Academic Standards

N.1.a: Show that between any two rational numbers there are an infinite number of rational numbers, and that between any two irrational numbers there are also an infinite number of irrational numbers

Rational Numbers, Opposites, and Absolute Values

N.2.b: Use technology to perform operations (addition, subtraction, multiplication, and division) on numbers written in scientific notation

N.3.a: Use combinatorics (Fundamental Counting Principle, permutations and combinations) to solve problems in real-world contexts

Binomial Probabilities

Permutations and Combinations

P.1.a: Determine when a relation is a function using a table, a graph, or an equation

Introduction to Functions

Linear Functions

P.1.b: Demonstrate the relationship between all representations of linear functions using point-slope, slope-intercept, and standard form of a line

Points, Lines, and Equations

Slope-Intercept Form of a Line

P.1.c: Represent linear, quadratic, absolute value, power, exponential, logarithmic, rational, trigonometric (sine and cosine), and step functions in a table, graph, and equation and convert from one representation to another

Compound Interest

Exponential Functions

General Form of a Rational Function

Introduction to Exponential Functions

Linear Functions

Logarithmic Functions

Points, Lines, and Equations

Quadratics in Factored Form

Quadratics in Polynomial Form

Quadratics in Vertex Form

Rational Functions

Slope-Intercept Form of a Line

Translating and Scaling Functions

P.1.d: Determine the inverse (expressed graphically or in tabular form) of a function from a graph or table

P.1.e: Categorize sequences as arithmetic, geometric, or neither and develop formulas for the general terms related to arithmetic and geometric sequences

Arithmetic Sequences

Geometric Sequences

P.2.a: Evaluate a function at a given point in its domain given an equation (including function notation), a table, and a graph

P.2.b: Identify the domain and range of a function given an equation (including function notation), a table, and a graph

Exponential Functions

Introduction to Functions

Logarithmic Functions

Radical Functions

P.2.c: Identify intercepts, zeros (or roots), maxima, minima, and intervals of increase and decrease, and asymptotes of a function given an equation (including function notation), a table, and a graph

Absolute Value with Linear Functions

Cat and Mouse (Modeling with Linear Systems)

Exponential Functions

General Form of a Rational Function

Introduction to Exponential Functions

Linear Functions

Logarithmic Functions

Points, Lines, and Equations

Quadratics in Factored Form

Quadratics in Polynomial Form

Quadratics in Vertex Form

Roots of a Quadratic

Slope-Intercept Form of a Line

P.2.d: Make qualitative statements about the rate of change of a function, based on its graph or table

Cat and Mouse (Modeling with Linear Systems)

Translating and Scaling Functions

P.3.a: Apply transformations (translation, reflection, dilation) to a parent function, f(x)

Absolute Value with Linear Functions

Exponential Functions

Translating and Scaling Functions

Translating and Scaling Sine and Cosine Functions

P.3.b: Interpret the results of these transformations verbally, graphically, and symbolically

Solving Equations on the Number Line

Using Algebraic Expressions

P.4.a: Perform and justify steps in generating equivalent expressions by identifying properties used including the commutative, associative, inverse, identity, and distributive properties

Equivalent Algebraic Expressions I

Equivalent Algebraic Expressions II

Simplifying Algebraic Expressions I

Simplifying Algebraic Expressions II

P.4.c: Solve equations for one variable in terms of the others

Solving Formulas for any Variable

P.5.a: Find solutions to quadratic and cubic equations and inequalities by using appropriate algebraic methods such as factoring, completing the square, graphing or using the quadratic formula

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

Quadratic Inequalities

Quadratics in Factored Form

Quadratics in Polynomial Form

Quadratics in Vertex Form

Roots of a Quadratic

P.5.b: Find solutions to equations involving power, exponential, rational and radical functions

Compound Interest

Exponential Functions

Radical Functions

P.5.c: Solve systems of linear equations and inequalities with two variables

Cat and Mouse (Modeling with Linear Systems)

Linear Programming

Solving Equations by Graphing Each Side

Solving Linear Systems (Matrices and Special Solutions)

Solving Linear Systems (Slope-Intercept Form)

Solving Linear Systems (Standard Form)

Systems of Linear Inequalities (Slope-intercept form)

P.6.a: Represent, solve, and interpret problems in various contexts using linear, quadratic, and exponential function

Addition and Subtraction of Functions

Arithmetic Sequences

Compound Interest

Exponential Functions

Introduction to Exponential Functions

Linear Functions

Logarithmic Functions

Points, Lines, and Equations

Quadratics in Factored Form

Quadratics in Polynomial Form

Quadratics in Vertex Form

Slope-Intercept Form of a Line

Translating and Scaling Functions

P.6.b: Represent, solve, and interpret problems involving direct and inverse variations and a combination of direct and inverse variation

P.6.c: Analyze the impact of interest rates on a personal financial plan

D.1.a: Formulate appropriate research questions that can be answered with statistical analysis

Describing Data Using Statistics

Real-Time Histogram

D.1.b: Determine appropriate data collection methods to answer a research question

Describing Data Using Statistics

D.1.c: Explain how data might be analyzed to provide answers to a research question

Box-and-Whisker Plots

Polling: City

Real-Time Histogram

D.2.a: Identify the characteristics of a well-designed and well-conducted survey

Correlation

Polling: City

Polling: Neighborhood

D.2.b: Identify the characteristics of a well-designed and well-conducted experiment

D.3.a: Identify and choose appropriate ways to summarize numerical or categorical data using tables, graphical displays, and numerical summary statistics (describing shape, center and spread) and accounting for outliers when appropriate

Box-and-Whisker Plots

Least-Squares Best Fit Lines

Mean, Median, and Mode

Reaction Time 1 (Graphs and Statistics)

Stem-and-Leaf Plots

D.3.b: Define and explain how sampling distributions (developed through simulation) are used to describe the sample-to-sample variability of sample statistics

Polling: City

Populations and Samples

D.3.d: When the relationship between two numerical variables is reasonably linear, apply the least-squares criterion for line fitting, use Pearson's correlation coefficient as a measure of strength, and interpret the slope and y-intercept in the context of the problem

Correlation

Least-Squares Best Fit Lines

Solving Using Trend Lines

D.4.a: Define and explain the meaning of significance (both practical and statistical)

Polling: City

Polling: Neighborhood

Populations and Samples

D.4.c: Determine the margin of error associated with an estimate of a population characteristic

Polling: City

Polling: Neighborhood

D.5.b: Apply and solve problems using the concepts of independence and conditional probability

Binomial Probabilities

Independent and Dependent Events

Theoretical and Experimental Probability

D.5.d: Evaluate and interpret probabilities using a normal distribution

D.5.e: Find and interpret the expected value and standard deviation of a discrete random variable X

S.1.b: Justify, interpret, and apply the use of formulas for the surface area, and volume of cones, pyramids, and spheres including real-world situations

Pyramids and Cones

Surface and Lateral Areas of Pyramids and Cones

S.1.c: Solve for unknown quantities in relationships involving perimeter, area, surface area, and volume

Area of Parallelograms

Area of Triangles

Circumference and Area of Circles

Perimeter and Area of Rectangles

Prisms and Cylinders

Pyramids and Cones

Surface and Lateral Areas of Prisms and Cylinders

Surface and Lateral Areas of Pyramids and Cones

S.2.a: Classify polygons according to their similarities and differences

Classifying Quadrilaterals

Classifying Triangles

Parallelogram Conditions

Special Parallelograms

S.2.c: Know and apply properties of angles including corresponding, exterior, interior, vertical, complementary, and supplementary angles to solve problems. Justify the results using two-column proofs, paragraph proofs, flow charts, or illustrations

Investigating Angle Theorems

Triangle Angle Sum

S.3.b: Represent transformations (reflection, translation, rotation, and dilation) using Cartesian coordinates

Dilations

Rotations, Reflections, and Translations

Translations

S.3.c: Develop arguments to establish what remains invariant and what changes after a transformation (reflection, translation, rotation, and dilations). Justify these conjectures using two-column proofs, paragraph proofs, flow charts, and/or illustrations

S.4.a: Apply right triangle trigonometry (sine, cosine, and tangent) to find indirect measures of lengths and angles

Cosine Function

Sine Function

Sine, Cosine, and Tangent Ratios

Tangent Function

S.4.b: Apply the Pythagorean theorem and its converse to solve real-world problems

Distance Formula

Pythagorean Theorem

Pythagorean Theorem with a Geoboard

S.4.c: Determine the midpoint of a line segment and the distance between two points in the Cartesian coordinate plane

Points in the Coordinate Plane

Correlation last revised: 4/4/2018

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