# Courses of Study: Mathematics

Number of Standards matching query: 24
NUMBER AND QUANTITY
 Mathematics (2015) Grade(s): 9 - 12 Discrete Mathematics All Resources: 2 Learning Activities: 0 Lesson Plans: 2 Multimedia: 0 Unit Plans: 0
1.) Analyze topics from elementary number theory, including perfect numbers and prime numbers, to determine properties of integers. (Alabama)

 Mathematics (2015) Grade(s): 9 - 12 Discrete Mathematics All Resources: 2 Learning Activities: 0 Lesson Plans: 2 Multimedia: 0 Unit Plans: 0
2.) Determine characteristics of sequences, including the Fibonacci sequence, the triangular numbers, and pentagonal numbers. (Alabama)

Example: Write a sequence of the first 10 triangular numbers and hypothesize a formula to find the nth triangular number.

 Mathematics (2015) Grade(s): 9 - 12 Discrete Mathematics All Resources: 6 Learning Activities: 0 Lesson Plans: 6 Multimedia: 0 Unit Plans: 0
3.) Use the recursive process and difference equations to create fractals, population growth models, sequences, series, and compound interest models. (Alabama)

 Mathematics (2015) Grade(s): 9 - 12 Discrete Mathematics All Resources: 1 Learning Activities: 0 Lesson Plans: 1 Multimedia: 0 Unit Plans: 0
4.) Convert between base ten and other bases. (Alabama)

ALGEBRA
 Mathematics (2015) Grade(s): 9 - 12 Discrete Mathematics All Resources: 0 Learning Activities: 0 Lesson Plans: 0 Multimedia: 0 Unit Plans: 0
5.) Determine results of operations upon 3 x 3 and larger matrices, including matrix addition and multiplication of a matrix by a matrix, vector, or scalar. (Alabama)

 Mathematics (2015) Grade(s): 9 - 12 Discrete Mathematics All Resources: 0 Learning Activities: 0 Lesson Plans: 0 Multimedia: 0 Unit Plans: 0
6.) Analyze determinants and inverses of 2 x 2, 3 x 3, and larger matrices to determine the nature of the solution set of the corresponding system of equations, including solving systems of equations in three variables by echelon row reduction and matrix inverse. (Alabama)

 Mathematics (2015) Grade(s): 9 - 12 Discrete Mathematics All Resources: 0 Learning Activities: 0 Lesson Plans: 0 Multimedia: 0 Unit Plans: 0
7.) Solve problems through investigation and application of existence and nonexistence of Euler paths, Euler circuits, Hamilton paths, and Hamilton circuits. (Alabama)

Example: Show why a 5 x 5 grid has no Hamilton circuit.

a. Develop optimal solutions of application-based problems using existing and student-created algorithms. (Alabama)

 Mathematics (2015) Grade(s): 9 - 12 Discrete Mathematics All Resources: 0 Learning Activities: 0 Lesson Plans: 0 Multimedia: 0 Unit Plans: 0
8.) Apply algorithms, including Kruskal's and Prim's, relating to minimum weight spanning trees, networks, flows, and Steiner trees. (Alabama)

a. Use shortest path techniques to find optimal shipping routes. (Alabama)

 Mathematics (2015) Grade(s): 9 - 12 Discrete Mathematics All Resources: 1 Learning Activities: 0 Lesson Plans: 1 Multimedia: 0 Unit Plans: 0
9.) Determine a minimum project time using algorithms to schedule tasks in order, including critical path analysis, the list-processing algorithm, and student-created algorithms. (Alabama)

GEOMETRY
 Mathematics (2015) Grade(s): 9 - 12 Discrete Mathematics All Resources: 1 Learning Activities: 0 Lesson Plans: 1 Multimedia: 0 Unit Plans: 0
10.) Use vertex-coloring techniques and matching techniques to solve application-based problems. (Alabama)

Example: Use graph-coloring techniques to color a map of the western states of the United States so no adjacent states are the same color, including determining the minimum number of colors needed and why no fewer colors may be used.

 Mathematics (2015) Grade(s): 9 - 12 Discrete Mathematics All Resources: 2 Learning Activities: 0 Lesson Plans: 2 Multimedia: 0 Unit Plans: 0
11.) Solve application-based logic problems using Venn diagrams, truth tables, and matrices. (Alabama)

STATISTICS AND PROBABILITY
 Mathematics (2015) Grade(s): 9 - 12 Discrete Mathematics All Resources: 7 Learning Activities: 0 Lesson Plans: 7 Multimedia: 0 Unit Plans: 0
12.) Use combinatorial reasoning and counting techniques to solve application-based problems. (Alabama)

Example: Determine the probability of a safe opening on the first attempt given the combination uses the digits 2, 4, 6, and 8 with the order unknown.

Answer: The probability of the safe opening on the first attempt is 1/24.

 Mathematics (2015) Grade(s): 9 - 12 Discrete Mathematics All Resources: 1 Learning Activities: 0 Lesson Plans: 1 Multimedia: 0 Unit Plans: 0
13.) Analyze election data to compare election methods and voting apportionment, including determining strength within specific groups. (Alabama)