


Mathematics (2015) 
Grade(s): 9  12 
Discrete Mathematics 
All Resources: 
2 
Learning Activities: 
0 
Lesson Plans: 
2 
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 
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 n^{th} triangular number.

Mathematics (2015) 
Grade(s): 9  12 
Discrete Mathematics 
All Resources: 
6 
Learning Activities: 
0 
Lesson Plans: 
6 
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 
Unit Plans: 
0 

4 ) Convert between base ten and other bases. (Alabama)


Mathematics (2015) 
Grade(s): 9  12 
Discrete Mathematics 
All Resources: 
0 
Learning Activities: 
0 
Lesson Plans: 
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 
Unit Plans: 
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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 
Unit Plans: 
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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 applicationbased problems using existing and studentcreated algorithms. (Alabama)

Mathematics (2015) 
Grade(s): 9  12 
Discrete Mathematics 
All Resources: 
0 
Learning Activities: 
0 
Lesson Plans: 
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 
Unit Plans: 
0 

9 ) Determine a minimum project time using algorithms to schedule tasks in order, including critical path analysis, the listprocessing algorithm, and studentcreated algorithms. (Alabama)


Mathematics (2015) 
Grade(s): 9  12 
Discrete Mathematics 
All Resources: 
1 
Learning Activities: 
0 
Lesson Plans: 
1 
Unit Plans: 
0 

10 ) Use vertexcoloring techniques and matching techniques to solve applicationbased problems. (Alabama)
Example: Use graphcoloring 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 
Unit Plans: 
0 

11 ) Solve applicationbased logic problems using Venn diagrams, truth tables, and matrices. (Alabama)


Mathematics (2015) 
Grade(s): 9  12 
Discrete Mathematics 
All Resources: 
7 
Learning Activities: 
0 
Lesson Plans: 
7 
Unit Plans: 
0 

12 ) Use combinatorial reasoning and counting techniques to solve applicationbased 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 
Unit Plans: 
0 

13 ) Analyze election data to compare election methods and voting apportionment, including determining strength within specific groups. (Alabama)
