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Skills available for Florida high school math standards

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Florida's B.E.S.T. Standards: Algebra 1 Florida's B.E.S.T. Standards: Algebra 1
Florida's B.E.S.T. Standards: Algebra 2 Florida's B.E.S.T. Standards: Algebra 2
Florida's B.E.S.T. Standards: Calculus Florida's B.E.S.T. Standards: Calculus
Florida's B.E.S.T. Standards: Discrete Math Honors Florida's B.E.S.T. Standards: Discrete Math Honors
Florida's B.E.S.T. Standards: Fourth Courses Florida's B.E.S.T. Standards: Fourth Courses
Florida's B.E.S.T. Standards: Geometry Florida's B.E.S.T. Standards: Geometry
Florida's B.E.S.T. Standards: Mathematical Thinking and Reasoning Standards Florida's B.E.S.T. Standards: Mathematical Thinking and Reasoning Standards
Florida's B.E.S.T. Standards: Mathematics for College Algebra Florida's B.E.S.T. Standards: Mathematics for College Algebra
Florida's B.E.S.T. Standards: Mathematics for College Liberal Arts Florida's B.E.S.T. Standards: Mathematics for College Liberal Arts

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AR Algebraic Reasoning

MA.912.AR.9 Write and solve a system of two- and three-variable equations and inequalities that describe quantities or relationships.
- MA.912.AR.9.6 Given a real-world context, represent constraints as systems of linear equations or inequalities. Interpret solutions to problems as viable or nonviable options.
- MA.912.AR.9.8 Solve real-world problems involving linear programming in two variables.
  - Find the vertices of a solution set (PC-O.3)
  - Linear programming (PC-O.4)
MA.912.AR.10 Solve problems involving sequences and series.
- MA.912.AR.10.1 Given a mathematical or real-world context, write and solve problems involving arithmetic sequences.
  - Find terms of an arithmetic sequence (A2-MM.1)
- MA.912.AR.10.2 Given a mathematical or real-world context, write and solve problems involving geometric sequences.
  - Find terms of a geometric sequence (A2-MM.2)
- MA.912.AR.10.5 Given a mathematical or real-world context, write a sequence using function notation, defined explicitly or recursively, to represent relationships between quantities from a written description.
- MA.912.AR.10.6 Given a mathematical or real-world context, find the domain of a given sequence defined recursively or explicitly.

GR Geometric Reasoning

MA.912.GR.2 Apply properties of transformations to describe congruence or similarity.
- MA.912.GR.2.4 Determine symmetries of reflection, symmetries of rotation and symmetries of translation of a geometric figure.

DP Data Analysis and Probability

MA.912.DP.4 Use and interpret independence and probability.
- MA.912.DP.4.1 Describe events as subsets of a sample space using characteristics, or categories, of the outcomes, or as unions, intersections or complements of other events.
  - Theoretical probability (G)
- MA.912.DP.4.9 Apply the addition and multiplication rules for counting to solve mathematical and real-world problems, including problems involving probability.
- MA.912.DP.4.10 Given a mathematical or real-world situation, calculate the appropriate permutation or combination.

LT Logic and Discrete Theory

MA.912.LT.1 Apply recursive methods to solve problems.
- MA.912.LT.1.1 Apply recursive and iterative thinking to solve problems.
- MA.912.LT.1.2 Solve problems involving recurrence relations.
MA.912.LT.2 Apply optimization and techniques from Graph Theory to solve problems.
- MA.912.LT.2.1 Define and explain the basic concepts of Graph Theory.
- MA.912.LT.2.2 Solve problems involving paths in graphs.
- MA.912.LT.2.3 Solve scheduling problems using critical path analysis and Gantt charts. Create a schedule using critical path analysis.
- MA.912.LT.2.4 Apply graph coloring techniques to solve problems.
- MA.912.LT.2.5 Apply spanning trees, rooted trees, binary trees and decision trees to solve problems.
MA.912.LT.3 Apply techniques from Election Theory and Fair Division Theory to solve problems.
- MA.912.LT.3.1 Define and explain the basic concepts of Election Theory and voting.
- MA.912.LT.3.2 Analyze election data using election theory techniques. Explain how Arrow's Impossibility Theorem may be related to the fairness of the outcome of the election.
- MA.912.LT.3.3 Decide voting power within a group using weighted voting techniques. Provide real-world examples of weighted voting and its pros and cons.
- MA.912.LT.3.4 Solve problems using fair division and apportionment techniques.
MA.912.LT.4 Develop an understanding of the fundamentals of propositional logic, arguments and methods of proof.
- MA.912.LT.4.1 Translate propositional statements into logical arguments using propositional variables and logical connectives.
- MA.912.LT.4.2 Determine truth values of simple and compound statements using truth tables.
  - Truth tables (G-A.7)
- MA.912.LT.4.3 Identify and accurately interpret "if…then," "if and only if," "all" and "not" statements. Find the converse, inverse and contrapositive of a statement.
- MA.912.LT.4.4 Represent logic operations, such as AND, OR, NOT, NOR, and XOR, using logical symbolism to solve problems.
  - Truth values (G-A.8)
- MA.912.LT.4.5 Determine whether two propositions are logically equivalent.
- MA.912.LT.4.6 Apply methods of direct and indirect proof and determine whether a logical argument is valid.
- MA.912.LT.4.7 Identify and give examples of undefined terms; axioms; theorems; proofs, including proofs using mathematical induction; and inductive and deductive reasoning.
- MA.912.LT.4.8 Construct proofs, including proofs by contradiction.
- MA.912.LT.4.9 Construct logical arguments using laws of detachment, syllogism, tautology, contradiction and Euler Diagrams.
- MA.912.LT.4.10 Judge the validity of arguments and give counterexamples to disprove statements.
  - Counterexamples (G-A.2)
MA.912.LT.5 Apply properties from Set Theory to solve problems.
- MA.912.LT.5.1 Given two sets, determine whether the two sets are equivalent and whether one set is a subset of another. Given one set, determine its power set.
  - Sets, subsets, and complements (A1-G.1)
- MA.912.LT.5.2 Given a relation on two sets, determine whether the relation is a function, determine the inverse of the relation if it exists and identify if the relation is bijective.
- MA.912.LT.5.3 Partition a set into disjoint subsets and determine an equivalence class given the equivalence relation on a set.
- MA.912.LT.5.4 Perform the set operations of taking the complement of a set and the union, intersection, difference and product of two sets.
  - Sets, subsets, and complements (A1-G.1)
  - Unions and intersections of sets (A1-G.4)
- MA.912.LT.5.5 Explore relationships and patterns and make arguments about relationships between sets by using Venn Diagrams.
- MA.912.LT.5.6 Prove set relations, including DeMorgan's Laws and equivalence relations.

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AR Algebraic Reasoning

MA.912.AR.9 Write and solve a system of two- and three-variable equations and inequalities that describe quantities or relationships.

MA.912.AR.9.6 Given a real-world context, represent constraints as systems of linear equations or inequalities. Interpret solutions to problems as viable or nonviable options.

MA.912.AR.9.8 Solve real-world problems involving linear programming in two variables.

MA.912.AR.10 Solve problems involving sequences and series.

MA.912.AR.10.1 Given a mathematical or real-world context, write and solve problems involving arithmetic sequences.

MA.912.AR.10.2 Given a mathematical or real-world context, write and solve problems involving geometric sequences.

MA.912.AR.10.5 Given a mathematical or real-world context, write a sequence using function notation, defined explicitly or recursively, to represent relationships between quantities from a written description.

MA.912.AR.10.6 Given a mathematical or real-world context, find the domain of a given sequence defined recursively or explicitly.

GR Geometric Reasoning

MA.912.GR.2 Apply properties of transformations to describe congruence or similarity.

MA.912.GR.2.4 Determine symmetries of reflection, symmetries of rotation and symmetries of translation of a geometric figure.

DP Data Analysis and Probability

MA.912.DP.4 Use and interpret independence and probability.

MA.912.DP.4.1 Describe events as subsets of a sample space using characteristics, or categories, of the outcomes, or as unions, intersections or complements of other events.

MA.912.DP.4.9 Apply the addition and multiplication rules for counting to solve mathematical and real-world problems, including problems involving probability.

MA.912.DP.4.10 Given a mathematical or real-world situation, calculate the appropriate permutation or combination.

LT Logic and Discrete Theory

MA.912.LT.1 Apply recursive methods to solve problems.

MA.912.LT.1.1 Apply recursive and iterative thinking to solve problems.

MA.912.LT.1.2 Solve problems involving recurrence relations.

MA.912.LT.2 Apply optimization and techniques from Graph Theory to solve problems.

MA.912.LT.2.1 Define and explain the basic concepts of Graph Theory.

MA.912.LT.2.2 Solve problems involving paths in graphs.

MA.912.LT.2.3 Solve scheduling problems using critical path analysis and Gantt charts. Create a schedule using critical path analysis.

MA.912.LT.2.4 Apply graph coloring techniques to solve problems.

MA.912.LT.2.5 Apply spanning trees, rooted trees, binary trees and decision trees to solve problems.

MA.912.LT.3 Apply techniques from Election Theory and Fair Division Theory to solve problems.

MA.912.LT.3.1 Define and explain the basic concepts of Election Theory and voting.

MA.912.LT.3.2 Analyze election data using election theory techniques. Explain how Arrow's Impossibility Theorem may be related to the fairness of the outcome of the election.

MA.912.LT.3.3 Decide voting power within a group using weighted voting techniques. Provide real-world examples of weighted voting and its pros and cons.

MA.912.LT.3.4 Solve problems using fair division and apportionment techniques.

MA.912.LT.4 Develop an understanding of the fundamentals of propositional logic, arguments and methods of proof.

MA.912.LT.4.1 Translate propositional statements into logical arguments using propositional variables and logical connectives.

MA.912.LT.4.2 Determine truth values of simple and compound statements using truth tables.

MA.912.LT.4.3 Identify and accurately interpret "if…then," "if and only if," "all" and "not" statements. Find the converse, inverse and contrapositive of a statement.

MA.912.LT.4.4 Represent logic operations, such as AND, OR, NOT, NOR, and XOR, using logical symbolism to solve problems.

MA.912.LT.4.5 Determine whether two propositions are logically equivalent.

MA.912.LT.4.6 Apply methods of direct and indirect proof and determine whether a logical argument is valid.

MA.912.LT.4.7 Identify and give examples of undefined terms; axioms; theorems; proofs, including proofs using mathematical induction; and inductive and deductive reasoning.

MA.912.LT.4.8 Construct proofs, including proofs by contradiction.

MA.912.LT.4.9 Construct logical arguments using laws of detachment, syllogism, tautology, contradiction and Euler Diagrams.

MA.912.LT.4.10 Judge the validity of arguments and give counterexamples to disprove statements.

MA.912.LT.5 Apply properties from Set Theory to solve problems.

MA.912.LT.5.1 Given two sets, determine whether the two sets are equivalent and whether one set is a subset of another. Given one set, determine its power set.

MA.912.LT.5.2 Given a relation on two sets, determine whether the relation is a function, determine the inverse of the relation if it exists and identify if the relation is bijective.

MA.912.LT.5.3 Partition a set into disjoint subsets and determine an equivalence class given the equivalence relation on a set.

MA.912.LT.5.4 Perform the set operations of taking the complement of a set and the union, intersection, difference and product of two sets.

MA.912.LT.5.5 Explore relationships and patterns and make arguments about relationships between sets by using Venn Diagrams.

MA.912.LT.5.6 Prove set relations, including DeMorgan's Laws and equivalence relations.