Discrete Mathematics
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Scope and Sequence Map
Mathematics: 2012-13 to 2017-18
Units of Study
Correlation of Standards
Hoover City Schools
Special Notes
Scope and Sequence Map
Conceptual Categories, Domains, Content Clusters, & Standard Numbers
Units of Study (expected proficiency)
1st nwks 2nd nwks 3rd nwks 4th nwks
NUMBER AND QUANTITY (N)




Analyze topics from elementary number theory, including perfect numbers and prime numbers, to
determine properties of integers: 1(AL)
Determine characteristics of sequences, including the Fibonacci sequence, the triangular numbers,
and pentagonal numbers: 2(AL)
Use the recursive process and difference equations to create fractals, population growth models,
sequences, series, and compound interest models: 3(AL)
Convert between base ten and other bases: 4(AL)
1, 2, 3, 4
ALGEBRA (A)





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: 5(AL)
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: 6(AL)
Solve problems through investigation and application of existence and nonexistence of Euler paths,
Euler circuits, Hamilton paths, and Hamilton circuits: 7(AL)
Apply algorithms, including Kruskal’s and Prim’s, relating to minimum weight spanning trees,
networks, flows, and Steiner trees: 8(AL)
Determine a minimum project time using algorithms to schedule tasks in order, including critical path
analysis, the list-processing algorithm, and student-created algorithms: 9(AL)
5, 6, 7
8, 9
GEOMETRY (G)


Use vertex-coloring techniques and matching techniques to solve application-based problems:
10(AL)
Solve application-based logic problems using Venn diagrams, truth tables, and matrices: 11(AL)
10
11
STATISTICS AND PROBABILITY (SP)


Use combinatorial reasoning and counting techniques to solve application-based problems: 12(AL)
Analyze election data to compare election methods and voting apportionment, including determining
strength within specific groups: 13(AL)
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Page 1 of 9
12, 13
Discrete Mathematics
Mathematics: 2012-13 to 2017-18
Hoover City Schools
Units of Study
Unit 1- Number Theory
Standards
COS #
Basic
Indicators of Proficiency
Proficient
Advanced
Simplify expressions,
classify numbers, state
perfect and prime numbers
Simplify expressions,
classify numbers, state
perfect and prime numbers
Simplify expressions,
classify numbers, state
perfect and prime numbers
Basic
Indicators of Proficiency
Proficient
CCSS #
Analyze topics from elementary number theory,
including perfect numbers and prime numbers, to
1
determine properties of integers
Instructional Recommendations / Resources: Include order of operations, simplifying expressions (including rational), and classifications of numbers.
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Unit 2- Sequences
Standards
Determine characteristics of sequences, including the
Fibonacci sequence, the triangular numbers, and
pentagonal numbers.
COS #
CCSS #
Recall sequences learned in
class, predict next number
in a sequence, write a
function rule from a basic
set of information
2
Apply sequences to solve a
problem, write a function
rule based on several types
of information
Advanced
Apply sequences to solve
problems and explain
reasoning, write a function
rule based on several types
of information and use the
rule to solve problems
Instructional Recommendations / Resources: Investigate patterns to write function rules. Include Pascal’s triangle.
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Unit 3- Growth Models
Standards
Use the recursive process and difference equations to
create fractals, population growth models, sequences,
series, and compound interest models.
Instructional Recommendations / Resources:
COS #
3
CCSS #
Basic
Solve basic problems using
formulas
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Page 2 of 9
Indicators of Proficiency
Proficient
Solve application based
problems using formulas
Advanced
Solve for variables using
various information and
explain the process
Discrete Mathematics
Unit 4- Change of Base
Standards
Convert between base ten and other bases.
Mathematics: 2012-13 to 2017-18
COS #
4
CCSS #
Basic
N/A
Hoover City Schools
Indicators of Proficiency
Proficient
N/A
Advanced
N/A
Instructional Recommendations / Resources: Possible computer programming applications. Website for help: mathbits.com/MathBits/CompSci/Introduction
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Unit 5- Matrix Operations
Standards
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.
Instructional Recommendations / Resources:
COS #
CCSS #
Basic
N/A
Indicators of Proficiency
Proficient
N/A
Advanced
N/A
5
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Unit 6- Solving Systems with Matrices
Standards
COS #
CCSS #
Basic
Solve basic problems to
Analyze determinants and inverses of 2 x 2, 3 x 3, and
find inverse, determinant,
larger matrices to determine the nature of the solution
and solutions
set of the corresponding system of equations,
6
including solving systems of equations in three
variables by echelon row reduction and matrix inverse.
Instructional Recommendations / Resources: Suggestion—split unit into 2x2 and 3x3 calculations.
Indicators of Proficiency
Proficient
Solve problems to find
solutions.
Advanced
Solve word problems using
these methods.
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Unit 7- Paths and Circuits
Standards
COS #
CCSS #
Page 3 of 9
Basic
Indicators of Proficiency
Proficient
Advanced
Discrete Mathematics
Unit 7- Paths and Circuits
Standards
Solve problems through investigation and application
of existence and nonexistence of Euler paths, Euler
circuits, Hamilton paths, and Hamilton circuits.
a) Develop optimal solutions of application-based
problems using existing and student-created
algorithms.
Instructional Recommendations / Resources:
Mathematics: 2012-13 to 2017-18
COS #
CCSS #
Basic
Solve problems using paths
and circuits.
Hoover City Schools
Indicators of Proficiency
Proficient
Understand what makes a
path and/or a circuit.
7
Advanced
Explain optimal solutions of
application based
problems.
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Unit 8- Graph Theory
Standards
COS #
CCSS #
Basic
Indicators of Proficiency
Proficient
Finds shortest path using
Finds shortest path using
Apply algorithms, including Kruskal’s and Prim’s,
algorithms. Recalls
algorithms. Recalls
relating to minimum weight spanning trees, networks,
definitions of trees,
definitions of trees,
flows, and Steiner trees.
8
networks, flows.
networks, flows.
a) Use shortest path techniques to find optimal
shipping routes.
Instructional Recommendations / Resources: Activity idea—road maps, shortest distance application problems.
Advanced
Explains reasoning in a
shortest path real world
problem to show
understanding of
algorthims.
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Unit 9- Project Algorithms
Standards
COS #
CCSS #
Basic
Indicators of Proficiency
Proficient
Draw a basic path analysis
Compare several paths to
Determine a minimum project time using algorithms to
to show minimum project
find the best. Explain
schedule tasks in order, including critical path analysis,
9
time.
reasoning that is clear.
the list-processing algorithm, and student-created
algorithms.
Instructional Recommendations / Resources: Assessment could be project-based for students to create a critical path analysis.
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Page 4 of 9
Advanced
Explain reasoning for their
path analysis in detail.
Discrete Mathematics
Unit 10- Vertex Coloring
Standards
Mathematics: 2012-13 to 2017-18
COS #
Use vertex-coloring techniques and matching
techniques to solve application-based problems.
Basic
Indicators of Proficiency
Proficient
Show colorings for problem
with vertices that have
same number of edges.
Show colorings/use
formula for varying number
of edges.
CCSS #
10
Hoover City Schools
Advanced
Explain process/formula for
any number of vertices.
Instructional Recommendations / Resources: Use several different geographic locations.
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Unit 11- Logic and its Applications
Standards
COS #
Solve application-based logic problems using Venn
diagrams, truth tables, and matrices.
CCSS #
Basic
Solve basic Venn diagram,
logic puzzles, and truth
tables.
11
Indicators of Proficiency
Proficient
Understand application
based problems.
Advanced
Explain reasoning for
answers of application
based problems.
Instructional Recommendations / Resources: Logic Puzzles.
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Unit 12- Probability
Standards
COS #
CCSS #
Basic
Indicators of Proficiency
Proficient
Use probability to solve
Use probability to solve
Use combinatorial reasoning and counting techniques
12
application problems.
application problems.
to solve application-based problems.
Instructional Recommendations / Resources: Include combinations, permutations, experimental/theoretical probabilities.
Advanced
Explain and solve
application problems.
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Unit 13- Analyzing Data
Standards
COS #
CCSS #
Page 5 of 9
Basic
Indicators of Proficiency
Proficient
Advanced
Discrete Mathematics
Unit 13- Analyzing Data
Standards
Mathematics: 2012-13 to 2017-18
COS #
CCSS #
Basic
Hoover City Schools
Indicators of Proficiency
Proficient
Advanced
Recall facts about election
Understand election data
Explain election data and
Analyze election data to compare election methods
data and determine
processes.
strength.
and voting apportionment, including determining
13
strength.
strength within specific groups.
Instructional Recommendations / Resources: Include history of electoral college. Use internet to look at populations and electoral votes over time.
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Correlation of Standards
AL COS #
Standards Key
CCSS #
HCS Unit #
NUMBER AND QUANTITY
Analyze topics from elementary number theory, including perfect numbers and prime numbers, to determine
properties of integers
Determine characteristics of sequences, including the Fibonacci sequence, the triangular numbers, and pentagonal
numbers.
Use the recursive process and difference equations to create fractals, population growth models, sequences, series,
and compound interest models.
Convert between base ten and other bases.
1
1
2
2
3
3
4
4
5
5
6
6
7
7
8
8
9
9
ALGEBRA
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.
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.
Solve problems through investigation and application of existence and nonexistence of Euler paths, Euler circuits,
Hamilton paths, and Hamilton circuits.
b) Develop optimal solutions of application-based problems using existing and student-created algorithms.
Apply algorithms, including Kruskal’s and Prim’s, relating to minimum weight spanning trees, networks, flows, and
Steiner trees.
b) Use shortest path techniques to find optimal shipping routes.
Determine a minimum project time using algorithms to schedule tasks in order, including critical path analysis, the
list-processing algorithm, and student-created algorithms.
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Discrete Mathematics
Mathematics: 2012-13 to 2017-18
Hoover City Schools
AL COS #
Standards Key
CCSS #
HCS Unit #
GEOMETRY
Use vertex-coloring techniques and matching techniques to solve application-based problems.
10
10
Solve application-based logic problems using Venn diagrams, truth tables, and matrices.
11
11
12
12
13
13
STATISTICS AND PROBABILITY
Use combinatorial reasoning and counting techniques to solve application-based problems.
Analyze election data to compare election methods and voting apportionment, including determining strength
within specific groups.
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Special Notes
This local curriculum document was developed from the 2010 Alabama Course of Study for Mathematics which was itself based on the newly
adopted Common Core State Standards for Mathematics. State COS standards are keyed to CCSS (i.e. Common Core) standards using the
lettering and number system employed by the CCSS so that instructional resources which are subsequently designed to support the CCSS can be
easily matched back to lessons based on state and local requirements. The symbol (+) is used to designate standards based on mathematics
content that students should learn in order to take advanced courses such as calculus. An asterisk (*) is used to designate standards where
modeling with mathematics should be stressed because modeling is best interpreted through a relevant context rather than as an isolated topic.
The state map of Alabama or the designation (AL) is used to denote additional standards required by the Alabama Board of Education which
extend beyond the minimum content defined by the CCSS.
The Standards for Mathematical Practice describe the varieties of expertise that mathematics educators at all levels should seek to develop in
their students. These standards were developed with input from the National Council of Teachers of Mathematics and the National Research
Council, and math teachers should reinforce these process skills when designing daily instructional lessons for students at all grade levels in the
Hoover school system:
1. Make sense of problems and persevere in solving them
2. Reason abstractly and quantitatively
3. Construct viable arguments and critique the reasoning of others
4. Model with mathematics
5. Use appropriate tools strategically
6. Attend to precision
7. Look for and make use of structure
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Discrete Mathematics
Mathematics: 2012-13 to 2017-18
Hoover City Schools
8. Look for and express regularity in repeated reasoning
According to the Alabama Quality Teaching Standards (AQTS), teachers of all grade levels and subjects are required to model and reinforce
literacy skills for all students. The Alabama Course of Study for Mathematics defines specific college and career readiness “anchor standards” for
grades 6-12 in the areas of reading and writing. Specific grade-appropriate criteria can be found in the state course of study document, but the
general anchor standards are defined below:
Reading
Key Ideas and Details
1. Read closely to determine what the text says explicitly and to make logical inferences from it; cite specific textual
evidence when writing or speaking to support conclusions drawn from the text.
2. Determine central ideas or themes of a text and analyze their development; summarize the key supporting details and
ideas.
3. Analyze how and why individuals, events, or ideas develop and interact over the course of a text.
Craft and Structure
4. Interpret words and phrases as they are used in a text, including determining technical, connotative, and figurative
meanings, and analyze how specific word choices shape meaning or tone.
5. Analyze the structure of texts, including how specific sentences, paragraphs, and larger portions of the text (e.g. a
section, chapter, scene, or stanza) relate to each other and the whole.
6. Assess how point of view or purpose shapes the content and style of a text.
Integration of Knowledge and Ideas
7. Integrate and evaluate content presented in diverse formats and media, including visually and quantitatively, as well as
in words.
8. Delineate and evaluate the argument and specific claims in a text, including the validity of the reasoning as well as the
relevance and sufficiency of the evidence.
9. Analyze how two or more texts address similar themes or topics in order to build knowledge or to compare the
approaches the authors take.
Range of Reading and Level of Text Complexity
10. Read and comprehend complex literary and informational texts independently and proficiently.
Writing
Text Types and Purposes
1. Write arguments to support claims in an analysis of substantive topics or texts using valid reasoning and relevant and
sufficient evidence.
2. Write informative / explanatory texts to examine and convey complex ideas and information clearly and accurate
through the effective selection, organization, and analysis of content.
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Discrete Mathematics
Mathematics: 2012-13 to 2017-18
Hoover City Schools
3. Write narratives to develop real or imagined experiences or events using effective technique, well-chosen details, and
well-structured event sequences.
Production and Distribution of Writing
4. Produce clear and coherent writing in which the development, organization, and style are appropriate to task, purpose,
and audience.
5. Develop and strengthen writing as needed by planning, revising, editing, rewriting, or trying a new approach.
6. Use technology, including the Internet, to produce and publish writing and to interact and collaborate with others.
Research to Build and Present Knowledge
7. Conduct short as well as more sustained research projects based on focused questions, demonstrating understanding
of the subject under investigation.
8. Gather relevant information from multiple print and digital sources, assess the credibility and accuracy of each source,
and integrate the information while avoiding plagiarism.
9. Draw evidence form literary or informational texts to support analysis, reflection, and research.
Range of Writing
10. Write routinely over extended time frames (time for research, reflection, and revision) and short time frames (a single
sitting or a day or two) for a range of tasks, purposes, and audiences.
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