanding of the equivalence of the methods.
Factoring Special Products
Modeling the Factorization of ax2+bx+c
Modeling the Factorization of x2+bx+c
Roots of a Quadratic
AI.P.13: Solve equations and inequalities, including those involving absolute value of linear expressions (e.g., |x – 2| > 5), and apply to the solution of problems.
Inequalities Involving Absolute Values
Solving Linear Inequalities using Addition and Subtraction
Solving Linear Inequalities using Multiplication and Division
AI.P.14: Solve everyday problems (e.g., compound interest and direct and inverse variation problems) that can be modeled using linear or quadratic functions. Apply appropriate graphical or symbolic methods to the solution.
Direct Variation
Direct and Inverse Variation
Linear Functions
Quadratic and Absolute Value Functions
Quadratics in Factored Form
Quadratics in Polynomial Form - Activity A
Roots of a Quadratic
Simple and Compound Interest
AI.P.15: Solve everyday problems (e.g., mixture, rate, and work problems) that can be modeled using systems of linear equations or inequalities. Apply algebraic and graphical methods to the solution.
Linear Programming - Activity A
Modeling Linear Systems - Activity A
Special Types of Solutions to Linear Systems
Systems of Linear Inequalities (Slope-intercept form) - Activity A
AI.D.1: Select, create, and interpret an appropriate graphical representation (e.g., scatter plot, table, stem-and-leaf plots, circle graph, line graph, and line plot) for a set of data, and use appropriate statistics (e.g., mean, median, range, and mode) to communicate information about the data. Use these notions to compare different sets of data.
Box-and-Whisker Plots
Describing Data Using Statistics
Line Plots
Mean, Median and Mode
Populations and Samples
Scatter Plots - Activity A
Stem-and-Leaf Plots
AII.P.1: Describe, complete, extend, analyze, generalize, and create a wide variety of patterns, including iterative and recursive patterns such as Fibonacci Numbers and Pascal’s Triangle.
Arithmetic Sequences
Arithmetic and Geometric Sequences
Finding Patterns
Geometric Sequences
AII.P.2: Identify arithmetic and geometric sequences and finite arithmetic and geometric series. Use the properties of such sequences and series to solve problems, including finding the formula for the general term and the sum, recursively and explicitly.
Arithmetic Sequences
Arithmetic and Geometric Sequences
Geometric Sequences
AII.P.3: Understand functional notation, evaluate a function at a specified point in its domain, and perform operations on functions with emphasis on the domain and range.
Addition and Subtraction of Polynomials
Logarithmic Functions: Translating and Scaling
AII.P.4: Understand exponential and logarithmic functions and their basic arithmetic properties, including change of base and formulas for exponential of a sum and logarithm of a product.
Exponential Functions - Activity A
Exponential Growth and Decay - Activity B
Logarithmic Functions - Activity A
Logarithmic Functions: Translating and Scaling
AII.P.5: Given algebraic, numeric, and/or graphical representations, recognize functions as polynomial, rational, logarithmic, or exponential, and describe their behavior.
Cubic Function Activity
Exponential Functions - Activity A
Fourth-Degree Polynomials - Activity A
General Form of a Rational Function
Logarithmic Functions - Activity A
Logarithmic Functions: Translating and Scaling
Rational Functions
Using Algebraic Equations
AII.P.6: Find solutions to radical equations; find solutions to quadratic equations (with real coefficients and real or complex roots) graphically, by factoring, by completing the square, or by using the quadratic formula.
Modeling the Factorization of ax2+bx+c
Modeling the Factorization of x2+bx+c
Roots of a Quadratic
AII.P.7: Solve a variety of equations and inequalities using algebraic, graphical, and numerical methods, including the quadratic formula. Include polynomial, exponential, and logarithmic functions, expressions involving the absolute values, and simple rational expressions.
Exponential Functions - Activity A
Fourth-Degree Polynomials - Activity A
General Form of a Rational Function
Inequalities Involving Absolute Values
Logarithmic Functions - Activity A
Logarithmic Functions: Translating and Scaling
Quadratic Inequalities - Activity A
Quadratic and Absolute Value Functions
Quadratics in Factored Form
Quadratics in Polynomial Form - Activity A
Rational Functions
Roots of a Quadratic
Solving Linear Inequalities using Addition and Subtraction
Solving Linear Inequalities using Multiplication and Division
AII.P.9: Use symbolic, numeric, and graphical methods to solve systems of equations and/or inequalities involving algebraic, exponential, and logarithmic expressions. Describe the relationships among the methods.
Modeling Linear Systems - Activity A
Special Types of Solutions to Linear Systems
Systems of Linear Inequalities (Slope-intercept form) - Activity A
AII.P.10: Solve everyday problems that can be modeled using polynomial, rational, exponential, logarithmic, and step functions; absolute values; and square roots. Apply appropriate graphical, tabular, or symbolic methods to the solution. Include compound interest, exponential growth and decay, and direct and inverse variation problems.
Determining a Spring Constant
Direct Variation
Direct and Inverse Variation
Exponential Functions - Activity A
Fourth-Degree Polynomials - Activity A
Functions Involving Square Roots
General Form of a Rational Function
Logarithmic Functions - Activity A
Logarithmic Functions: Translating and Scaling
Quadratic and Absolute Value Functions
Radical Functions
Rational Functions
Simple and Compound Interest
AII.P.11: Recognize translations and scale changes of a given function f(x) resulting from substitutions for the various parameters a, b, c, and d in y = af(b(x + c/b)) + d. In particular, describe qualitatively the effect of such changes on polynomial, rational, exponential, and logarithmic functions.
Exponential Functions - Activity A
Fourth-Degree Polynomials - Activity A
General Form of a Rational Function
Logarithmic Functions - Activity A
Logarithmic Functions: Translating and Scaling
Rational Functions
AII.P.12: Simplify rational expressions. Solve rational equations and inequalities.
Dividing Exponential Expressions
Solving Linear Inequalities using Addition and Subtraction
Solving Linear Inequalities using Multiplication and Division
AII.G.1: Define the sine, cosine, and tangent of an acute angle. Apply to the solution of problems.
Cosine Function
Sine Function
Sine and Cosine Ratios - Activity A
Sine, Cosine and Tangent
Tangent Function
Tangent Ratio
Unit Circle
AII.G.2: Explain the identity sin²q + cos²q = 1. Relate the identity to the Pythagorean theorem.
Distance Formula - Activity A
Geoboard: The Pythagorean Theorem
Pythagorean Theorem - Activity A
Pythagorean Theorem - Activity B
Simplifying Trigonometric Expressions
AII.G.3: Relate geometric and algebraic representations of lines and simple curves.
Cosine Function
Ellipse - Activity A
Hyperbola - Activity A
Point-Slope Form of a Line - Activity A
Sine Function
Slope-Intercept Form of a Line - Activity A
Tangent Function
AII.D.1: Select an appropriate graphical representation for a set of data and use appropriate statistics (e.g., quartile or percentile distribution) to communicate information about the data, including box plots.
Box-and-Whisker Plots
Histograms
Line Plots
Scatter Plots - Activity A
Stem-and-Leaf Plots
AII.D.2: Use combinatorics (e.g., fundamental counting principle, permutations, and combinations) to solve problems, including computing geometric probabilities and probabilities of compound events.
Binomial Probabilities
Compound Independent Events
Compound Independent and Dependent Events
Geometric Probability - Activity A
Independent and Dependent Events
Permutations
Permutations and Combinations
G.G.1: Know correct geometric notation, including the notation for line segment (AB) and angle (
Classifying Quadrilaterals - Activity B
G.G.2: Recognize special types of polygons (e.g., isosceles triangles, parallelograms, and rhombuses).
G.G.3: Apply properties of sides, diagonals, and angles in special polygons; identify their parts and special segments (e.g., altitudes, midsegments); determine interior angles for regular polygons.
Classifying Triangles
G.G.5: Detect symmetries of geometric figures.
G.G.6: Apply the triangle inequality and other inequalities associated with triangles (e.g., the longest side is opposite the greatest angle) to prove theorems and to solve problems.
G.G.7: Use properties and theorems about congruent and similar figures and about perpendicular and parallel lines to solve problems.
Congruence in Right Triangles
G.G.8: Write simple proofs of theorems in geometric situations, such as theorems about triangles, congruent and similar figures, and perpendicular and parallel lines (e.g., the longest side is opposite the greatest angle, two lines parallel to a third are parallel to each other; perpendicular bisectors of line segments are the set of all points equidistant from the two end points).
Congruence in Right Triangles
G.G.9: Distinguish between postulates and theorems. Use inductive and deductive reasoning, as well as proof by contradiction. Given a conditional statement, write its inverse, converse, and contrapositive.
Biconditional Statement
G.G.11: Draw congruent and similar figures using a compass, straightedge, or protractor. Justify the constructions by logical argument.
Congruence in Right Triangles
G.G.12: Apply congruence and similarity correspondences (e.g., DABC @ DXYZ) and properties of the figures to find missing parts of geometric figures, and provide logical justification.
Classifying Quadrilaterals - Activity B
G.G.13: Apply properties of angles, parallel lines, arcs, radii, chords, tangents, and secants to solve problems.
G.G.14: Solve simple triangle problems using the triangle angle sum property and/or the Pythagorean theorem; study and understand more than one proof of this theorem.
Biconditional Statement
G.G.15: Use the properties of special triangles (e.g., isosceles, equilateral, 30º-60º-90º, 45º-45º-90º) to solve problems.
Isosceles and Equilateral Triangles
G.G.16: Define the sine, cosine, and tangent of an acute angle. Apply to the solution of problems.
Cosine Function
G.G.17: Demonstrate an understanding of the relationship between various representations of a line. Determine a line's slope and x- and y-intercepts from its graph or from a linear equation that represents the line. Find a linear equation describing a line from a graph or a geometric description of the line (e.g., by using the point-slope or slope y-intercept formulas). Explain the significance of a positive, negative, zero, or undefined slope.
Defining a Line with Two Points
G.G.18: Using rectangular coordinates, calculate midpoints of segments, slopes of lines and segments, and distances between two points, and apply the results to the solutions of problems.
Distance Formula - Activity A
G.G.19: Find linear equations that represent lines either perpendicular or parallel to a given line and through a point (e.g., by using the point-slope form of the equation).
Construct Parallel and Perpendicular Lines
G.G.20: Draw the results and interpret transformations on figures in the coordinate plane such as translations, reflections, rotations, scale factors, and the results of successive transformations. Apply transformations to the solution of problems.
Dilations
G.G.21: Demonstrate the ability to visualize solid objects and recognize their projections, cross sections, and graph points in 3-D.
3D and Orthographic Views - Activity A
G.G.22: Find and use measures of perimeter, circumference, and area of common geometric figures such as parallelograms, trapezoids, circles, and triangles.
Circle: Circumference and Area
G.G.23: Find and use measures of lateral areas, surface areas, and volumes of prisms, pyramids, spheres, cylinders, and cones, and relate these measures to each other using formulas.
Prisms and Cylinders - Activity A
G.G.24: Relate changes in the measurement (including units) of one attribute of an object to changes in other attributes.
Prisms and Cylinders - Activity A
PCT.N.2: Plot complex numbers using both rectangular and polar coordinates systems. Represent complex numbers using polar coordinates, i.e., a + bi = r (cos theta + i sin theta).
PCT.P.1: Relate the number of roots of a polynomial to its degree. Solve quadratic equations with complex coefficients, including use of completing the square.
Polynomials and Linear Factors
PCT.P.2: Demonstrate an understanding of the trigonometric functions (sine, cosine, tangent, cosecant, secant, and cotangent). Relate the functions to their geometric definitions.
Cosine Function
PCT.P.4: Given algebraic, numeric, and/or graphical representations, recognize functions as polynomial, rational, logarithmic, or exponential.
Cubic Function Activity
PCT.P.5: Combine functions by composition, as well as by addition, subtraction, multiplication, and division.
Addition and Subtraction of Polynomials
PCT.P.6: Identify whether a function has an inverse and when functions are inverses of each other; explain why the graph of a function and its inverse are reflections of one another over the line y = x.
Absolute Value with Linear Functions - Activity B
PCT.P.7: Identify maximum and minimum values of functions. Apply to the solution of problems.
Cubic Function Activity
PCT.P.8: Describe the translations and scale changes of a given function f(x) resulting from substitutions for the various parameters a, b, c, and d in y = a f(b (x + c/b)) + d. In particular, describe the effect of such changes on polynomial, rational, exponential, and logarithmic functions.
Exponential Functions - Activity A
PCT.P.9: Derive and apply basic trigonometric identities i.e., sin²theta + cos²theta = 1, tan²theta + 1 = sec²theta and the laws of sines and cosines.
Simplifying Trigonometric Expressions
PCT.P.10: Demonstrate an understanding of the formulas for the sine and cosine of the sum or the difference of two angles. Relate the formulas to DeMoivre's theorem and use them to prove other trigonometric identities. Apply to the solution of problems.
Simplifying Trigonometric Expressions
PCT.P.11: Understand, predict, and interpret the effects of the parameters a, w, b, and c on the graph of y = asin (infinity (x — b)) + c; do the same for the cosine and tangent. Use to model periodic processes.
Translating and Scaling Sine and Cosine Functions - Activity A
PCT.P.16: Identify maximum and minimum values of functions in simple situations. Apply to the solution of problems.
Cubic Function Activity
PCT.G.2: Use vectors to solve problems. Describe addition of vectors, multiplication of a vector by a scalar, and the dot product of two vectors, both symbolically and geometrically. Use vector methods to obtain geometric results.
PCT.G.3: Apply properties of angles, parallel lines, arcs, radii, chords, tangents, and secants to solve problems.
PCT.D.3: Compare the results of simulations (e.g., random number tables, random functions, and area models) with predicted probabilities.
Geometric Probability - Activity A
Compound Independent Events
Compound Independent Events
Describing Data Using Statistics
Describing Data Using Statistics
Box-and-Whisker Plots
Correlation Correlation last revised: 12/2/2009
Isosceles and Equilateral Triangles
Constructing Congruent Segments and Angles
Perimeters and Areas of Similar Figures
Proving Triangles Congruent
Similar Figures - Activity A
Similar Polygons
Constructing Congruent Segments and Angles
Perimeters and Areas of Similar Figures
Proving Triangles Congruent
Similar Figures - Activity A
Similar Polygons
Triangle Angle Sum - Activity A
Conditional Statement
Simplifying Trigonometric Expressions
Sum and Difference Identities for Sine and Cosine
Constructing Congruent Segments and Angles
Perimeters and Areas of Similar Figures
Proving Triangles Congruent
Similar Figures - Activity A
Similar Polygons
Congruence in Right Triangles
Constructing Congruent Segments and Angles
Perimeters and Areas of Similar Figures
Proving Triangles Congruent
Similar Figures - Activity A
Similar Polygons
Conditional Statement
Geoboard: The Pythagorean Theorem
Investigating Angle Theorems - Activity A
Pythagorean Theorem - Activity B
Triangle Angle Sum - Activity A
Triangle Angle Sum - Activity A
Sine Function
Sine and Cosine Ratios - Activity A
Sine, Cosine and Tangent
Tangent Function
Tangent Ratio
Unit Circle
Linear Functions
Point-Slope Form of a Line - Activity A
Slope - Activity B
Slope-Intercept Form of a Line - Activity A
Solving Equations By Graphing Each Side
Standard Form of a Line
Using Tables, Rules and Graphs
Geoboard: The Pythagorean Theorem
Pythagorean Theorem - Activity A
Slope - Activity B
Linear Functions
Point-Slope Form of a Line - Activity A
Reflections
Rotations, Reflections and Translations
Translations
Parallelogram Conditions
Perimeter, Circumference, and Area - Activity B
Pyramids and Cones - Activity A
Surface and Lateral Area of Prisms and Cylinders
Surface and Lateral Area of Pyramids and Cones
PCT: Precalculus
Roots of a Quadratic
Sine Function
Sine, Cosine and Tangent
Tangent Function
Tangent Ratio
Unit Circle
Exponential Functions - Activity A
Fourth-Degree Polynomials - Activity A
General Form of a Rational Function
Logarithmic Functions - Activity A
Logarithmic Functions: Translating and Scaling
Rational Functions
Using Algebraic Equations
Fourth-Degree Polynomials - Activity A
Parabolas - Activity A
Quadratic and Absolute Value Functions
Quadratics in Factored Form
Quadratics in Polynomial Form - Activity A
Roots of a Quadratic
Fourth-Degree Polynomials - Activity A
General Form of a Rational Function
Logarithmic Functions - Activity A
Logarithmic Functions: Translating and Scaling
Rational Functions
Sum and Difference Identities for Sine and Cosine
Sum and Difference Identities for Sine and Cosine
Fourth-Degree Polynomials - Activity A
Parabolas - Activity A
Quadratic and Absolute Value Functions
Quadratics in Factored Form
Quadratics in Polynomial Form - Activity A
Roots of a Quadratic
Probability Simulations
PS: Probability and Statistics
PS.1: Demonstrate understanding of the definition of the notion of independent events and use the rules for addition, multiplication, and complementation to solve for probabilities of particular events in finite sample spaces.
Compound Independent and Dependent Events
Independent and Dependent Events
PS.3: Demonstrate understanding of the notion of discrete random variables by using them to solve for the probabilities of outcomes (e.g., the probability of the occurrences of five heads in 14 coin tosses).
Compound Independent and Dependent Events
Independent and Dependent Events
PS.4: Apply uniform, normal, and binomial distributions to the solutions of problems.
PS.6: Know the definitions of the mean, median, and mode of a distribution of data, and compute each in particular situations.
Line Plots
Mean, Median and Mode
PS.7: Describe a set of frequency distribution data by spread (variance and standard deviation), skewness, symmetry, number of modes, or other characteristics. Use these concepts in everyday applications.
PS.8: Organize and describe distributions of data by using a number of different methods, including frequency tables, histograms, standard line and bar graphs, stem-and-leaf displays, scatter plots, and box-and-whisker plots.
Correlation
Histograms
Scatter Plots - Activity A
Solving Using Trend Lines
Stem-and-Leaf Plots
PS.9: Describe and explain how the relative sizes of a sample and the population affect the validity of predictions from a set of data.
PS.10: Approximate a line of best fit (trend line) given a set of data (e.g., scatter plot).
Lines of Best Fit Using Least Squares - Activity A
Solving Using Trend Lines