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 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
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 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.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: 5/14/2018