Download BCSS Mathematics Pacing Guide 2012

BCSS Mathematics Pacing Guide 2012 - 2013
Discrete Math
Domain
Content
Standard #
and
Identifier
11
4
1st 9 Weeks
Textbook Resources
Content Standard Description
Text: Math in Our World
Solve application-based logic
problems using Venn diagrams,
truth tables and matrices.
Lessons 2.3, 2.4, 3.2, 3.3, 3.4
Convert between base ten and
other bases.
Lesson 4.3(examples 1-4)
http://illuminations.nctm.org/LessonDetail.aspx?id=L384
http://csunplugged.org/binary-numbers
1|Page
BCSS Mathematics Pacing Guide 2012 - 2013
Discrete Math
2nd 9 Weeks
Domain
Content
Standard
# and
Identifier
13
5
Content Standard
Description
Analyze election data to
compare election
methods and voting
apportionment, including
determining strength
within specific groups.
Determine the results of
operations upon a 3x3
and larger matrices,
including matrix addition
and multiplication of a
matrix by a matrix,
vector, or scalar.
Textbook Resources
Text: Math in Our World
Lessons 14.1-14.5
Supplementary Material:
Precalculus Textbook:
Pages P23-P27
http://www.analyzemath.com/matrices/matrices.html
http://www.intmath.com/matrices-determinants/matrix-determinant-intro.php
6
2|Page
Analyze determinants
and inverses of 2x2, 3x3,
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.
http://player.discoveryeducation.com/index.cfm?guidAssetId=226AD508-851A-4C93-8748F0C86ADF2D48&blnFromSearch=1&productcode=DETB
Lesson 7.3
Supplementary Material: Algebra 2 Textbook:
Lessons 3.7, 3.8
Precalculus Textbook:
Lessons 6.1-6.3
BCSS Mathematics Pacing Guide 2012 - 2013
Discrete Math
3rd 9 Weeks
Domain
Content
Standard
# and
Identifier
1
Content Standard
Description
Analyze topics from elementary
number theory, including
perfect numbers and prime
numbers, to determine
properties of integers.
Textbook Resources
Text: Math in Our World
Lesson 5.1
(Include sidelight on page 202)
http://mathforum.org/alejandre/frisbie/locker.html
http://illuminations.nctm.org/LessonDetail.aspx?id=L620
2
3
Determine characteristics of
sequences, including the
Fibonacci sequence, the
triangular numbers, and
pentagonal numbers.
Ex. Write a sequence of the
first 10 triangular numbers and
hypothesize a formula to find
the nth triangular number.
Use the recursive process and
difference equations to create
fractals, population growth
models, sequences, series, and
compound interest models.
Lesson 5.7
(Include sidelight on page 264)
http://mathforum.org/workshops/usi/pascal/pascal_hsdiscans.html
Lesson 5.7
(Include sidelight on page 264)
http://alex.state.al.us/lesson_view.php?id=7362
http://www.shodor.org/interactivate/lessons/FractalsAndTheChaos/
3|Page
BCSS Mathematics Pacing Guide 2012 - 2013
Discrete Math
3rd 9 Weeks
Domain
4|Page
Content
Standard
# and
Identifier
12
Content Standard
Description
Use combinatorial reasoning
and counting techniques to
solve application-based
problems.
Ex. 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.
Textbook Resources
Text: Math in Our World
Lessons 11.1-11.8 (skip lesson 11.6)
http://alex.state.al.us/lesson_view.php?id=14515
http://www.khanacademy.org/math/probability/v/permutations-and-combinations-1
BCSS Mathematics Pacing Guide 2012 - 2013
Discrete Math
4th 9 Weeks
Domain
Content
Standard
# and
Identifier
9
10
7
7a
8
8a
5|Page
Content Standard Description
Textbook Resources
Text: Math in Our World
Determine a minimum project time using algorithms
to schedule tasks in order, including critical path
analysis, the list-processing algorithm, and studentcreated algorithms.
Use vertex-coloring techniques and matching
techniques to solve application-based problems.
Ex. 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.
Solve problems through investigation and application
of existence and nonexistence of Euler paths, Euler
circuits, Hamilton paths, and Hamilton circuits.
Ex: Show why a 5x5 grid has no Hamilton
circuit.
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.
Chapter 15
Use shortest path techniques to find optimal shipping
routes.
Lesson 15.4
Lesson 15.1
http://csunplugged.org/graph-colouring
Lessons 15.2 and 15.3
http://illuminations.nctm.org/ActivityDetail.aspx?ID=20
Lessons 15.2 and 15.3
Lesson 15.4
http://csunplugged.org/minimal-spanning-trees
BCSS Mathematics Pacing Guide 2012 - 2013
Discrete Math
Essential Vocabulary
1st 9 Weeks
Venn Diagram, Truth Table,
tautology, self-contradiction, logically
equivalent statements, converse,
inverse contrapositive, De Morgan’s
laws
Base number system
2nd 9 Weeks
Preference table, Plurality method,
head-to-head comparison criterion,
Borda count method, majority
criterion, plurality-with-elimination
method, monotonicity criterion,
pairwise comparision method,
irrelevant alternatives criterion,
Arrow’s impossibility theorem,
approval voting, apportionment,
standard divisor, standard quota,
upper and lower quotas, Hamilton’s
method, Jefferson’s method, Adams’
method, Webster’s method, The
Huntington-Hill method, Alabama
paradox, Population paradox, new
states paradox, quota rule
Matrix, augmented matrix, row
operations, row echelon form,
Gaussian elimination, determinant,
diagonal rule, Cramer’s Rule,
coefficient matrix, identity matrix,
square matrix, inverse matrix, matrix
equation, variable matrix, constant
matrix
6|Page
3rd 9 Weeks
Natural number, factor, divisor,
divisible, multiples, prime number,
prime factorization, composite
number, fundamental theorem of
arithmetic, greatest common factor,
relatively prime, least common
multiple, perfect numbers
Sequence, arithmetic sequence,
common difference, geometric
sequence, common ratio
Fundamental counting principle,
factorial notation, permutation,
permutation rule, tree diagram,
combination, combination rule,
probability experiment, outcome,
sample space, event, classical
probability, empirical probability,
observed frequency, mutually
exclusive events, addition rules,
multiplication rules, independent
events, dependent events, conditional
probability
4th 9 Weeks
Graph, vertex, edge, loop, equivalent
graphs, degree of a vertex, odd
vertex, even vertex, adjacent vertices,
path, circuit, connected graph,
disconnected graph, bridge
Euler path, Euler circuit, Euler’s
theorem, Fleury’s algorithm,
Hamilton path, Hamilton circuit,
complete graph, complete weighted
graph, optimal solution, Brute force
method, approximate optimal
solution
Tree, spanning tree, minimum
spanning tree, Kruskal’s algorithm