MA 12.1: Students will communicate number sense concepts using multiple representations to reason, solve problems, and make connections within mathematics and across disciplines.

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

 Rational Numbers, Opposites, and Absolute Values

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))

 Fractions with Unlike Denominators
 Square Roots

MA 12.1.3: Students will compute fluently and accurately using appropriate strategies and tools.

MA 12.1.3.c: Multiply and divide numbers using scientific notation

 Unit Conversions

MA 12.2: Students will communicate geometric concepts and measurement concepts using multiple representations to reason, solve problems, and make connections within mathematics and across disciplines.

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

MA 12.2.1.a: Identify and explain the necessity of and give examples of definitions and theorems

 Biconditional Statements

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

 Congruence in Right Triangles
 Constructing Congruent Segments and Angles
 Parallel, Intersecting, and Skew Lines
 Perimeters and Areas of Similar Figures
 Proving Triangles Congruent
 Similar Figures
 Similarity in Right Triangles

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

 Circles
 Cosine Function
 Distance Formula
 Pythagorean Theorem
 Pythagorean Theorem with a Geoboard
 Sine Function
 Sine, Cosine, and Tangent Ratios
 Surface and Lateral Areas of Pyramids and Cones
 Tangent Function

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
 Circles
 Inscribed Angles

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)

 Circles

MA 12.2.2.b: Apply the midpoint formula

 Circles

MA 12.2.2.c: Apply the distance formula

 Circles
 Distance Formula

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

 Isosceles and Equilateral Triangles
 Parallelogram Conditions
 Pythagorean Theorem
 Pythagorean Theorem with a Geoboard
 Special Parallelograms
 Triangle Angle Sum
 Triangle Inequalities

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

 Rotations, Reflections, and Translations
 Translations

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

MA 12.2.5.c: Convert between various units of area and volume, such as square feet to square yards

 Unit Conversions

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

 Pyramids and Cones
 Surface and Lateral Areas of Prisms and Cylinders
 Surface and Lateral Areas of Pyramids and Cones

MA 12.3: Students will communicate algebraic concepts using multiple representations to reason, solve problems, and make connections within mathematics and across disciplines.

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)

 Absolute Value Equations and Inequalities
 Absolute Value with Linear Functions
 Arithmetic Sequences
 Compound Interest
 Exponential Functions
 Geometric Sequences
 Introduction to Exponential Functions
 Introduction to Functions
 Linear Functions
 Points, Lines, and Equations
 Quadratics in Factored Form
 Quadratics in Polynomial Form
 Quadratics in Vertex Form
 Radical Functions

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

 Exponential Functions
 Introduction to Functions
 Logarithmic Functions
 Radical Functions

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

 Cat and Mouse (Modeling with Linear Systems)
 Point-Slope Form of a Line
 Points, Lines, and Equations
 Slope-Intercept Form of a Line
 Standard Form of a Line

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

 Absolute Value with Linear Functions
 Graphs of Polynomial Functions
 Linear Functions
 Slope-Intercept Form of a Line

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

 Absolute Value with Linear Functions
 Arithmetic Sequences
 Compound Interest
 Exponential Functions
 Linear Functions
 Points, Lines, and Equations
 Quadratics in Vertex Form
 Slope-Intercept Form of a Line

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

 Exponential Functions
 Translating and Scaling Functions

MA 12.3.1.g: Graph and interpret linear inequalities

 Exploring Linear Inequalities in One Variable
 Linear Inequalities in Two Variables
 Solving Linear Inequalities in One Variable
 Systems of Linear Inequalities (Slope-intercept form)

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

 Logarithmic Functions

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

 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)

 Quadratics in Polynomial Form
 Slope-Intercept Form of a Line
 Solving Linear Systems (Matrices and Special Solutions)
 Solving Linear Systems (Standard Form)
 Systems of Linear Inequalities (Slope-intercept form)
 Using Algebraic Expressions

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

 Linear Functions

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

 Linear Functions

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

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

 Dividing Exponential Expressions
 Multiplying Exponential Expressions
 Simplifying Algebraic Expressions I
 Simplifying Algebraic Expressions II

MA 12.3.3.c: Add and subtract polynomials

 Addition and Subtraction of Functions
 Addition of Polynomials

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
 Modeling the Factorization of x2+bx+c

MA 12.3.3.e: Factor polynomials

 Factoring Special Products
 Modeling the Factorization of ax2+bx+c
 Modeling the Factorization of x2+bx+c

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

 Compound Inequalities
 Exploring Linear Inequalities in One Variable
 Linear Inequalities in Two Variables
 Modeling One-Step Equations
 Modeling and Solving Two-Step Equations
 Solving Algebraic Equations II
 Solving Equations by Graphing Each Side
 Solving Linear Inequalities in One Variable
 Solving Two-Step Equations
 Systems of Linear Inequalities (Slope-intercept form)

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

 Solving Algebraic Equations II

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

 Modeling the Factorization of x2+bx+c
 Quadratics in Factored Form
 Quadratics in Polynomial Form
 Quadratics in Vertex Form
 Roots of a Quadratic

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

 Arithmetic 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 Functions

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

 Solving Formulas for any Variable

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

 Cat and Mouse (Modeling with Linear Systems)
 Solving Equations by Graphing Each Side
 Solving Linear Systems (Matrices and Special Solutions)
 Solving Linear Systems (Slope-Intercept Form)
 Solving Linear Systems (Standard Form)

MA 12.4: Students will communicate data analysis/probability concepts using multiple representations to reason, solve problems, and make connections within mathematics and across disciplines.

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.a: Interpret data represented by the normal distribution and formulate conclusions

 Polling: City

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

 Box-and-Whisker Plots
 Describing Data Using Statistics
 Mean, Median, and Mode
 Populations and Samples
 Reaction Time 1 (Graphs and Statistics)
 Sight vs. Sound Reactions
 Stem-and-Leaf Plots

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

 Polling: City
 Populations and Samples
 Reaction Time 1 (Graphs and Statistics)

MA 12.4.1.d: Describe the shape and determine spread (variance, standard deviation) and outliers of a data set

 Describing Data Using Statistics
 Least-Squares Best Fit Lines
 Mean, Median, and Mode
 Polling: City
 Real-Time Histogram
 Sight vs. Sound Reactions

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

 Correlation
 Least-Squares Best Fit Lines
 Solving Using Trend Lines
 Trends in Scatter Plots

MA 12.4.1.g: Explain the impact of sampling methods, bias, and the phrasing of questions asked during data collection and the conclusions that can rightfully be made

 Polling: City
 Polling: Neighborhood

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

 Box-and-Whisker Plots
 Describing Data Using Statistics
 Mean, Median, and Mode
 Reaction Time 1 (Graphs and Statistics)

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

 Correlation
 Least-Squares Best Fit Lines
 Solving Using Trend Lines

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

 Correlation

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

 Polling: City
 Probability Simulations
 Theoretical and Experimental Probability

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

 Independent and Dependent Events
 Theoretical and Experimental Probability

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

 Binomial Probabilities
 Permutations and Combinations

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.