10: Mathematics

10.N: Number Sense and Operations

10.N.1: Identify and use the properties of operations on real numbers, including the associative, commutative, and distributive properties; the existence of the identity and inverse elements for addition and multiplication; the existence of nth roots of positive

 Equivalent Algebraic Expressions I
 Equivalent Algebraic Expressions II
 Simplifying Algebraic Expressions I
 Square Roots

10.N.3: Find the approximate value for solutions to problems involving square roots and cube roots without the use of a calculator, e.g. the square root of (3²-1) is approximately equal to 2.8.

 Square Roots

10.P: Patterns, Relations, and Algebra

10.P.1: Describe, complete, extend, analyze, generalize, and create a wide variety of patterns, including iterative, recursive (e.g., Fibonacci Numbers), linear, quadratic, and exponential functional relationships.

 Arithmetic Sequences
 Arithmetic and Geometric Sequences
 Finding Patterns
 Function Machines 1 (Functions and Tables)
 Function Machines 2 (Functions, Tables, and Graphs)
 Function Machines 3 (Functions and Problem Solving)
 Geometric Sequences

10.P.2: Demonstrate an understanding of the relationship between various representations of a line. Determine a line's slope and x- and y-intercepts from its graph or from a linear equation that represents the line. Find a linear equation describing a line from a graph or a geometric description of the line, e.g., by using the "point-slope" or "slope y-intercept" formulas. Explain the significance of a positive, negative, zero, or undefined slope.

 Linear Inequalities in Two Variables
 Point-Slope Form of a Line
 Points, Lines, and Equations
 Slope-Intercept Form of a Line
 Standard Form of a Line

10.P.3: Add, subtract, and multiply polynomials. Divide polynomials by monomials.

 Addition and Subtraction of Functions
 Addition of Polynomials
 Dividing Polynomials Using Synthetic Division
 Modeling the Factorization of x2+bx+c

10.P.4: Demonstrate facility in symbolic manipulation of polynomial and rational expressions by rearranging and collecting terms; factoring (e.g., a² - b² = (a + b)(a - b), x² + 10x + 21 = (x + 3)(x + 7), 5x to the 4th + 10x³ - 5x² = 5x² (x² + 2x - 1)); identifying and canceling common factors in rational expressions; and applying the properties of positive integer exponents.

 Addition of Polynomials
 Factoring Special Products
 Modeling the Factorization of ax2+bx+c
 Simplifying Algebraic Expressions II

10.P.5: Find solutions to quadratic equations (with real roots) by factoring, completing the square, or using the quadratic formula. Demonstrate an understanding of the equivalence of the methods.

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

10.P.6: Solve equations and inequalities including those involving absolute value of linear expressions (e.g., |x - 2| > 5) and apply to the solution of problems.

 Absolute Value Equations and Inequalities
 Absolute Value with Linear Functions
 Compound Inequalities
 Exploring Linear Inequalities in One Variable
 Linear Inequalities in Two Variables
 Modeling One-Step Equations
 Modeling and Solving Two-Step Equations
 Point-Slope Form of a Line
 Solving Algebraic Equations II
 Solving Equations by Graphing Each Side
 Solving Linear Inequalities in One Variable
 Standard Form of a Line
 Systems of Linear Inequalities (Slope-intercept form)

10.P.7: Solve everyday problems that can be modeled using linear, reciprocal, quadratic, or exponential functions. Apply appropriate tabular, graphical, or symbolic methods to the solution. Include compound interest, and direct and inverse variation problems. Use technology when appropriate.

 Compound Interest
 Direct and Inverse Variation

10.P.8: Solve everyday problems that can be modeled using systems of linear equations or inequalities. Apply algebraic and graphical methods to the solution. Use technology when appropriate. Include mixture, rate, and work problems.

 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)

10.G: Geometry

10.G.1: Identify figures using properties of sides, angles, and diagonals. Identify the figures' type(s) of symmetry.

 Classifying Quadrilaterals
 Classifying Triangles
 Parallelogram Conditions
 Special Parallelograms

10.G.4: Apply congruence and similarity correspondences (e.g., delta ABC is approximately equal to delta XYZ) and properties of the figures to find missing parts of geometric figures, and provide logical justification.

 Constructing Congruent Segments and Angles

10.G.5: Solve simple triangle problems using the triangle angle sum property and/or the Pythagorean theorem.

 Circles
 Cosine Function
 Distance Formula
 Isosceles and Equilateral Triangles
 Polygon Angle Sum
 Pythagorean Theorem
 Pythagorean Theorem with a Geoboard
 Sine Function
 Surface and Lateral Areas of Pyramids and Cones
 Tangent Function
 Triangle Angle Sum

10.G.6: Use the properties of special triangles (e.g., isosceles, equilateral, 30°-60°-90º, 45°-45°-90°) to solve problems.

 Classifying Triangles
 Concurrent Lines, Medians, and Altitudes
 Cosine Function
 Isosceles and Equilateral Triangles
 Pythagorean Theorem
 Pythagorean Theorem with a Geoboard
 Sine Function
 Tangent Function
 Triangle Inequalities

10.G.9: Draw the results, and interpret transformations on figures in the coordinate plane, e.g., translations, reflections, rotations, scale factors, and the results of successive transformations. Apply transformations to the solutions of problems.

 Dilations
 Rotations, Reflections, and Translations
 Translations

10.G.10: Demonstrate the ability to visualize solid objects and recognize their projections and cross sections.

 3D and Orthographic Views

10.M: Measurement

10.M.1: Calculate perimeter, circumference, and area of common geometric figures such as parallelograms, trapezoids, circles, and triangles.

 Area of Parallelograms
 Area of Triangles
 Perimeter and Area of Rectangles
 Perimeters and Areas of Similar Figures

10.M.2: Given the formula, find the lateral area, surface area, and volume of prisms, pyramids, spheres, cylinders, and cones, e.g., find the volume of a sphere with a specified surface area.

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

10.D: Data Analysis, Statistics, and Probability

10.D.1: Select, create, and interpret an appropriate graphical representation (e.g., scatterplot, table, stem-and-leaf plots, box-and-whisker plots, circle graph, line graph, and line plot) for a set of data and use appropriate statistics (e.g., mean, median, range, and mode) to communicate information about the data. Use these notions to compare different sets of data.

 Describing Data Using Statistics
 Mean, Median, and Mode
 Reaction Time 1 (Graphs and Statistics)
 Real-Time Histogram
 Stem-and-Leaf Plots

10.D.2: Approximate a line of best fit (trend line) given a set of data (e.g., scatterplot). Use technology when appropriate.

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

10.D.3: Describe and explain how the relative sizes of a sample and the population affect the validity of predictions from a set of data.

 Polling: City

AI: Algebra I

AI.N: Number Sense and Operations

AI.N.1: Identify and use the properties of operations on real numbers, including the associative, commutative, and distributive properties; the existence of the identity and inverse elements for addition and multiplication; the existence of nth roots of positive real numbers for any positive integer n; the inverse relationship between taking the nth root of and the nth power of a positive real number; and the density of the set of rational numbers in the set of real numbers.

 Equivalent Algebraic Expressions I
 Equivalent Algebraic Expressions II
 Rational Numbers, Opposites, and Absolute Values
 Simplifying Algebraic Expressions I
 Square Roots

AI.N.3: Find the approximate value for solutions to problems involving square roots and cube roots without the use of a calculator, e.g., the square root of 3²-1 is approximately equal to 2.8

 Square Roots

AI.P: Patterns, Relations, and Algebra

AI.P.1: Describe, complete, extend, analyze, generalize, and create a wide variety of patterns, including iterative, recursive (e.g., Fibonacci Numbers), linear, quadratic, and exponential functional relationships.

 Arithmetic Sequences
 Arithmetic and Geometric Sequences
 Finding Patterns
 Function Machines 1 (Functions and Tables)
 Function Machines 2 (Functions, Tables, and Graphs)
 Function Machines 3 (Functions and Problem Solving)
 Geometric Sequences

AI.P.3: Demonstrate an understanding of relations and functions. Identify the domain, range, dependent, and independent variables of functions.

 Function Machines 3 (Functions and Problem Solving)
 Introduction to Functions
 Linear Functions
 Logarithmic Functions
 Radical Functions

AI.P.4: Translate between different representations of functions and relations: graphs, equations, point sets, and tabular.

 Absolute Value Equations and Inequalities
 Function Machines 1 (Functions and Tables)
 Function Machines 2 (Functions, Tables, and Graphs)
 Introduction to Functions
 Linear Functions
 Points, Lines, and Equations
 Quadratics in Polynomial Form

AI.P.5: Demonstrate an understanding of the relationship between various representations of a line. Determine a line's slope and x- and y-intercepts from its graph or from a linear equation that represents the line. Find a linear equation describing a line from a graph or a geometric description of the line, e.g., by using the "point-slope" or "slope y-intercept" formulas. Explain the significance of a positive, negative, zero, or undefined slope.

 Linear Inequalities in Two Variables
 Point-Slope Form of a Line
 Points, Lines, and Equations
 Slope-Intercept Form of a Line
 Standard Form of a Line

AI.P.6: Find linear equations that represent lines either perpendicular or parallel to a given line and through a point, e.g., by using the "point-slope" form of the equation.

 Point-Slope Form of a Line
 Points, Lines, and Equations
 Standard Form of a Line

AI.P.7: Add, subtract, and multiply polynomials. Divide polynomials by monomials.

 Addition and Subtraction of Functions
 Addition of Polynomials
 Dividing Polynomials Using Synthetic Division
 Modeling the Factorization of x2+bx+c

AI.P.8: Demonstrate facility in symbolic manipulation of polynomial and rational expressions by rearranging and collecting terms, factoring (e.g., a² - b² = (a + b)(a - b), x² + 10x + 21 = (x + 3)(x + 7), 5x to the 4th + 10x³ - 5x² = 5x² (x² + 2x - 1)), identifying and canceling common factors in rational expressions, and applying the properties of positive integer exponents.

 Addition of Polynomials
 Factoring Special Products
 Modeling the Factorization of ax2+bx+c
 Simplifying Algebraic Expressions II

AI.P.9: Find solutions to quadratic equations (with real roots) by factoring, completing the square, or using the quadratic formula. Demonstrate an understanding of the equivalence of the methods.

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

AI.P.10: Solve equations and inequalities including those involving absolute value of linear expressions (e.g., |x - 2| > 5) and apply to the solution of problems.

 Absolute Value Equations and Inequalities
 Absolute Value with Linear Functions

AI.P.11: Solve everyday problems that can be modeled using linear, reciprocal, quadratic, or exponential functions. Apply appropriate tabular, graphical, or symbolic methods to the solution. Include compound interest, and direct and inverse variation problems. Use technology when appropriate.

 Compound Interest
 Direct and Inverse Variation

AI.P.12: Solve everyday problems that can be modeled using systems of linear equations or inequalities. Apply algebraic and graphical methods to the solution. Use technology when appropriate. Include mixture, rate, and work problems.

 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)

AI.D: Data Analysis, Statistics, and Probability

AI.D.1: Select, create, and interpret an appropriate graphical representation (e.g., scatterplot, table, stem-and-leaf plots, circle graph, line graph, and line plot) for a set of data and use appropriate statistics (e.g., mean, median, range, and mode) to communicate information about the data. Use these notions to compare different sets of data.

 Describing Data Using Statistics
 Mean, Median, and Mode
 Reaction Time 1 (Graphs and Statistics)
 Real-Time Histogram
 Stem-and-Leaf Plots

AI.D.2: Approximate a line of best fit (trend line) given a set of data (e.g., scatterplot). Use technology when appropriate.

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

AI.D.3: Describe and explain how the relative sizes of a sample and the population affect the validity of predictions from a set of data.

 Polling: City

G: Geometry

G.G: Geometry

G.G.1: Recognize special types of polygons (e.g., isosceles triangles, parallelograms, and rhombuses). Apply properties of sides, diagonals, and angles in special polygons; identify their parts and special segments (e.g., altitudes, midsegments); determine interior angles for regular polygons. Draw and label sets of points such as line segments, rays, and circles. Detect symmetries of geometric figures.

 Classifying Quadrilaterals
 Holiday Snowflake Designer
 Parallelogram Conditions
 Polygon Angle Sum
 Similarity in Right Triangles
 Special Parallelograms
 Triangle Angle Sum

G.G.2: Write simple proofs of theorems in geometric situations, such as theorems about congruent and similar figures, parallel or perpendicular lines. Distinguish between postulates and theorems. Use inductive and deductive reasoning, as well as proof by contradiction. Given a conditional statement, write its inverse, converse, and contrapositive.

 Biconditional Statements
 Conditional Statements
 Investigating Angle Theorems
 Isosceles and Equilateral Triangles
 Similar Figures

G.G.5: Apply congruence and similarity correspondences (e.g., delta ABC is approximately equal to delta XYZ) and properties of the figures to find missing parts of geometric figures, and provide logical justification.

 Constructing Congruent Segments and Angles

G.G.6: Apply properties of angles, parallel lines, arcs, radii, chords, tangents, and secants to solve problems.

 Chords and Arcs
 Constructing Congruent Segments and Angles
 Inscribed Angles
 Parallel, Intersecting, and Skew Lines

G.G.7: Solve simple triangle problems using the triangle angle sum property, and/or the Pythagorean theorem.

 Circles
 Cosine Function
 Distance Formula
 Isosceles and Equilateral Triangles
 Polygon Angle Sum
 Pythagorean Theorem
 Pythagorean Theorem with a Geoboard
 Sine Function
 Surface and Lateral Areas of Pyramids and Cones
 Tangent Function
 Triangle Angle Sum

G.G.8: Use the properties of special triangles (e.g., isosceles, equilateral, 30°-60°-90°, 45°-45°-90°) to solve problems.

 Classifying Triangles
 Concurrent Lines, Medians, and Altitudes
 Cosine Function
 Isosceles and Equilateral Triangles
 Pythagorean Theorem
 Pythagorean Theorem with a Geoboard
 Sine Function
 Tangent Function
 Triangle Inequalities

G.G.9: Define the sine, cosine, and tangent of an acute angle. Apply to the solution of problems.

 Sine, Cosine, and Tangent Ratios

G.G.10: Apply the triangle inequality and other inequalities associated with triangles (e.g., the longest side is opposite the greatest angle) to prove theorems and solve problems.

 Triangle Inequalities

G.G.11: Demonstrate an understanding of the relationship between various representations of a line. Determine a line's slope and x- and y-intercepts from its graph or from a linear equation that represents the line. Find a linear equation describing a line from a graph or a geometric description of the line, e.g., by using the "point-slope" or "slope y-intercept" formulas. Explain the significance of a positive, negative, zero, or undefined slope.

 Linear Inequalities in Two Variables
 Point-Slope Form of a Line
 Points, Lines, and Equations
 Slope-Intercept Form of a Line
 Standard Form of a Line

G.G.15: Draw the results, and interpret transformations on figures in the coordinate plane, e.g., translations, reflections, rotations, scale factors, and the results of successive transformations. Apply transformations to the solution of problems.

 Dilations
 Rotations, Reflections, and Translations
 Translations

G.G.16: Demonstrate the ability to visualize solid objects and recognize their projections and cross sections.

 3D and Orthographic Views

G.G.18: Use the notion of vectors to solve problems. Describe addition of vectors and multiplication of a vector by a scalar, both symbolically and pictorially. Use vector methods to obtain geometric results.

 Adding Vectors
 Vectors

G.M: Measurement

G.M.1: Calculate perimeter, circumference, and area of common geometric figures such as parallelograms, trapezoids, circles, and triangles.

 Area of Parallelograms
 Area of Triangles
 Perimeter and Area of Rectangles
 Perimeters and Areas of Similar Figures

G.M.2: Given the formula, find the lateral area, surface area, and volume of prisms, pyramids, spheres, cylinders, and cones, e.g., find the volume of a sphere with a specified surface area.

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

Correlation last revised: 1/20/2017

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