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Standards for Mathematical Practices
Standards for Mathematical Practices
MP.1. Make sense of problems and persevere in solving them.
MP.2. Reason abstractly and quantitatively.
MP.7. Look for and make use of structure.
MP.8. Look for and express regularity in repeated reasoning.
Conceptual Category Number and Quantity
Conceptual Category Number and Quantity
Number and Quantity—The Real Number System Cluster: Use properties of rational and irrational numbers.KY.HS.N.3(+). Justify why the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational. (MP.3, MP.6)
Cluster: Extend the properties of exponents to rational exponents.KY.HS.N.2. Rewrite expressions involving radicals and rational exponents using the properties of exponents. (MP.7)
Conceptual Category Algebra
Conceptual Category Algebra
Algebra—Reasoning with Equations and Inequalities Cluster: Represent and solve equations and inequalities graphically.KY.HS.A.24. Justify that the solutions of the equations f(x)=g(x) are the x-coordinates of the points where the graphs of y=f(x) and y=g(x) intersect. Find the approximate solutions graphically, using technology or tables. (MP.3, MP.5)
KY.HS.A.25. Graph linear inequalities in two variables. (MP.5, MP.6)KY.HS.A.25.a. Graph the solutions to a linear inequality as a half-plane (excluding the boundary in the case of a strict inequality).
Cluster: Solve equations and inequalities in one variable.KY.HS.A.18. Solve linear equations and inequalities in one variable, including literal equations with coefficients represented by letters. (MP.2, MP.7)
Cluster: Solve systems of equations.KY.HS.A.20. Solve systems of linear equations in two variables. (MP.3, MP.6)KY.HS.A.20.a. Understand a system of two equations in two variables has the same solution as a new system formed by replacing one of the original equations with an equivalent equation.
KY.HS.A.20.b. Solve systems of linear equations with graphs, substitution and elimination, focusing on pairs of linear equations in two variables.
Cluster: Understand solving equations as a process of reasoning and explain the reasoning.KY.HS.A.16. Understand each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method. (M
Algebra—Arithmetic with Polynomials and Rational Expressions Cluster: Perform arithmetic operations on polynomials.KY.HS.A.5. Add, subtract and multiply polynomials. (MP.7, MP.8)
Algebra—Creating Equations Cluster: Create equations that describe numbers or relationships.KY.HS.A.12. Create equations and inequalities in one variable and use them to solve problems. (MP.1, MP.4)
KY.HS.A.13. Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. (MP.2, MP.5)
KY.HS.A.14. Create a system of equations or inequalities to represent constraints within a modeling context. Interpret the solution(s) to the corresponding system as viable or nonviable options within the context. (MP.4, MP.5)
KY.HS.A.15. Rearrange formulas to solve a literal equation, highlighting a quantity of interest, using the same reasoning as in solving equations. (MP.2, MP.7)
Algebra—Seeing Structure in Expressions Cluster: Write expressions in equivalent forms to solve problems.KY.HS.A.3. Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression. (MP.5, MP.7)KY.HS.A.3.c. Use the properties of exponents to rewrite exponential expressions.
Conceptual Category Functions
Conceptual Category Functions
Functions—Building Functions Cluster: Build a function that models a relationship between two quantities.KY.HS.F.6. Write a function that describes a relationship between two quantities. (MP.4, MP.7)KY.HS.F.6.a. Determine an explicit expression, a recursive process, or steps for calculation from a context.
KY.HS.F.7. Use arithmetic and geometric sequences to model situations and scenarios. (MP.4, MP.8)KY.HS.F.7.a. Use formulas (explicit and recursive) to generate terms for arithmetic and geometric sequences.Quiz, Flash Cards, Worksheet, Game & Study Guide Sequences
Functions—Linear, Quadratic and Exponential Functions Cluster: Construct and compare linear, quadratic and exponential models and solve problems.KY.HS.F.11. Distinguish between situations that can be modeled with linear functions and with exponential functions. (MP.3, MP.8)KY.HS.F.11.a. Recognize and justify that linear functions grow by equal differences over equal intervals and that exponential functions grow by equal factors over equal intervals.Quiz, Flash Cards, Worksheet, Game & Study Guide Functions
Functions—Interpreting Functions Cluster: Interpret functions that arise in applications in terms of the context.KY.HS.F.3. Understand average rate of change of a function over an interval. (MP.2, MP.4)KY.HS.F.3.a. Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval.
KY.HS.F.3.b. Estimate the rate of change from a graph.
Cluster: Analyze functions using different representations.KY.HS.F.4. Graph functions expressed symbolically and show key features of the graph, with and without using technology (computer, graphing calculator). (MP.4, MP.5)KY.HS.F.4.a. Graph linear and quadratic functions and show intercepts, maxima and minima.
KY.HS.F.5. Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function. (MP.3, MP.6)KY.HS.F.5.b. Use the properties of exponents to interpret expressions for exponential functions and classify the exponential function as representing growth or decay.Quiz, Flash Cards, Worksheet, Game & Study Guide Functions
Cluster: Understand the concept of a function and use function notation.KY.HS.F.1. Understand properties and key features of functions and the different ways functions can be represented. (MP.2, MP.4, MP.7)KY.HS.F.1.a. Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f cQuiz, Flash Cards, Worksheet, Game & Study Guide Functions
KY.HS.F.1.c. For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities and sketch graphs showing key features given a verbal description of the relationship.
KY.HS.F.2. Recognize that arithmetic and geometric sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. (MP.7, MP.8)Quiz, Flash Cards, Worksheet, Game & Study Guide Sequences
Conceptual Category Geometry
Conceptual Category Geometry
Geometry—Geometric Measurement and Dimensions Cluster: Explain volume formulas and use them to solve problems.KY.HS.G.25. Analyze and determine the validity of arguments for the formulas for the various figures and shapes. (MP.3, MP.7)KY.HS.G.25.a. Finding the circumference and area of a circle.
KY.HS.G.25.b. Finding the volume of a sphere, prism, cylinder, pyramid and cone.
KY.HS.G.27. Use volume formulas to solve problems for cylinders, pyramids, cones, spheres, prisms. (MP.4, MP.6)
Geometry—Similarity, Right Triangles and Trigonometry Cluster: Prove theorems involving similarity.KY.HS.G.11. Understand theorems about triangles. (MP.1, MP.3)KY.HS.G.11.c. Use similarity criteria for triangles to solve problems and to prove relationships in geometric figures.
Cluster: Understand similarity in terms of similarity transformations.KY.HS.G.9. Understand properties of dilations. (MP.5, MP.7)KY.HS.G.9.a. Verify the properties that result from that dilations given by a center and a scale factor.
KY.HS.G.9.b. Verify that a dilation produces an image that is similar to the pre-image.
Geometry—Expressing Geometric Properties with Equations Cluster: Use coordinates to prove simple geometric theorems algebraically.KY.HS.G.24. Use coordinates within the coordinate plane to calculate measurements of two dimensional figures. (MP.2, MP.4)KY.HS.G.24.a. Compute the perimeters of various polygons.
KY.HS.G.24.b. Compute the areas of triangles, rectangles and other quadrilaterals.
Geometry—Congruence Cluster: Experiment with transformations in the plane.KY.HS.G.1. Know and apply precise definitions of the language of Geometry: (MP.3, MP.6)KY.HS.G.1.a. Understand properties of line segments, angles and circle.
KY.HS.G.1.b. Understand properties of and differences between perpendicular and parallel lines.
KY.HS.G.2. Representing transformations in the plane. (MP.5, MP.7)KY.HS.G.2.b. Compare transformations that preserve distance and angle measures to those that do not.
KY.HS.G.2.c. Given a rectangle, parallelogram, trapezoid, or regular polygon, formally describe the rotations and reflections that carry it onto itself, using properties of these figures.
KY.HS.G.3(+). Develop formal definitions of rotations, reflections and translations in terms of angles, circles, perpendicular lines, parallel lines and line segments. (MP.6, MP.7)
KY.HS.G.4. Understand the effects of transformations of geometric figures. (MP.2, MP.8)KY.HS.G.4.a. Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure.
KY.HS.G.4.c. Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure. Given two figures, use the definition of congruence in terms of rigid motions to decide if they are congruent.
Conceptual Category Statistics and Probability
Conceptual Category Statistics and Probability
Statistics and Probability—Conditional Probability and the Rules of Probability Cluster: Use the rules of probability to compute probabilities of compound events.KY.HS.SP.19. Use permutations and combinations to compute probabilities. (MP.1, MP.8)KY.HS.SP.19.a. Distinguish between situations that can be modeled using counting techniques, including Fundamental Counting Principle, permutations and combinations.
KY.HS.SP.19.b. Perform calculations using the appropriate counting technique, including simple probabilities.
Cluster: Understand independence and conditional probability and use them to interpret data.KY.HS.SP.15. Understand the concept of independence. (MP.1, MP.6)KY.HS.SP.15.a. Understand that two events A and B are independent if the probability of A and B occurring together is the product of their individual probabilities, P(A)×P(B).
KY.HS.SP.15.b. (+) Determine whether two events are independent and provide a justification to support the decision.
KY.HS.SP.15.c. Recognize and explain the concept of independence in everyday language and everyday situations.
KY.HS.SP.17(+). Construct and interpret two-way frequency tables of data when two categories are associated with each object being classified. Use the two-way table as a sample space to decide whether events are independent and to approximate conditional probabilities. (
Statistics and Probability—Interpreting Categorical and Quantitative Data Cluster: Interpret linear models.KY.HS.SP.8. Understand the role and purpose of correlation in linear regression. (MP.5, MP.6)KY.HS.SP.8.b. Interpret the meaning of the correlation within the context of the data.
Cluster: Summarize, represent and interpret data on two categorical and quantitative variables.KY.HS.SP.5. Summarize categorical data for two or more categories in frequency tables. Calculate and interpret joint, marginal and conditional relative frequencies (probabilities) in the context of the data, recognizing possible associations and trends in the data. (