Curriculum Frameworks

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.

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

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 *x*^{2}+*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 *ax*^{2}+*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 *x*^{2}+*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

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.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.

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.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.

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

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

Geometric Sequences

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

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

Introduction to Functions

Linear Functions

Points, Lines, and Equations

Quadratics in Polynomial Form

Quadratics in Vertex 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 *x*^{2}+*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 *ax*^{2}+*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 *x*^{2}+*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.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.

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.

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.

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.

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: 4/4/2018

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