Academic Standards

MA 12.1.1: Students will represent and show relationships among real numbers.

MA 12.1.1.b: Compare, contrast and apply the properties of numbers and the real number system, including rational, irrational, imaginary, and complex numbers

Points in the Complex Plane - Activity A

MA 12.1.2: Students will demonstrate the meaning and effects of arithmetic operations with real numbers.

MA 12.1.2.a: Use drawings, words, and symbols to explain the effects of such operations as multiplication and division, and computing positive powers and roots on the magnitude of quantities (e.g., if you take the square root of a number, will the result always be smaller than the original number? (e.g., square root of 1/4 = 1/2))

Dividing Exponential Expressions

Exponents and Power Rules

Multiplying Exponential Expressions

Using Algebraic Equations

Using Algebraic Expressions

MA 12.1.2.b: Use drawings, words, and symbols to explain that the distance between two numbers on the number line is the absolute value of their difference

Using Algebraic Equations

Using Algebraic Expressions

MA 12.2.1: Students will analyze characteristics, properties, and relationships among geometric shapes and objects.

MA 12.2.1.b: Analyze properties and relationships among classes of two and three dimensional geometric objects using inductive reasoning and counterexamples

Classifying Quadrilaterals - Activity B

Classifying Triangles

Parallelogram Conditions

Polygon Angle Sum - Activity A

Prisms and Cylinders - Activity A

Special Quadrilaterals

Triangle Angle Sum - Activity A

MA 12.2.1.c: State and prove geometric theorems using deductive reasoning (e.g., parallel lines with transversals, congruent triangles, similar triangles)

Biconditional Statement

Conditional Statement

Simplifying Trigonometric Expressions

MA 12.2.1.d: Apply geometric properties to solve problems (e.g., parallel lines, line transversals, similar triangles, congruent triangles, proportions)

Classifying Quadrilaterals - Activity B

Congruence in Right Triangles

Investigating Angle Theorems - Activity A

Parallelogram Conditions

Proving Triangles Congruent

Similar Figures - Activity A

Similar Polygons

Special Quadrilaterals

MA 12.2.1.e: Identify and apply right triangle relationships (e.g., sine, cosine, tangent, special right triangles, converse of Pythagorean Theorem)

Distance Formula - Activity A

Geoboard: The Pythagorean Theorem

Pythagorean Theorem - Activity A

Pythagorean Theorem - Activity B

Sine Function

Sine and Cosine Ratios - Activity A

Sine, Cosine and Tangent

Tangent Ratio

MA 12.2.1.g: Know the definitions and basic properties of a circle and use them to prove basic theorems and solve problems

Chords and Arcs

Classifying Triangles

Inscribing Angles

Parallelogram Conditions

Simplifying Trigonometric Expressions

MA 12.2.2: Student will use coordinate geometry to analyze and describe relationships in the coordinate plane.

MA 12.2.2.a: Use coordinate geometry to analyze geometric situations (e.g., parallel lines, perpendicular lines, circle equations)

MA 12.2.2.c: Apply the distance formula

Distance Formula - Activity A

Geoboard: The Pythagorean Theorem

Pythagorean Theorem - Activity A

Pythagorean Theorem - Activity B

MA 12.2.2.d: Prove special types of triangles and quadrilaterals (e.g., right triangles, isosceles trapezoid, parallelogram, rectangle, square)

Area of Parallelograms - Activity A

Classifying Quadrilaterals - Activity B

Classifying Triangles

Isosceles and Equilateral Triangles

Parallelogram Conditions

Triangle Angle Sum - Activity A

MA 12.2.3: Students will apply and analyze transformations.

MA 12.2.3.a: Explain and justify the effects of simple transformations on the ordered pairs of two-dimensional shapes

Dilations

Reflections

Rotations, Reflections and Translations

Translations

MA 12.2.3.b: Perform and describe multiple transformations

Dilations

Reflections

Rotations, Reflections and Translations

MA 12.2.4: Students will use visualization, spatial reasoning, and geometric modeling to solve problems.

MA 12.2.4.a: Sketch and draw appropriate representations of geometric objects using ruler, protractor, or technology

3D and Orthographic Views - Activity A

Classifying Quadrilaterals - Activity B

Surface and Lateral Area of Prisms and Cylinders

Surface and Lateral Area of Pyramids and Cones

MA 12.2.4.b: Use geometric models to visualize, describe, and solve problems (e.g., find the height of a tree; find the amount of paint needed for a room; scale model)

3D and Orthographic Views - Activity A

MA 12.2.5: Students will apply the units, systems, and formulas to solve problems.

MA 12.2.5.a: Use strategies to find surface area and volume of complex objects

Surface and Lateral Area of Prisms and Cylinders

MA 12.2.5.f: Determine surface area and volume of three-dimensional objects (e.g., spheres, cones, pyramids)

Pyramids and Cones - Activity A

Surface and Lateral Area of Prisms and Cylinders

Surface and Lateral Area of Pyramids and Cones

MA 12.2.5.g: Know that the effect of a scale factor k on length, area and volume is to multiply each by k, k² and k³, respectively

MA 12.3.1: Students will generalize, represent, and analyze relationships using algebraic symbols.

MA 12.3.1.a: Represent, interpret, and analyze functions with graphs, tables, and algebraic notation and convert among these representations (e.g., linear, non-linear)

Cosine Function

Cubic Function Activity

Distance-Time Graphs

Exponential Functions - Activity A

Fourth-Degree Polynomials - Activity A

Function Machines 1 (Functions and Tables)

Function Machines 2 (Functions, Tables, and Graphs)

Function Machines 3 (Functions and Problem Solving)

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

Rational Functions

Sine Function

Tangent Function

Using Tables, Rules and Graphs

MA 12.3.1.b: Identify domain and range of functions represented in either symbolic or graphical form (e.g., linear, non-linear)

Function Machines 1 (Functions and Tables)

Function Machines 2 (Functions, Tables, and Graphs)

Function Machines 3 (Functions and Problem Solving)

Introduction to Functions

Linear Functions

Using Tables, Rules and Graphs

MA 12.3.1.c: Identify the slope and intercepts of a linear relationship from an equation or graph

Defining a Line with Two Points

Function Machines 2 (Functions, Tables, and Graphs)

Linear Functions

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

MA 12.3.1.d: Identify characteristics of linear and non-linear functions

Function Machines 1 (Functions and Tables)

Function Machines 2 (Functions, Tables, and Graphs)

Function Machines 3 (Functions and Problem Solving)

Linear Functions

Using Tables, Rules and Graphs

MA 12.3.1.e: Graph linear and non-linear functions

Function Machines 1 (Functions and Tables)

Function Machines 2 (Functions, Tables, and Graphs)

Function Machines 3 (Functions and Problem Solving)

Introduction to Functions

Linear Functions

Point-Slope Form of a Line - Activity A

Slope-Intercept Form of a Line - Activity A

Using Tables, Rules and Graphs

MA 12.3.1.f: Compare and analyze the rate of change by using ordered pairs, tables, graphs, and equations

Distance-Time Graphs

Function Machines 2 (Functions, Tables, and Graphs)

MA 12.3.1.g: Graph and interpret linear inequalities

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

MA 12.3.1.h: Represent, interpret, and analyze functions and their inverses

Cosine Function

Distance-Time Graphs

Fourth-Degree Polynomials - Activity A

Function Machines 1 (Functions and Tables)

Function Machines 2 (Functions, Tables, and Graphs)

Function Machines 3 (Functions and Problem Solving)

Logarithmic Functions - Activity A

Logarithmic Functions: Translating and Scaling

Quadratics in Factored Form

Quadratics in Polynomial Form - Activity A

Using Tables, Rules and Graphs

MA 12.3.1.i: Determine if a relation is a function

Function Machines 1 (Functions and Tables)

Function Machines 2 (Functions, Tables, and Graphs)

Function Machines 3 (Functions and Problem Solving)

Introduction to Functions

Linear Functions

MA 12.3.2: Students will model and analyze quantitative relationships.

MA 12.3.2.a: Model contextualized problems using various representations (e.g., graphs, tables, one variable equalities, one variable inequalities, linear equations in slope intercept form, inequalities in slope intercept form, system of linear equations with two variables)

Linear Inequalities in Two Variables - Activity A

Modeling Linear Systems - Activity A

Slope-Intercept Form of a Line - Activity A

Using Tables, Rules and Graphs

MA 12.3.2.b: Represent a variety of quantitative relationships using linear equations and one variable inequalities

Linear Functions

Slope-Intercept Form of a Line - Activity A

MA 12.3.2.c: Analyze situations to determine the type of algebraic relationship (e.g., linear, nonlinear)

Linear Functions

Slope-Intercept Form of a Line - Activity A

MA 12.3.2.d: Model contextualized problems using various representations for non-linear functions (e.g., quadratic, exponential, square root, and absolute value)

Exponential Functions - Activity A

MA 12.3.3: Students will represent and solve equations and inequalities.

MA 12.3.3.a: Explain/apply the reflexive, symmetric, and transitive properties of equality

Modeling and Solving Two-Step Equations

Solving Formulas for any Variable

Solving Two-Step Equations

MA 12.3.3.b: Simplify algebraic expressions involving exponents (e.g., (3x to the 4th power)²)

Dividing Exponential Expressions

Multiplying Exponential Expressions

MA 12.3.3.c: Add and subtract polynomials

Addition of Polynomials - Activity A

MA 12.3.3.d: Multiply and divide polynomials (e.g., divide x³ ? 8 by x ? 2, divide x to the 4th power ? 5x³ ? 2x by x²)

Dividing Polynomials Using Synthetic Division

MA 12.3.3.e: Factor polynomials

Factoring Special Products

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

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

MA 12.3.3.f: Identify and generate equivalent forms of linear equations

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

Using Tables, Rules and Graphs

MA 12.3.3.g: Solve linear equations and inequalities including absolute value

Inequalities Involving Absolute Values

Modeling and Solving Two-Step Equations

Solving Equations By Graphing Each Side

Solving Linear Inequalities using Addition and Subtraction

Solving Linear Inequalities using Multiplication and Division

Solving Two-Step Equations

MA 12.3.3.h: Identify and explain the properties used in solving equations and inequalities

Modeling and Solving Two-Step Equations

Solving Two-Step Equations

MA 12.3.3.i: Solve quadratic equations (e.g., factoring, graphing, quadratic formula)

Factoring Special Products

Roots of a Quadratic

MA 12.3.3.k: Multiply, divide, and simplify rational expressions

Dividing Exponential Expressions

MA 12.3.3.l: Evaluate polynomial and rational expressions and expressions containing radicals and absolute values at specified values of their variables

Dividing Exponential Expressions

MA 12.3.3.m: Derive and use the formulas for the general term and summation of finite arithmetic and geometric series

Arithmetic Sequences

Arithmetic and Geometric Sequences

Geometric Sequences

MA 12.3.3.n: Combine functions by composition, as well as by addition, subtraction, multiplication, and division

Addition and Subtraction of Polynomials

Function Machines 1 (Functions and Tables)

Function Machines 2 (Functions, Tables, and Graphs)

Function Machines 3 (Functions and Problem Solving)

MA 12.3.3.o: Solve an equation involving several variables for one variable in terms of the others

Modeling and Solving Two-Step Equations

Solving Formulas for any Variable

Solving Two-Step Equations

MA 12.3.3.p: Analyze and solve systems of two linear equations in two variables algebraically and graphically

Modeling Linear Systems - Activity A

Solving Linear Systems by Graphing

Special Types of Solutions to Linear Systems

Systems of Linear Equations - Activity A

MA 12.4.1: Students will formulate a question and design a survey or an experiment in which data is collected and displayed in a variety of formats, then select and use appropriate statistical methods to analyze the data.

MA 12.4.1.b: Compute, identify, and interpret measures of central tendency (mean, median, mode) when provided a graph or data set

Describing Data Using Statistics

Line Plots

Mean, Median and Mode

Populations and Samples

MA 12.4.1.c: Explain how sample size and transformations of data affect measures of central tendency

Line Plots

Mean, Median and Mode

Populations and Samples

MA 12.4.1.f: Create scatter plots, analyze patterns, and describe relationships in paired data

Correlation

Scatter Plots - Activity A

Solving Using Trend Lines

MA 12.4.2: Students will develop and evaluate inferences to make predictions.

MA 12.4.2.a: Compare data sets and evaluate conclusions using graphs and summary statistics

Line Plots

Mean, Median and Mode

Populations and Samples

MA 12.4.2.c: Develop linear equations for linear models to predict unobserved outcomes using regression line and correlation coefficient

MA 12.4.2.d: Recognize when arguments based on data confuse correlation with causation

MA 12.4.3: Students will apply and analyze concepts of probability.

MA 12.4.3.a: Construct a sample space and a probability distribution

MA 12.4.3.b: Identify dependent and independent events and calculate their probabilities

Compound Independent Events

Compound Independent and Dependent Events

MA 12.4.3.c: Use the appropriate counting techniques to determine the probability of an event (e.g., combinations, permutations)

Binomial Probabilities

Permutations

Permutations and Combinations

MA 12.4.3.e: Determine the relative frequency of a specified outcome of an event to estimate the probability of the outcome

Geometric Probability - Activity A

Correlation last revised: 3/29/2010

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