Grade Level Content Expectations

L1.1.2: Explain why the multiplicative inverse of a number has the same sign as the number, while the additive inverse of a number has the opposite sign.

Solving Formulas for any Variable

L1.1.6: Explain the importance of the irrational numbers square root of 2 and square root of 3 in basic right triangle trigonometry; the importance of π because of its role in circle relationships; and the role of e in applications such as continuously compounded interest.

L1.2.3: Use vectors to represent quantities that have magnitude and direction; interpret direction and magnitude of a vector numerically, and calculate the sum and difference of two vectors.

L1.2.4: Organize and summarize a data set in a table, plot, chart, or spreadsheet; find patterns in a display of data; understand and critique data displays in the media.

Arithmetic and Geometric Sequences

Describing Data Using Statistics

Geometric Sequences

L1.3.1: Describe, explain, and apply various counting techniques (e.g., finding the number of different 4-letter passwords; permutations; and combinations); relate combinations to Pascal’s triangle; know when to use each technique.

Binomial Probabilities

Permutations

Permutations and Combinations

L1.3.2: Define and interpret commonly used expressions of probability (e.g., chances of an event, likelihood, odds).

Estimating Population Size

Geometric Probability - Activity A

L1.3.3: Recognize and explain common probability misconceptions such as “hot streaks” and “being due.”

L2.1.1: Explain the meaning and uses of weighted averages (e.g., GNP, consumer price index, grade point average).

Describing Data Using Statistics

Mean, Median and Mode

L2.1.4: Know that the complex number i is one of two solutions to x² = -1.

Points in the Complex Plane - Activity A

L2.1.5: Add, subtract, and multiply complex numbers; use conjugates to simplify quotients of complex numbers.

Points in the Complex Plane - Activity A

L2.2.1: Find the nth term in arithmetic, geometric, or other simple sequences.

L2.2.2: Compute sums of finite arithmetic and geometric sequences.

Arithmetic Sequences

Arithmetic and Geometric Sequences

Geometric Sequences

L2.2.3: Use iterative processes in such examples as computing compound interest or applying approximation procedures.

L4.1.1: Distinguish between inductive and deductive reasoning, identifying and providing examples of each.

Biconditional Statement

Conditional Statement

L4.1.2: Differentiate between statistical arguments (statements verified empirically using examples or data) and logical arguments based on the rules of logic.

Biconditional Statement

Conditional Statement

L4.2.1: Know and use the terms of basic logic (e.g., proposition, negation, truth and falsity, implication, if and only if, contrapositive, and converse).

L4.2.3: Use the quantifiers “THERE EXISTS” and “ALL” in mathematical and everyday settings and know how to logically negate statements involving them.

Biconditional Statement

Conditional Statement

L4.3.3: Explain the difference between a necessary and a sufficient condition within the statement of a theorem; determine the correct conclusions based on interpreting a theorem in which necessary or sufficient conditions in the theorem or hypothesis are satisfied.

A1.1.1: Give a verbal description of an expression that is presented in symbolic form, write an algebraic expression from a verbal description, and evaluate expressions given values of the variables.

Using Algebraic Equations

Using Algebraic Expressions

A1.1.3: Factor algebraic expressions using, for example, greatest common factor, grouping, and the special product identities (e.g., differences of squares and cubes).

Factoring Special Products

Modeling the Factorization of *x*^{2}+*bx*+*c*

A1.1.4: Add, subtract, multiply, and simplify polynomials and rational expressions (e.g., multiply (x – 1) (1 – x² + 3); simplify (9x - x³)/(x + 3))

Addition of Polynomials - Activity A

A1.1.5: Divide a polynomial by a monomial.

Dividing Exponential Expressions

Dividing Polynomials Using Synthetic Division

A1.1.6: Transform exponential and logarithmic expressions into equivalent forms using the properties of exponents and logarithms including the inverse relationship between exponents and logarithms.

Dividing Exponential Expressions

A1.2.1: Write equations and inequalities with one or two variables to represent mathematical or applied situations, and solve.

Inequalities Involving Absolute Values

Linear Inequalities in Two Variables - Activity A

Modeling One-Step Equations - Activity A

Modeling and Solving Two-Step Equations

Solving Linear Inequalities using Addition and Subtraction

Solving Linear Inequalities using Multiplication and Division

Solving Two-Step Equations

Using Algebraic Equations

A1.2.2: Associate a given equation with a function whose zeros are the solutions of the equation.

Linear Functions

Polynomials and Linear Factors

Using Algebraic Equations

A1.2.3: Solve (and justify steps in the solutions) linear and quadratic equations and inequalities, including systems of up to three linear equations with three unknowns; apply the quadratic formula appropriately.

Quadratic Inequalities - Activity A

Roots of a Quadratic

Solving Equations By Graphing Each Side

Solving Linear Inequalities using Addition and Subtraction

Solving Linear Inequalities using Multiplication and Division

A1.2.4: Solve absolute value equations and inequalities, (e.g. solve l x - 3 l ≤ 6), and justify steps in the solution.

Inequalities Involving Absolute Values

Solving Linear Inequalities using Addition and Subtraction

Solving Linear Inequalities using Multiplication and Division

A1.2.6: Solve power equations (e.g., (x + 1)³ = 8) and equations including radical expressions (e.g., the square root of (3x - 7) = 7), justify steps in the solution, and explain how extraneous solutions may arise.

Simplifying Radicals - Activity A

A1.2.8: Solve an equation involving several variables (with numerical or letter coefficients) for a designated variable, and justify steps in the solution.

Solving Formulas for any Variable

A1.2.9: Know common formulas (e.g., slope, distance between two points, quadratic formula, compound interest, distance = velocity x time), and apply appropriately in contextual situations.

Distance Formula - Activity A

Distance-Time Graphs

Distance-Time and Velocity-Time Graphs

Roots of a Quadratic

Slope - Activity B

A2.1.1: Recognize whether a relationship (given in contextual, symbolic, tabular, or graphical form) is a function; and identify its domain and range.

Functions Involving Square Roots

Introduction to Functions

Linear Functions

Logarithmic Functions: Translating and Scaling

A2.1.2: Read, interpret, and use function notation, and evaluate a function at a value in its domain.

Logarithmic Functions: Translating and Scaling

A2.1.3: Represent functions in symbols, graphs, tables, diagrams, or words, and translate among representations.

Cosine Function

Cubic Function Activity

Exponential Functions - Activity A

Fourth-Degree Polynomials - Activity A

General Form of a Rational Function

Introduction to Functions

Linear Functions

Logarithmic Functions - Activity A

Logarithmic Functions: Translating and Scaling

Polynomials and Linear Factors

Quadratic and Absolute Value Functions

Quadratics in Factored Form

Quadratics in Polynomial Form - Activity A

Radical Functions

Rational Functions

Sine Function

Slope-Intercept Form of a Line - Activity A

Tangent Function

Using Algebraic Equations

Using Algebraic Expressions

Using Tables, Rules and Graphs

A2.1.4: Recognize that functions may be defined by different expressions over different intervals of their domains; such functions are piecewise-defined (e.g., absolute value and greatest integer functions).

Quadratic and Absolute Value Functions

A2.1.5: Recognize that functions may be defined recursively, and compute values of and graph simple recursively defined functions (e.g., f(0) = 5, and f(n) = f(n-1) + 2).

Arithmetic Sequences

Arithmetic and Geometric Sequences

Geometric Sequences

A2.1.6: Identify the zeros of a function and the intervals where the values of a function are positive or negative, and describe the behavior of a function, as x approaches postive or negative infinity, given the symbolic and graphical representations.

Polynomials and Linear Factors

A2.1.7: Identify and interpret the key features of a function from its graph or its formula(e), (e.g. slope, intercept(s), asymptote(s), maximum and minimum value(s), symmetry, average rate of change over an interval, and periodicity).

Cosine Function

Cubic Function Activity

Direct Variation

Direct and Inverse Variation

Distance-Time Graphs

Distance-Time and Velocity-Time Graphs

Fourth-Degree Polynomials - Activity A

Modeling Linear Systems - Activity A

Point-Slope Form of a Line - Activity A

Polynomials and Linear Factors

Quadratic and Absolute Value Functions

Quadratics in Factored Form

Quadratics in Polynomial Form - Activity A

Sine Function

Slope - Activity B

Slope-Intercept Form of a Line - Activity A

Tangent Function

Translating and Scaling Functions

Translating and Scaling Sine and Cosine Functions - Activity A

Using Tables, Rules and Graphs

A2.2.1: Combine functions by addition, subtraction, multiplication, and division.

Addition and Subtraction of Polynomials

A2.2.2: Apply given transformations (e.g., vertical or horizontal shifts, stretching or shrinking, or reflections about the x- and y-axes) to basic functions, and represent symbolically.

Absolute Value with Linear Functions - Activity B

Logarithmic Functions: Translating and Scaling

Reflections of a Linear Function

Reflections of a Quadratic Function

Translating and Scaling Functions

Translating and Scaling Sine and Cosine Functions - Activity A

A2.2.3: Recognize whether a function (given in tabular or graphical form) has an inverse and recognize simple inverse pairs (e.g., f(x) = x³ and g(x) = x to the 1/3 power).

A2.3.1: Identify a function as a member of a family of functions based on its symbolic, or graphical representation; recognize that different families of functions have different asymptotic behavior at infinity, and describe these behaviors.

Cosine Function

Cubic Function Activity

Exponential Functions - Activity A

Fourth-Degree Polynomials - Activity A

Functions Involving Square Roots

General Form of a Rational Function

Linear Functions

Logarithmic Functions - Activity A

Logarithmic Functions: Translating and Scaling

Point-Slope Form of a Line - Activity A

Polynomials and Linear Factors

Quadratic and Absolute Value Functions

Quadratics in Factored Form

Quadratics in Polynomial Form - Activity A

Radical Functions

Rational Functions

Roots of a Quadratic

Sine Function

Slope-Intercept Form of a Line - Activity A

Tangent Function

Translating and Scaling Functions

Translating and Scaling Sine and Cosine Functions - Activity A

Unit Circle

Using Algebraic Equations

A2.3.2: Describe the tabular pattern associated with functions having constant rate of change (linear); or variable rates of change.

Arithmetic Sequences

Arithmetic and Geometric Sequences

Distance-Time Graphs

Distance-Time and Velocity-Time Graphs

Linear Functions

Point-Slope Form of a Line - Activity A

Slope-Intercept Form of a Line - Activity A

Using Tables, Rules and Graphs

A2.4.1: Write the symbolic forms of linear functions (standard [i.e., Ax + By = C, where B ≠ 0], point-slope, and slope-intercept) given appropriate information, and convert between forms.

Defining a Line with Two Points

Linear Functions

Point-Slope Form of a Line - Activity A

Slope-Intercept Form of a Line - Activity A

Standard Form of a Line

Using Tables, Rules and Graphs

A2.4.2: Graph lines (including those of the form x = h and y = k) given appropriate information.

Defining a Line with Two Points

Point-Slope Form of a Line - Activity A

Slope-Intercept Form of a Line - Activity A

Standard Form of a Line

A2.4.3: Relate the coefficients in a linear function to the slope and x- and y-intercepts of its graph.

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

Standard Form of a Line

Using Tables, Rules and Graphs

A2.4.4: Find an equation of the line parallel or perpendicular to given line, through a given point; understand and use the facts that non-vertical parallel lines have equal slopes, and that non-vertical perpendicular lines have slopes that multiply to give -1.

Point-Slope Form of a Line - Activity A

Slope - Activity B

A2.5.1: Write the symbolic form and sketch the graph of an exponential function given appropriate information. (e.g., given an initial value of 4 and a rate of growth of 1.5, write f(x) = 4 (1.5) to the x power).

Exponential Functions - Activity A

Exponential Growth and Decay - Activity B

A2.5.2: Interpret the symbolic forms and recognize the graphs of exponential and logarithmic functions (e.g., f(x) = 10 to the x power, f(x) = log x, f(x) = e to the x power, f(x) = ln x); recognize the logarithmic function as the inverse of the exponential function.

Exponential Functions - Activity A

Exponential Growth and Decay - Activity B

Logarithmic Functions - Activity A

Logarithmic Functions: Translating and Scaling

A2.5.3: Apply properties of exponential and logarithmic functions (e.g., a ot the x+y power = a to the x power times a to the y power; log(ab)= log a + log b).

Exponential Functions - Activity A

Exponential Growth and Decay - Activity B

Logarithmic Functions - Activity A

Logarithmic Functions: Translating and Scaling

A2.5.4: Understand and use the fact that the base of an exponential function determines whether the function increases or decreases and understand how the base affects the rate of growth or decay.

Exponential Functions - Activity A

Exponential Growth and Decay - Activity B

Half-life

A2.5.5: Relate exponential and logarithmic functions to real phenomena, including half-life and doubling time.

Exponential Functions - Activity A

Exponential Growth and Decay - Activity B

Half-life

Logarithmic Functions - Activity A

Logarithmic Functions: Translating and Scaling

A2.6.1: Write the symbolic form and sketch the graph of a quadratic function given appropriate information (e.g., vertex, intercepts, etc.).

Parabolas - Activity A

Quadratic and Absolute Value Functions

Quadratics in Factored Form

Quadratics in Polynomial Form - Activity A

Roots of a Quadratic

A2.6.2: Identify the elements of a parabola (vertex, axis of symmetry, direction of opening) given its symbolic form or its graph, and relate these elements to the coefficient(s) of the symbolic form of the function.

Holiday Snowflake Designer

Parabolas - Activity A

Quadratics in Factored Form

A2.6.3: Convert quadratic functions from standard to vertex form by completing the square.

Parabolas - Activity A

Quadratic and Absolute Value Functions

Quadratics in Factored Form

Quadratics in Polynomial Form - Activity A

Roots of a Quadratic

A2.6.4: Relate the number of real solutions of a quadratic equation to the graph of the associated quadratic function.

Parabolas - Activity A

Quadratic and Absolute Value Functions

Quadratics in Factored Form

Quadratics in Polynomial Form - Activity A

Roots of a Quadratic

A2.6.5: Express quadratic functions in vertex form to identify their maxima or minima, and in factored form to identify their zeros.

Modeling the Factorization of *x*^{2}+*bx*+*c*

Parabolas - Activity A

Polynomials and Linear Factors

Quadratic and Absolute Value Functions

Quadratics in Factored Form

Quadratics in Polynomial Form - Activity A

Roots of a Quadratic

A2.7.2: Express direct and inverse relationships as functions (e.g., y = kx to the n power and y = kx to the -n power, n > 0) and recognize their characteristics (e.g., in y = x³, note that doubling x results in multiplying y by a factor of 8).

Determining a Spring Constant

Direct Variation

Direct and Inverse Variation

A2.7.3: Analyze the graphs of power functions, noting reflectional or rotational symmetry.

A2.8.1: Write the symbolic form and sketch the graph of simple polynomial functions.

Cubic Function Activity

Fourth-Degree Polynomials - Activity A

Polynomials and Linear Factors

A2.8.2: Understand the effects of degree, leading coefficient, and number of real zeros on the graphs of polynomial functions of degree greater than 2.

Cubic Function Activity

Fourth-Degree Polynomials - Activity A

Parabolas - Activity A

Polynomials and Linear Factors

Quadratic and Absolute Value Functions

A2.8.3: Determine the maximum possible number of zeros of a polynomial function, and understand the relationship between the x-intercepts of the graph and the factored form of the function.

Cubic Function Activity

Fourth-Degree Polynomials - Activity A

Modeling the Factorization of *x*^{2}+*bx*+*c*

Polynomials and Linear Factors

A2.9.1: Write the symbolic form and sketch the graph of simple rational functions.

General Form of a Rational Function

Rational Functions

A2.9.2: Analyze graphs of simple rational functions (e.g., f(x) = (2x + 1)/(x - 1); g(x) = x/(x² - 4)) and understand the relationship between the zeros of the numerator and denominator and the function’s intercepts, asymptotes, and domain.

General Form of a Rational Function

Rational Functions

A2.10.1: Use the unit circle to define sine and cosine; approximate values of sine and cosine (e.g., sin 3, or cos 0.5); use sine and cosine to define the remaining trigonometric functions; explain why the trigonometric functions are periodic.

Cosine Function

Sine Function

Sine and Cosine Ratios - Activity A

Sine, Cosine and Tangent

Tangent Function

Translating and Scaling Sine and Cosine Functions - Activity A

Unit Circle

A2.10.3: Use the unit circle to determine the exact values of sine and cosine, for integer multiples of pi/6 and pi/4.

Cosine Function

Sine Function

Sine, Cosine and Tangent

Tangent Function

Unit Circle

A2.10.4: Graph the sine and cosine functions; analyze graphs by noting domain, range, period, amplitude, and location of maxima and minima.

Cosine Function

Sine Function

Sine, Cosine and Tangent

Translating and Scaling Functions

Translating and Scaling Sine and Cosine Functions - Activity A

A2.10.5: Graph transformations of basic trigonometric functions (involving changes in period, amplitude, and midline) and understand the relationship between constants in the formula and the transformed graph.

Translating and Scaling Functions

Translating and Scaling Sine and Cosine Functions - Activity A

A3.1.1: Identify the family of function best suited for modeling a given real-world situation (e.g., quadratic functions for motion of an object under the force of gravity; exponential functions for compound interest; trigonometric functions for periodic phenomena. In the example above, recognize that the appropriate general function is exponential (P = P0a to the t power)

Cosine Function

Exponential Functions - Activity A

Exponential Growth and Decay - Activity B

Half-life

Quadratic and Absolute Value Functions

Quadratics in Factored Form

Quadratics in Polynomial Form - Activity A

Roots of a Quadratic

Simple and Compound Interest

Sine Function

Tangent Function

A3.1.2: Adapt the general symbolic form of a function to one that fits the specifications of a given situation by using the information to replace arbitrary constants with numbers. In the example above, substitute the given values P0 = 300 and a = 1.02 to obtain P = 300(1.02) to the t power.

Cosine Function

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

Quadratic and Absolute Value Functions

Quadratics in Factored Form

Quadratics in Polynomial Form - Activity A

Radical Functions

Rational Functions

Sine Function

Tangent Function

Using Algebraic Equations

G1.1.1: Solve multi-step problems and construct proofs involving vertical angles, linear pairs of angles supplementary angles, complementary angles, and right angles.

Biconditional Statement

Conditional Statement

Investigating Angle Theorems - Activity A

G1.1.2: Solve multi-step problems and construct proofs involving corresponding angles, alternate interior angles, alternate exterior angles, and same-side (consecutive) interior angles.

Biconditional Statement

Conditional Statement

Investigating Angle Theorems - Activity A

G1.1.3: Perform and justify constructions, including midpoint of a line segment and bisector of an angle, using straightedge and compass.

Construct Parallel and Perpendicular Lines

Constructing Congruent Segments and Angles

G1.1.4: Given a line and a point, construct a line through the point that is parallel to the original line using straightedge and compass; given a line and a point, construct a line through the point that is perpendicular to the original line; justify the steps of the constructions.

Construct Parallel and Perpendicular Lines

Constructing Congruent Segments and Angles

G1.2.1: Prove that the angle sum of a triangle is 180° and that an exterior angle of a triangle is the sum of the two remote interior angles.

Investigating Angle Theorems - Activity A

Triangle Angle Sum - Activity A

G1.2.2: Construct and justify arguments and solve multi-step problems involving angle measure, side length, perimeter, and area of all types of triangles.

Classifying Triangles

Minimize Perimeter

Perimeter, Circumference, and Area - Activity B

G1.2.3: Know a proof of the Pythagorean Theorem and use the Pythagorean Theorem and its converse to solve multi-step problems.

Biconditional Statement

Conditional Statement

Distance Formula - Activity A

Geoboard: The Pythagorean Theorem

Pythagorean Theorem - Activity A

Pythagorean Theorem - Activity B

G1.2.5: Solve multi-step problems and construct proofs about the properties of medians, altitudes, and perpendicular bisectors to the sides of a triangle, and the angle bisectors of a triangle; using a straightedge and compass, construct these lines.

Biconditional Statement

Concurrent Lines, Medians, and Altitudes

Conditional Statement

Constructing Congruent Segments and Angles

G1.3.1: Define the sine, cosine, and tangent of acute angles in a right triangle as ratios of sides; solve problems about angles, side lengths, or areas using trigonometric ratios in right triangles.

Sine Function

Sine and Cosine Ratios - Activity A

Sine, Cosine and Tangent

Tangent Ratio

Unit Circle

G1.3.3: Determine the exact values of sine, cosine, and tangent for 0°, 30°, 45°, 60°, and their integer multiples, and apply in various contexts.

Cosine Function

Sine Function

Sine and Cosine Ratios - Activity A

Sine, Cosine and Tangent

Tangent Function

Tangent Ratio

Unit Circle

G1.4.1: Solve multi-step problems and construct proofs involving angle measure, side length, diagonal length, perimeter, and area of squares, rectangles, parallelograms, kites, and trapezoids.

Area of Parallelograms - Activity A

Biconditional Statement

Conditional Statement

Perimeter, Circumference, and Area - Activity B

Rectangle: Perimeter and Area

Special Quadrilaterals

G1.4.2: Solve multi-step problems and construct proofs involving quadrilaterals (e.g., prove that the diagonals of a rhombus are perpendicular) using Euclidean methods or coordinate geometry.

Biconditional Statement

Classifying Quadrilaterals - Activity B

Conditional Statement

Special Quadrilaterals

G1.4.3: Describe and justify hierarchical relationships among quadrilaterals, (e.g. every rectangle is a parallelogram).

Area of Parallelograms - Activity A

Classifying Quadrilaterals - Activity B

Parallelogram Conditions

Prisms and Cylinders - Activity A

Pyramids and Cones - Activity A

Special Quadrilaterals

G1.4.4: Prove theorems about the interior and exterior angle sums of a quadrilateral.

Parallelogram Conditions

Polygon Angle Sum - Activity A

Triangle Angle Sum - Activity A

G1.5.1: Know and use subdivision or circumscription methods to find areas of polygons (e.g., regular octagon, non-regular pentagon).

Area of Parallelograms - Activity A

G1.5.2: Know, justify, and use formulas for the perimeter and area of a regular n-gon and formulas to find interior and exterior angles of a regular n-gon and their sums.

Area of Parallelograms - Activity A

Perimeter, Circumference, and Area - Activity B

Polygon Angle Sum - Activity A

Rectangle: Perimeter and Area

Triangle Angle Sum - Activity A

G1.6.1: Solve multi-step problems involving circumference and area of circles.

Circle: Circumference and Area

Perimeter, Circumference, and Area - Activity B

G1.6.2: Solve problems and justify arguments about chords (e.g., if a line through the center of a circle is perpendicular to a chord, it bisects the chord) and lines tangent to circles (e.g., a line tangent to a circle is perpendicular to the radius drawn to the point of tangency).

G1.6.3: Solve problems and justify arguments about central angles, inscribed angles and triangles in circles.

Chords and Arcs

Inscribing Angles

G.1.7.1: Find an equation of a circle given its center and radius; given the equation of a circle, find its center and radius.

G1.7.2: Identify and distinguish among geometric representations of parabolas, circles, ellipses, and hyperbolas; describe their symmetries, and explain how they are related to cones.

Circles

Ellipse - Activity A

Holiday Snowflake Designer

Hyperbola - Activity A

Parabolas - Activity A

Pyramids and Cones - Activity A

Surface and Lateral Area of Pyramids and Cones

G1.7.3: Graph ellipses and hyperbolas with axes parallel to the x- and y-axes, given equations.

Ellipse - Activity A

Hyperbola - Activity A

G1.8.1: Solve multi-step problems involving surface area and volume of pyramids, prisms, cones, cylinders, hemispheres, and spheres.

Prisms and Cylinders - Activity A

Pyramids and Cones - Activity A

G1.8.2: Identify symmetries of pyramids, prisms, cones, cylinders, hemispheres, and spheres.

Holiday Snowflake Designer

Prisms and Cylinders - Activity A

Pyramids and Cones - Activity A

Surface and Lateral Area of Pyramids and Cones

G2.1.1: Know and demonstrate the relationships between the area formula of a triangle, the area formula of a parallelogram, and the area formula of a trapezoid.

Area of Parallelograms - Activity A

Perimeter, Circumference, and Area - Activity B

G2.1.2: Know and demonstrate the relationships between the area formulas of various quadrilaterals (e.g., explain how to find the area of a trapezoid based on the areas of parallelograms and triangles).

Area of Parallelograms - Activity A

Perimeter, Circumference, and Area - Activity B

G2.1.3: Know and use the relationship between the volumes of pyramids and prisms (of equal base and height) and cones and cylinders (of equal base and height).

Prisms and Cylinders - Activity A

Pyramids and Cones - Activity A

G2.2.1: Identify or sketch a possible 3-dimensional figure, given 2-dimensional views (e.g., nets, multiple views); create a 2-dimensional representation of a 3-dimensional figure.

3D and Orthographic Views - Activity A

Surface and Lateral Area of Prisms and Cylinders

Surface and Lateral Area of Pyramids and Cones

G2.2.2: Identify or sketch cross-sections of 3-dimensional figures; identify or sketch solids formed by revolving 2-dimensional figures around lines.

Prisms and Cylinders - Activity A

Pyramids and Cones - Activity A

G2.3.1: Prove that triangles are congruent using the SSS, SAS, ASA, and AAS criteria, and for right triangles, the hypotenuse-leg criterion.

Congruence in Right Triangles

Proving Triangles Congruent

G2.3.2: Use theorems about congruent triangles to prove additional theorems and solve problems, with and without use of coordinates.

Congruence in Right Triangles

Proving Triangles Congruent

G2.3.3: Prove that triangles are similar by using SSS, SAS, and AA conditions for similarity.

Perimeters and Areas of Similar Figures

Similar Figures - Activity A

Similar Polygons

G2.3.4: Use theorems about similar triangles to solve problems with and without use of coordinates.

Perimeters and Areas of Similar Figures

Similar Figures - Activity A

Similar Polygons

G2.3.5: Know and apply the theorem stating that the effect of a scale factor of k relating one two dimensional figure to another or one three dimensional figure to another, on the length, area, and volume of the figures is to multiply each by k, k², and k³, respectively.

Area of Parallelograms - Activity A

Perimeters and Areas of Similar Figures

Prisms and Cylinders - Activity A

Pyramids and Cones - Activity A

Similar Figures - Activity A

Similar Polygons

G3.1.1: Define reflection, rotation, translation, and glide reflection and find the image of a figure under a given isometry.

Reflections

Rotations, Reflections and Translations

Translations

G3.1.2: Given two figures that are images of each other under an isometry, find the isometry and describe it completely.

Dilations

Reflections

Rotations, Reflections and Translations

G3.1.3: Find the image of a figure under the composition of two or more isometries, and determine whether the resulting figure is a reflection, rotation, translation, or glide reflection image of the original figure.

Reflections

Rotations, Reflections and Translations

Translations

G3.2.1: Know the definition of dilation, and find the image of a figure under a given dilation.

G3.2.2: Given two figures that are images of each other under some dilation, identify the center and magnitude of the dilation.

S1.1.1: Construct and interpret dot plots, histograms, relative frequency histograms, bar graphs, basic control charts, and box plots with appropriate labels and scales; determine which kinds of plots are appropriate for different types of data; compare data sets and interpret differences based on graphs and summary statistics.

Box-and-Whisker Plots

Histograms

Line Plots

Populations and Samples

S1.1.2: Given a distribution of a variable in a data set, describe its shape, including symmetry or skewness, and state how the shape is related to measures of center (mean and median) and measures of variation (range and standard deviation) with particular attention to the effects of outliers on these measures.

Describing Data Using Statistics

Line Plots

Mean, Median and Mode

S1.2.1: Calculate and interpret measures of center including: mean, median, and mode; explain uses, advantages and disadvantages of each measure given a particular set of data and its context.

Describing Data Using Statistics

Line Plots

Mean, Median and Mode

S1.2.2: Estimate the position of the mean, median, and mode in both symmetrical and skewed distributions, and from a frequency distribution or histogram.

Describing Data Using Statistics

Histograms

Line Plots

Mean, Median and Mode

Populations and Samples

S1.2.3: Compute and interpret measures of variation, including percentiles, quartiles, interquartile range, variance, and standard deviation.

S1.3.2: Describe characteristics of the normal distribution, including its shape and the relationships among its mean, median, and mode.

Describing Data Using Statistics

Line Plots

Mean, Median and Mode

S2.1.1: Construct a scatterplot for a bivariate data set with appropriate labels and scales.

Correlation

Scatter Plots - Activity A

Solving Using Trend Lines

S2.1.2: Given a scatterplot, identify patterns, clusters, and outliers; recognize no correlation, weak correlation, and strong correlation.

Correlation

Scatter Plots - Activity A

Solving Using Trend Lines

S2.1.3: Estimate and interpret Pearson’s correlation coefficient for a scatterplot of a bivariate data set; recognize that correlation measures the strength of linear association.

Correlation

Scatter Plots - Activity A

Solving Using Trend Lines

S2.1.4: Differentiate between correlation and causation; know that a strong correlation does not imply a cause-and-effect relationship; recognize the role of lurking variables in correlation.

Correlation

Solving Using Trend Lines

S2.2.1: For bivariate data which appear to form a linear pattern, find the least squares regression line by estimating visually and by calculating the equation of the regression line; interpret the slope of the equation for a regression line.

Correlation

Slope - Activity B

Solving Using Trend Lines

S2.2.2: Use the equation of the least squares regression line to make appropriate predictions.

Correlation

Solving Using Trend Lines

S3.1.2: Identify possible sources of bias in data collection and sampling methods and simple experiments; describe how such bias can be reduced and controlled by random sampling; explain the impact of such bias on conclusions made from analysis of the data; and know the effect of replication on the precision of estimates.

S3.1.3: Distinguish between an observational study and an experimental study, and identify, in context, the conclusions that can be drawn from each.

Geometric Probability - Activity A

Probability Simulations

S4.1.1: Understand and construct sample spaces in simple situations (e.g., tossing two coins, rolling two number cubes and summing the results).

Compound Independent Events

Compound Independent and Dependent Events

Independent and Dependent Events

S4.1.2: Define mutually exclusive events, independent events, dependent events, compound events, complementary events and conditional probabilities; and use the definitions to compute probabilities.

Compound Independent Events

Compound Independent and Dependent Events

Independent and Dependent Events

S4.2.1: Compute probabilities of events using tree diagrams, formulas for combinations and permutations, Venn diagrams, or other counting techniques.

Binomial Probabilities

Permutations

Permutations and Combinations

S4.2.2: Apply probability concepts to practical situations, in such settings as finance, health, ecology, or epidemiology, to make informed decisions.

Binomial Probabilities

Geometric Probability - Activity A

Correlation last revised: 10/24/2008

This correlation lists the recommended Gizmos for this state's curriculum standards. Click any Gizmo title below for more information.