Next Generation Sunshine State Standards

MA.912.D: Discrete Mathematics

MA.912.D.2: Understand how graphs of vertices joined by edges can model relationships and be used to solve various problems with relation to directed graphs, weighted graphs, networks, tournaments, transportation flows, matching, and coverage.

MA.912.D.2.4: Use spanning trees, rooted trees, binary trees, and decision trees to solve problems.

Binomial Probabilities

Permutations and Combinations

MA.912.D.3: Analyze election data to evaluate different election methods and use weighted voting techniques to decide voting power within a group. Understand and use fair division techniques to solve apportionment problems.

MA.912.D.3.1: Use election theory techniques to analyze election data.

MA.912.D.6: Develop an understanding of the fundamentals of propositional logic, arguments, and methods of proof.

MA.912.D.6.2: Find the converse, inverse, and contrapositive of a statement.

Biconditional Statements

Conditional Statements

MA.912.D.6.3: Determine whether two propositions are logically equivalent.

Biconditional Statements

Conditional Statements

MA.912.D.6.4: Use methods of direct and indirect proof and determine whether a short proof is logically valid.

Biconditional Statements

Conditional Statements

MA.912.D.6.6: Construct logical arguments using laws of detachment (modus ponens), syllogism, tautology, and contradiction; judge the validity of arguments, and give counterexamples to disprove statements.

Biconditional Statements

Conditional Statements

MA.912.D.6.7: Use applications of the universal and existential quantifiers to propositional statements.

MA.912.D.7: Operate with sets and use set theory to solve problems.

MA.912.D.7.1: Perform set operations such as union and intersection, complement, and cross product.

MA.912.D.8: Understand how matrices can be used to store and organize data and to solve systems of equations. They also use matrices to solve Markov chain problems that link present events to future events using probabilities.

MA.912.D.8.1: Use matrices to organize and store data. Perform matrix operations (addition, subtraction, scalar multiplication, multiplication).

MA.912.D.8.2: Use matrix operations to solve problems.

MA.912.D.8.5: Use determinants of 2 x 2 and 3 x 3 matrices as well as higher order matrices with and without the use of technology.

Solving Linear Systems (Matrices and Special Solutions)

MA.912.D.9: Recognize vectors in both two- and three-dimensions. Recognize that vectors are represented geometrically and algebraically. Perform basic operations on vectors, including addition, scalar multiplication, dot product, and cross product. Solve problems using vectors.

MA.912.D.9.1: Demonstrate an understanding of the geometric interpretation of vectors and vector operations including addition, scalar multiplication, dot product and cross product in the plane and in three-dimensional space.

MA.912.D.9.2: Demonstrate an understanding of the algebraic interpretation of vectors and vector operations including addition, scalar multiplication, dot product and cross product in the plane and in three-dimensional space.

MA.912.D.11: Define and use arithmetic and geometric sequences and series.

MA.912.D.11.3: Find specified terms of arithmetic and geometric sequences.

Arithmetic Sequences

Arithmetic and Geometric Sequences

Geometric Sequences

MA.912.D.11.5: Explore and use other sequences found in nature such as the Fibonacci sequence and the golden ratio.

Arithmetic Sequences

Arithmetic and Geometric Sequences

Geometric Sequences

Correlation last revised: 5/10/2018