Download 2017 Discrete Math Pacing Guide

Huntsville City Schools
2016 – 2017 Pacing Guide
Discrete Math Twelfth Grade
Math Practices:
The Standards for Mathematical Practice describe varieties of expertise that mathematics educators at all levels should seek to develop in their students. These
practices rest on important “processes and proficiencies” with longstanding importance in mathematics education. The first of these are the NCTM process
standards of problem solving, reasoning and proof, communication, representation, and connections. The second are the strands of mathematical proficiency
specified in the National Research Council’s report Adding It Up: adaptive reasoning, strategic competence, conceptual understanding (comprehension of
mathematical concepts, operations and relations), procedural fluency (skill in carrying out procedures flexibly, accurately, efficiently and appropriately), and
productive disposition (habitual inclination to see mathematics as sensible, useful, and worthwhile, coupled with a belief in diligence and one’s own efficacy).
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.
8. Look for and express regularity in repeated reasoning.
Elaboration on each standard: www.corestandards.org/Math/Practice/
Kid friendly language: www.buncombe.k12.nc.us/Page/37507
Online Resources:
 Dan Meyer’s Ted Talk about teaching math: : https://youtu.be/qocAoN4jNwc
 Links to Dan Meyer’s 3-act activities, sorted by standard:
https://docs.google.com/spreadsheet/ccc?key=0AjIqyKM9d7ZYdEhtR3BJMmdBWnM2YWxWYVM1UWowTEE#gid=0
 Granite City Math Vocabulary: http://www.graniteschools.org/mathvocabulary/
 Open Curriculum - activities from all over the internet sorted by standard: www.opencurriculum.org
 MARS - Mathematics Assessment Resource Service – formative assessments and group activities: http://map.mathshell.org/lessons.php
 Desmos – free online calculator – excellent for working with linear equations, scatterplots, and best-fit lines : www.desmos.com Teacher
version includes lessons and activities: https://teacher.desmos.com/
 Illuminations – lessons developed by NCTM: http://illuminations.nctm.org/
Huntsville City Schools
2016 – 2017 Pacing Guide
Discrete Math Twelfth Grade
First Nine Weeks
Chapter 2 Vocabulary:
set, subset, element, empty set, universal set, roster form, set-builder notation, proper subset, Infinite set, complement, intersection, union, Cartesian
product, De Morgan’s Laws, countable sets
Chapter 3 Vocabulary:
Quantifiers, Connectives, statement, Negation, conjunction, disjunction, conditional, biconditional, Truth tables, De Morgan’s Laws, conditional,
converse, inverse, contrapositive, Law of Detachment, Law of Contraposition, Law of Syllogism, Disjunctive Syllogism, Fallacy of the Converse, Fallacy of
the Inverse, Symbolic argument, syllogistic argument, switches
Chapter 4 Vocabulary:
Positional values, base
Huntsville City Schools
2016 – 2017 Pacing Guide
Discrete Math Twelfth Grade
First Nine Weeks
Standard
Resources
11. Solve application-based logic problems using Venn
diagrams, truth tables and matrices
A Survey of Mathematics – Angel, Abbott, and
Runde
(Chapter 2)
 Sec. 2.1 Set Concepts
 Sec. 2.2 Subsets
 Sec. 2.3 Venn Diagrams and Set Operations
 Sec. 2.4 Venn Diagrams with three sets and
Verification of Equality of Sets
 Sec. 2.5 Applications of Sets
 Sec. 2.6 Infinite Sets
Topics include:
 solve application-based logic problems using
Venn diagrams.
11. Solve application-based logic problems using Venn
diagrams, truth tables and matrices
Topics include:
 solve application-based logic problems using
Truth tables diagrams.
4. Convert between base ten and other bases.
A Survey of Mathematics – Angel, Abbott, and
Runde
(Chapter 3)
 Sec. 3.1 Statements and Logical Connectives
 Sec. 3.2 Truth tables for Negation,
Conjunction, and Disjunction
 Sec. 3.3 Truth Tables for Conditional and
Biconditional
 Sec. 3.4 Equivalent Statements
 Sec. 3.5 Symbolic Statements
 Sec. 3.6 Euler Diagrams and Syllogistic
Arguments
 Sec. 3.7 Switching Circuits
A Survey of Mathematics, Angel, Abbott, Runde
Approximate
Pacing
Number of
Days
10 days
14 days
10 days


(Chapter 4: Sec. 4.3 and 4.4)
(Sec. 4.1 and 4.2 are optional)
Sec. 4.3 Other Bases
Sec. 4.4 Computation in Other Bases
34 days total
Huntsville City Schools
2016 – 2017 Pacing Guide
Discrete Math Twelfth Grade
Second Nine Weeks
Chapter 5 Vocabulary:
Natural numbers, counting numbers, whole numbers, Integers, rational numbers, irrational numbers, real numbers, rational numbers, radicals, quotient
rule, product rule, commutative property, associative property, distributive property, zero exponent rule, power rule, arithmetic sequence, geometric
sequence, Fibonacci Sequence, Triangular numbers, Pentagonal numbers
Chapter 6 Vocabulary:
Order of Operations, Properties of Equality, Formula, Direct Variation, Indirect Variation, Joint Variation, Inequalities, Intercepts, Quadratic Equations,
Slope-Intercept Form, Quadratic Formula, Axis of Symmetry, Parabola, Exponential Function
Chapter 7 Vocabulary:
Matrices, Augmented Matrix, System of Linear Equations
Huntsville City Schools
2016 – 2017 Pacing Guide
Discrete Math Twelfth Grade
Second Nine Weeks
Standard
1. Analyze topics from elementary number theory,
including perfect numbers and prime numbers, to
determine properties of integers.
Resources
A Survey of Mathematics – Angel, Abbott, and
Runde
(Chapter 5)
 Sec. 5.1 Number Theory
 Sec. 5.2 The Integers
 Sec. 5.3 Rational Numbers
 Sec. 5.4 The Irrational Numbers and the Real
number System
 Sec. 5.5 Properties of Real numbers
 Sec. 5.6 Rules of Exponents
Approximate
Pacing
Number of
Days
8 days
Website:
For Prime numbers
www.mathsisfun.com/numbers/prime-numbersadvanced.html
2. Determine characteristics of sequences, including
the Fibonacci sequence, the triangular numbers, and
pentagonal numbers.
A Survey of Mathematics – Angel, Abbott, and
Runde
(Chapter 5: Sections 5.7 and 5.8)
 Sec. 5.7 Arithmetic and geometric Sequences
 Sec. 5.8 Fibonacci Sequence
6 days
*Need Resources for Triangular number and
pentagonal numbers.
Algebra review
(not in standards, but helpful for college
placement exams/ACT)
*Will be on Benchmark Test
5. Determine results of operations upon 3 × 3 and
larger matrices, including matrix addition and
multiplication of a matrix by a matrix, vector, or scalar.
6. Analyze determinants and inverses of 2 × 2, 3 × 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.
A Survey of Mathematics, Angel, Abbott, Runde
(Chapter 6)
 Sec. 6.1 Order of Operations
 Sec. 6.2 Linear Equations in One Variable
 Sec. 6.3 Formulas
 Sec. 6.4 Applications of Linear Equations in
One Variable
 Sec. 6.5 Variation
 Sec. 6.6 Linear Inequalities
 Sec. 6.7 Graphing Linear Equations
 Sec. 6.8 Linear Inequalities in Two Variables
 Sec. 6.9 Solving Quadratic Equations by
Using Factoring and the Quadratic Formula
 Sec. 6.10 Functions and their graphs
15 days
A Survey of Mathematics, Angel, Abbott, Runde
(Chapter 7)
8 days




Sec. 7.1 Systems of Linear Equations
(Optional)
Sec. 7.2 Solving Systems of Linear Equations
by the Substitution and Addition Methods
(Optional)
Sec. 7.3 Matrices (Required)
Sec. 7.4 Solving Systems of Linear Equations
by Using Matrices (Required)
37 days
Huntsville City Schools
2016 – 2017 Pacing Guide
Discrete Math Twelfth Grade
Third Nine Weeks
Chapter 11 Vocabulary:
Percent change, Percent markup, Simple Interest, Compound Interest, Percent Value, Installment Payment, Mortgage Principal and Interest
Chapter 12 Vocabulary:
Empirical Probability, The Law of Large Numbers, Theoretical Probability, Odds, Expected Value, Counting Principle, Conditional Probability,
Permutation, Combination
Chapter 13 Vocabulary:
Random Sampling, Systematic Sampling, Cluster sampling, Stratified sampling, Convenience sampling, Frequency Distribution, Histogram,
Frequency Polygon, Stem-and-Leaf Display, Circle Graph, Measures of Central Tendency, Median, Mode, Mean , Midrange, Percentiles, Quartiles,
range, standard deviation
Huntsville City Schools
2016 – 2017 Pacing Guide
Discrete Math Twelfth Grade
Third Nine Weeks
Standard
Resources
3. Use the recursive process and difference equations
to create fractals, population growth models,
sequences, series, and compound interest models.
A Survey of Mathematics – Angel, Abbott, and
Runde
 Sec. 11.1 Percent
 Sec. 11.2 Personal Loans and Simple Interest
 Sec. 11.3 Compound Interest
 Sec. 11.4 Installment Buying
 Sec. 11.5 Buying a House with a Mortgage
12. Use combinatorial reasoning and counting
techniques to solve application-based problems.
A Survey of Mathematics – Angel, Abbott, and
Runde
(Chapter 12)
 Sec. 12.1 The Nature of Probability
 Sec. 12.2 Theoretical Probability
 Sec. 12.3 Odds (optional)
 Sec. 12.4 Expected Value
 Sec. 12.5 Tree Diagrams
 Sec. 12.6 OR and AND Problems
 Sec. 12.7 Conditional Probability (optional)
 Sec. 12.8 The Counting Principle and
Permutations
 Sec. 12.9 Combinations
Approximate
Pacing
Number of
Days
12
12

Sec. 12.10 Solving Probability Problems by
Using Combinations
NMSI Lessons:
N/A
Calculating Tree Diagrams
Probability Rules
A Survey of Mathematics – Angel, Abbott, and
Runde
(Chapter 13 this unit is optional)
 Sec. 13.1 Sampling Techniques
 Sec. 13.2 The misuses of Statistics
 Sec. 13.3 Frequency Distributions and
Statistical Graphs
 Sec. 13.4 Measures of Central Tendency
 Sec. 13.5 Measures of Dispersion
12
36 days
Huntsville City Schools
2016 – 2017 Pacing Guide
Discrete Math Twelfth Grade
Fourth Nine Weeks
Chapter 14 Vocabulary:
Path, Circuit, Euler Path, Euler Circuit, Hamilton Path, Hamilton Circuit, Complete Graph, Vertex Edge Graph, Brute Force Method, Nearest
Neighbor Method, Traveling Salesman Problems, Kruskal’s Algorithm
Chapter 15 Vocabulary:
Plurality, Borda Count, Plurality with Elimination, Pairwise Comparison, Majority Criterion, Head-to-Head Criterion, Monotonicity Criterion,
Irrelevant Alternatives Criterion, Apportionment Methods, Alabama Paradox, Population Paradox, New-States Paradox
Huntsville City Schools
2016 – 2017 Pacing Guide
Discrete Math Twelfth Grade
Fourth Nine Weeks
Standard
7. Solve problems through investigation and
application of existence and nonexistence of
Euler paths, Euler circuits, Hamilton paths, and
Hamilton circuits.
Resources
A Survey of Mathematics – Angel, Abbott, and Runde
(Chapter 14)
 Sec. 14.1 Graphs, Paths, and Circuits
 Sec. 14.2 Euler Paths and Euler Circuits
 Sec. 14.3 Hamilton Paths and Circuits
Approximate
Pacing
Number of
Days
10 days
Sec
Website:
Mathmaniacs.org/lessons/12-euler/index.html
8. Apply algorithms, including Kruskal’s and
Prim’s, relating to minimum weight spanning
trees, networks, flows, and Steiner trees.
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.
A Survey of Mathematics – Angel, Abbott, and Runde
(Chapter 14)

Sec. 14.4 Trees
Use more outside resources (maybe a project)
Websites:
10 days
10. Use vertex-coloring techniques and
matching techniques to solve application-based
problems.
(optional resources)
http://www.ams.org/samplings/featurecolumn/fcarc-trees
http://sciencenetlinks.com/science-news/scienceupdates/art-algorithms/
http://illuminations.nctm.org/Lesson.aspx?id=2995
http://alex.state.al.us/lesson_view.php?id=24803
13. Analyze election data to compare election
methods and voting apportionment, including
determining strength within specific groups.
A Survey of Mathematics – Angel, Abbott, and Runde
(Chapter 15)
 Sec. 15.1 Voting Methods
 Sec. 15.2 Flaws of Voting Methods
 Sec. 15.3 Apportionment Methods
 Sec. 15.4 Flaws of Apportionment Method
12 days
Sec
Use the lesson: Will the Best Candidate Win? From the
websiteIlluminations.nctm.org
32 days
Listed below are the technology standards for grades nine through twelve. You are to make every effort to incorporate the
applicable standards into your daily classroom lessons. These standards should be noted in your lesson plans.
Alabama Technology Standards Ninth – Twelfth Grade
Operations and Concepts
Students will:
2.
Diagnose hardware and software problems.
Examples: viruses, error messages
Applying strategies to correct malfunctioning hardware and software
Performing routine hardware maintenance
Describing the importance of antivirus and security software
3.
Demonstrate advanced technology skills, including compressing, converting, importing, exporting, and backing up files.
Transferring data among applications
Demonstrating digital file transfer
Examples: attaching, uploading, downloading
4.
Utilize advanced features of word processing software, including outlining, tracking changes, hyperlinking, and mail merging.
5.
Utilize advanced features of spreadsheet software, including creating charts and graphs, sorting and filtering data, creating formulas, and applying functions.
6.
Utilize advanced features of multimedia software, including image, video, and audio editing.
Digital Citizenship
9.
Practice ethical and legal use of technology systems and digital content.
Explaining consequences of illegal and unethical use of technology systems and digital content
Examples: cyberbullying, plagiarism
Interpreting copyright laws and policies with regard to ownership and use of digital content
Citing sources of digital content using a style manual
Examples: Modern Language Association (MLA), American Psychological Association (APA)
Research and Information Fluency
11. Critique digital content for validity, accuracy, bias, currency, and relevance.
Communication and Collaboration
12. Use digital tools to publish curriculum-related content.
Examples: Web page authoring software, coding software, wikis, blogs, podcasts
13. Demonstrate collaborative skills using curriculum-related content in digital environments.
Examples: completing assignments online; interacting with experts and peers in a structured, online learning environment
Critical Thinking, Problem Solving, and Decision Making
14. Use digital tools to defend solutions to authentic problems.
Example: disaggregating data electronically
Creativity and Innovation
1. Create a product that integrates information from multiple software applications.
Example: pasting spreadsheet-generated charts into a presentation