### 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

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: 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.

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.

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

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.

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.

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.

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.

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.

#### 10.G: Geometry

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

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.

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

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

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.

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

#### 10.M: Measurement

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

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.

#### 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.

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

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: 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.

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: 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.

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

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

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.

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.

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

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.

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.

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.

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.

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.

#### 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.

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

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: 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.

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.

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.

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

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

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

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

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.

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.

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: Measurement

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

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.

Correlation last revised: 5/14/2018

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