Grade Level Expectations

1.1.1: Understand the concept and symbolic representation of real numbers, including rational exponents.

1.1.1.a: Explain the meaning of the square root of a number, including why negative numbers have no real square roots.

1.1.5: Understand the concept and symbolic representation of rational numbers including absolute values.

1.1.5.d: Perform arithmetic operations with expressions involving absolute value.

Exponents and Power Rules

Operations with Radical Expressions

1.1.6: Complete multi-step computations of real numbers in all forms, including rational exponents and scientific notation, using order of operations and properties of operations.

1.1.6.a: Compute using rational numbers.

Fractions with Unlike Denominators

1.2.2: Understand and apply rate and other derived units of measure.

1.2.2.a: Use vectors to represent velocity and direction: multiply a vector by a scalar and adds vectors both algebraically and graphically.

1.2.2.b: Solve problems involving rates such as speed, density, population density, or flow rates.

Density Experiment: Slice and Dice

Density Laboratory

Determining Density via Water Displacement

Distance-Time Graphs

Distance-Time and Velocity-Time Graphs

1.2.5: Recognize and apply the basic right triangle trigonometric relationships of sine, cosine, and tangent to solve problems.

1.2.5.a: Use sine, cosine or tangent to find unknown distances and angles.

Sine Function

Sine and Cosine Ratios - Activity A

Sine, Cosine and Tangent

Tangent Ratio

Unit Circle

1.2.5.c: Recognize the dependence of definitions of the trigonometric relations (sine, cosine and tangent) on the properties of similar triangles.

Cosine Function

Perimeters and Areas of Similar Figures

Similar Figures - Activity A

Similar Polygons

Sine Function

Sine, Cosine and Tangent

Tangent Function

Tangent Ratio

Unit Circle

1.2.5.d: Use sine, cosine or tangent in a right triangle to solve problems about measure of angles.

Sine Function

Sine and Cosine Ratios - Activity A

Sine, Cosine and Tangent

Tangent Ratio

Unit Circle

1.2.5.e: Interpret and use the identity sin_(theta)+ cos_(theta) = 1 for angles between 0¡ and 90¡; recognize this identity as a special representation of the Pythagorean Theorem.

Geoboard: The Pythagorean Theorem

Pythagorean Theorem - Activity B

Simplifying Trigonometric Expressions

1.3.1: Make and test conjectures about 2-D figures (polygons and circles) and 3-D figures (spheres, right prisms and pyramids, right circular cylinders and cones), or figures constructed from these shapes.

1.3.1.b: Recall and interpret definitions and basic properties of congruent and similar triangles, circles, quadrilaterals, polygons, parallel, perpendicular, and intersecting lines, and associated angle relationships.

Chords and Arcs

Congruence in Right Triangles

Construct Parallel and Perpendicular Lines

Constructing Congruent Segments and Angles

Inscribing Angles

Parallelogram Conditions

Perimeters and Areas of Similar Figures

Proving Triangles Congruent

Similar Figures - Activity A

Similar Polygons

Special Quadrilaterals

1.3.1.c: Analyze properties of circles and spheres.

Chords and Arcs

Classifying Triangles

Inscribing Angles

1.3.2: Use properties of and relationships between 2-D or 3-D figures to draw and justify conclusions about a situation represented with such figures with or without a coordinate system.

1.3.2.a: Inductively generate a conjecture and deductively support it.

Biconditional Statement

Conditional Statement

1.3.2.b: Apply and justify the applicability of transformations, congruence, similarity, ratios, and proportions in problem-solving situations.

Dilations

Perimeters and Areas of Similar Figures

Reflections

Rotations, Reflections and Translations

Similar Figures - Activity A

Similar Polygons

1.3.2.c: Distinguish between area and perimeter of 2-D figures, surface area, and volume of 3-D figures.

Perimeter, Circumference, and Area - Activity B

Prisms and Cylinders - Activity A

Pyramids and Cones - Activity A

Rectangle: Perimeter and Area

Surface and Lateral Area of Prisms and Cylinders

Surface and Lateral Area of Pyramids and Cones

1.3.2.d: Calculate the area and perimeter of circles, triangles, quadrilaterals, and regular polygons.

Area of Parallelograms - Activity A

Circle: Circumference and Area

Perimeter, Circumference, and Area - Activity B

Rectangle: Perimeter and Area

1.3.2.e: Use the Pythagorean Theorem (or distance formula) in 2-D and 3-D situations when appropriate to compute unknown distances.

Distance Formula - Activity A

Geoboard: The Pythagorean Theorem

Pythagorean Theorem - Activity A

Pythagorean Theorem - Activity B

1.3.2.f: Calculate the volume and surface area of spheres, right rectangular prisms, and right circular cylinders.

Prisms and Cylinders - Activity A

Surface and Lateral Area of Prisms and Cylinders

1.3.3: Represent the relevant features of a physical situation using 2-D figures with and without a coordinate system.

1.3.3.a: Use basic 2-D figures such as circles or polygons to represent objects essential to a situation.

1.3.3.d: Solve problems involving the coordinate plane such as the distance between two points, the midpoint of a segment, or slopes of perpendicular or parallel lines.

Construct Parallel and Perpendicular Lines

Distance Formula - Activity A

Geoboard: The Pythagorean Theorem

Pythagorean Theorem - Activity A

Slope - Activity B

1.4.2: Use empirical/ experimental and theoretical probability to investigate, represent, solve, and interpret the solutions to problems involving uncertainty (probability) or counting techniques.

1.4.2.a: Describe and apply the concepts of complementary, mutually exclusive, independent, and compound events.

Compound Independent Events

Compound Independent and Dependent Events

Independent and Dependent Events

1.4.2.b: Describe and apply procedures for computing and comparing theoretical probabilities and empirical/experimental results.

Compound Independent Events

Compound Independent and Dependent Events

Independent and Dependent Events

Polling: City

Probability Simulations

Theoretical and Experimental Probability

1.4.2.c: Describe and apply procedures for counting techniques such as the Fundamental Counting Principle, permutations, and combinations.

Permutations

Permutations and Combinations

1.4.3: Understand and apply the key characteristics of a normal distribution.

1.4.3.a: Know and interpret the key characteristics of a normal distribution such as shape, center (mean), and spread (standard deviation).

1.4.4: Develop and evaluate inferences and predictions that are based on data.

1.4.4.a: Use measures of central tendency (mean, median, mode) and spread (range, quartiles) to summarize data, draw inferences, make predictions, and justify conclusions.

Box-and-Whisker Plots

Describing Data Using Statistics

Line Plots

Mean, Median and Mode

1.4.4.b: Develop and conduct an investigation drawing appropriate conclusions through the use of statistical measures of center, frequency, and spread, combined with graphical displays.

Box-and-Whisker Plots

Line Plots

Mean, Median and Mode

1.4.5: Create and evaluate the suitability of linear models for a data set.

1.4.5.c: Recognize when arguments based on data confuse correlation with causation.

Correlation

Solving Using Trend Lines

1.4.5.d: Recognize that the correlation coefficient is a number between -1 and +1 that measures the strength of the linear relationship between two variables: usually estimate the correlation coefficient (e.g., positive or negative, closer to 0, 0.5, or 1.0) of a scatter plot.

Correlation

Scatter Plots - Activity A

1.4.6: Develop informative tables, plots, and graphic displays to accurately represent and study data.

1.4.6.a: Use and interprets circle graphs, bar graphs, histograms, box-and-whisker plots, scatter plots, stem and leaf, and line graphs.

Box-and-Whisker Plots

Correlation

Histograms

Populations and Samples

Scatter Plots - Activity A

Solving Using Trend Lines

Stem-and-Leaf Plots

1.4.6.b: Analyze data displays to evaluate the reasonableness of claims, reports, studies, and conclusions.

Box-and-Whisker Plots

Histograms

Line Plots

Scatter Plots - Activity A

Stem-and-Leaf Plots

1.4.6.c: Justify the use of appropriate graphical displays to accurately represent and study data.

Box-and-Whisker Plots

Describing Data Using Statistics

Histograms

Line Plots

Scatter Plots - Activity A

Stem-and-Leaf Plots

1.4.6.d: Determine trends, predicted values and possible causes of skewed and clustered distributions.

1.5.1: Represent, analyze, and interpret basic functions (linear, quadratic, cubic, exponential, and reciprocal) and piecewise-defined functions (varying over subintervals of the domain) using and translating among words, tables, graphs, and symbols.

1.5.1.a: Evaluate functions to generate a graph.

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

Quadratic and Absolute Value Functions

Quadratics in Factored Form

Quadratics in Polynomial Form - Activity A

Radical Functions

Rational Functions

Sine Function

Tangent Function

Using Tables, Rules and Graphs

1.5.1.b: Describe relationships between the algebraic features of a function and the features of its graph and/or its tabular representation.

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 Tables, Rules and Graphs

1.5.1.c: Use simple transformations (horizontal and vertical shifts, reflections about axes, shrinks and stretches to create the graphs of new functions using linear, quadratic, and/ or absolute value functions.

Absolute Value with Linear Functions - Activity B

Linear Functions

Quadratic and Absolute Value Functions

Quadratics in Factored Form

Quadratics in Polynomial Form - Activity A

Reflections of a Linear Function

Reflections of a Quadratic Function

Roots of a Quadratic

Translating and Scaling Functions

1.5.1.d: Algebraically construct new functions using addition and subtraction (e.g., profit function).

Addition and Subtraction of Polynomials

1.5.1.e: Describe whether a relation, given verbal, symbolic, tabular, or graphical form is a function.

Introduction to Functions

Linear Functions

1.5.1.f: Identify and analyze the general forms of linear, quadratic, reciprocal (y=k/x), exponential, or trigonometric functions.

Cosine Function

Direct and Inverse Variation

Exponential Functions - Activity A

Quadratic and Absolute Value Functions

Quadratics in Factored Form

Quadratics in Polynomial Form - Activity A

Roots of a Quadratic

Sine Function

Tangent Function

1.5.1.g: Identify patterns in the function's rate of change, identifying intervals of increase, decrease, constancy, and, if possible, relate them to the function's description in words or graphically (using graphing calculator).

Arithmetic Sequences

Arithmetic and Geometric Sequences

Direct Variation

Direct and Inverse Variation

Distance-Time Graphs

Distance-Time and Velocity-Time Graphs

Finding Patterns

Geometric Sequences

Modeling Linear Systems - Activity A

1.5.1.h: Identify y-intercepts and zeros using symbols, graphs, and tables.

Point-Slope Form of a Line - Activity A

Polynomials and Linear Factors

Slope-Intercept Form of a Line - Activity A

Using Tables, Rules and Graphs

1.5.1.i: Identify extrema and trends using graphs and tables.

Linear Functions

Solving Using Trend Lines

Using Tables, Rules and Graphs

1.5.2: Determine an equation or rule for linear and non-linear functions represented in a patterns, tables, graphs, or models.

1.5.2.a: Determine an equation from a set of ordered pairs.

1.5.2.c: Write an equation or rule to describe a sequence.

Arithmetic Sequences

Arithmetic and Geometric Sequences

Geometric Sequences

Using Algebraic Equations

1.5.2.d: Write an equation for a line given a graph of the line.

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

1.5.2.e: Write a rule for a recursive geometric pattern.

Arithmetic Sequences

Arithmetic and Geometric Sequences

Finding Patterns

Geometric Sequences

1.5.2.f: Write an expression, equation, or inequality with two variables representing a linear and/or non-linear model of a real-world problem.

Solving Linear Inequalities using Addition and Subtraction

Solving Linear Inequalities using Multiplication and Division

Using Algebraic Equations

Using Algebraic Expressions

1.5.2.g: Write an equation for a reasonable line to describe a set of bivariate data from a table or scatter plot.

Point-Slope Form of a Line - Activity A

1.5.3: Recognize functional relationships presented in words, tables, graphs and symbols.

1.5.3.a: Recognize whether a relationship given in a symbolic, graphical, or tabular form is a function.

Distance-Time Graphs

Distance-Time and Velocity-Time Graphs

Introduction to Functions

Linear Functions

Using Tables, Rules and Graphs

1.5.3.b: Determine the domain of the function.

Functions Involving Square Roots

1.5.3.c: Understand and interpret function notation, particularly as it relates of graphic displays of data.

Distance-Time Graphs

Distance-Time and Velocity-Time Graphs

1.5.4: Recognize and use appropriate concepts, procedures, definitions, and properties to simplify expressions and solve equations.

1.5.4.b: Explain the distinction between expression and equation.

1.5.4.d: Know what it means to have a solution to an equation.

1.5.4.e: Use properties of equality to solve an equation through a series of equivalent equations.

Modeling One-Step Equations - Activity A

Modeling and Solving Two-Step Equations

Solving Formulas for any Variable

Solving Two-Step Equations

1.5.4.h: Find an equation of a circle given its center and radius and, given an equation of a circle, finds its center and radius.

1.5.5: Combine and simplify algebraic expressions that contain polynomials, rational expressions, radicals, or rational exponents.

1.5.5.a: Find the sum, difference, or product of two polynomials, then simplifies the result.

Addition of Polynomials - Activity A

1.5.5.b: Factor out the greatest common factor from polynomials of any degree.

1.5.5.c: Factor quadratic polynomials with integer coefficients into a product of linear terms.

Factoring Special Products

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

1.5.5.d: Simplify quotients of polynomials given in factored form, or in a form which can be factored.

Addition of Polynomials - Activity A

Dividing Polynomials Using Synthetic Division

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

1.5.6: Solve various types of equations and inequalities numerically, graphically, and algebraically; interpret solutions algebraically and in the context of the problem; distinguish between exact and approximate answers.

1.5.6.a: Solve linear equations in one variable.

Modeling One-Step Equations - Activity A

Modeling and Solving Two-Step Equations

Solving Equations By Graphing Each Side

Solving Two-Step Equations

1.5.6.b: Solve linear inequalities in one variable, including those involving "and" and "or."

Inequalities Involving Absolute Values

Linear Inequalities in Two Variables - Activity A

Solving Linear Inequalities using Addition and Subtraction

Solving Linear Inequalities using Multiplication and Division

Systems of Linear Inequalities (Slope-intercept form) - Activity A

1.5.6.c: Solve systems of linear equations in two variables.

Solving Linear Systems by Graphing

Special Types of Solutions to Linear Systems

Systems of Linear Equations - Activity A

1.5.6.d: Solve linear inequalities in two variables (graphically only).

Inequalities Involving Absolute Values

Linear Inequalities in Two Variables - Activity A

Linear Programming - Activity A

Solving Linear Inequalities using Addition and Subtraction

Solving Linear Inequalities using Multiplication and Division

Systems of Linear Inequalities (Slope-intercept form) - Activity A

1.5.6.f: Use a variety of strategies to solve quadratic equations including those with irrational solutions and recognize when solutions are non-real.

1.5.6.i: Solve rational equations in one variable that can be transformed into an equivalent linear or quadratic equation (limited to monomial or binomial denominators).

Roots of a Quadratic

Solving Equations By Graphing Each Side

1.5.6.j: Solve literal equations (formulas) for a particular variable.

Solving Formulas for any Variable

2.2.4: Use logical reasoning and mathematical knowledge to obtain and justify mathematically correct solutions.

2.2.4.f: Use a variety of approaches - inductive and deductive, estimations, generalizations, formal, and/or informal methods of proof - to justify solutions.

Biconditional Statement

Conditional Statement

Simplifying Trigonometric Expressions

Sum and Difference Identities for Sine and Cosine

3.1.1: Model situations and relationships using a variety of basic functions (linear, quadratic, logarithmic, cubic, exponential, and reciprocal) and piecewise-defined functions.

3.1.1.b: Determine and interprets the meaning of rates of change, intercepts, zeros, extrema, and trends.

Distance-Time Graphs

Distance-Time and Velocity-Time Graphs

Polynomials and Linear Factors

Solving Using Trend Lines

4.2.2: Summarize and interpret mathematical information which may be in oral or written formats.

4.2.2.a: Summarize and interprets many different types of graphs.

Linear Programming - Activity A

5.1.1: Understand the importance of mathematics as a language. (aligns with CRS 3.2) Make connections by using multiple representations--analytic, numeric, and geometric.

5.1.1.b: Use multiple representations to demonstrate understanding of links between math and other disciplines, and real world situations.

5.1.1.d: Transfer mathematical vocabulary, concepts, and procedures to other disciplinary contexts and the real world.

5.1.2: Abstract mathematical models from word problems, geometric problems, and applications.

5.1.2.b: Describe geometric objects and shapes algebraically.

5.3.1: Use mathematical ideas and strategies to analyze relationships within mathematics and in other disciplines and real life situations.

5.3.1.b: Recognize patterns and apply mathematical concepts and procedures in other subject areas and real world situations.

Estimating Population Size

Finding Patterns

Correlation last revised: 1/20/2017