Huntsville City Schools - Instructional Guide
2015 - 2016
Course Discrete Math Grade 11 – 12
Math Practices
Online Resources
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).
Dan Meyer’s Ted Talk about teaching math:
https://youtu.be/qocAoN4jNwc
1.
2.
3.
4.
5.
6.
7.
8.
Links to his 3-act activities, sorted by standard:
https://docs.google.com/spreadsheet/ccc?key=0AjIqyKM9d7ZYd
EhtR3BJMmdBWnM2YWxWYVM1UWowTEE#gid=0
Granite City Math Vocabulary:
http://www.graniteschools.org/mathvocabulary/
Make sense of problems and persevere in solving them.
Reason abstractly and quantitatively.
Construct viable arguments and critique the reasoning of others.
Model with mathematics
Use appropriate tools strategically.
Attend to precision.
Look for and make use of structure.
Look for and express regularity in repeated reasoning .
For more:
1st
Nine
Other online resources
Weeks
1
Elaboration on each practice from the Common Core website:
www.corestandards.org/Math/Practice/
www.opencurriculum.org is a website that curates activities from all
over the web, sorted by standard.
Kid-friendly language:
www.buncombe.k12.nc.us/Page/37507
http://map.mathshell.org/lessons.php has great formative
assessments and group activities, searchable by standard.
Online tools
www.desmos.com is a free online calculator. Excellent for working
with linear equations, scatterplots, and best-fit lines.
https://teacher.desmos.com/ has some great activities for introducing
and working with functions.
www.geogebra.org is a free online geometry tool. It is great for
working with transformations.
“I Can” Statements
Resources
Standard
N/A
N/A
A Survey of Mathematics – Angel,
Abbott, and Runde
(Chapter 1)
11. Solve applicationbased logic problems using
Venn diagrams, truth
tables and matrices
1. I can solve application-based
logic problems using Venn
diagrams.
2. I can solve application-based
logic problems using truth tables.
3. I can solve application-based
logic problems using matrices
A Survey of Mathematics – Angel,
Abbott, and Runde
(Chapter 2 and 3)
Pacing
Recommendation
/ Date(s) Taught
5 Days
(Optional)
22 Days
Quality Core Unit 3 Algebra II B-5 to
D-6
2
1. Analyze topics from
elementary number theory,
including perfect numbers
and prime numbers, to
determine properties of
integers.
2. Determine
characteristics of
sequences, including the
Fibonacci sequence, the
triangular numbers, and
pentagonal numbers.
3. Use the recursive
process and difference
equations to create
fractals, population growth
models, sequences, series,
and compound interest
models.
1. I can use the recursive process
and difference equations to create
fractals.
2. I can use the recursive process
and difference equations to create
population grown models.
3. I can use the recursive process
and difference equations to create
sequences.
4. I can use the recursive process
and difference equations to create
series.
5. I can use the recursive process
and difference equations to create
compound interest models.
A Survey of Mathematics – Angel,
Abbott, and Runde
(Chapter 5 with emphasis on Sections
5.1, 5.2, 5.7 and 5.8)
Days
Website:
For Prime numbers
www.mathsisfun.com/numbers/primenumbers-advanced.html
NMSI Lesson:
Exponential Growth and Decay
TOTAL DAYS:
39 DAYS
3
2nd Nine Weeks
Standard
4. Convert between base ten
and other bases.
3. Use the recursive process
and difference equations to
create fractals, population
growth models, sequences,
series, and compound interest
models.
“I Can” Statements
Resources
1. I can convert between base ten
and other bases.
A Survey of Mathematics,
Angel, Abbott, Runde
(Chapter 4)
1. I can use the recursive process
and difference equations to
create population growth models.
A Survey of Mathematics,
Angel, Abbott, Runde
(Chapter 6 with emphasis on
6.10)
Pacing
Recommendation
/ Date(s) Taught
11 Days
14 Days
4
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.
1. I can determine results of
addition upon 3x3 and larger
matrices
2. I can determine results of
multiplication of a matrix by a
matrix, vector, or scalar.
3. I can analyze determinants of of
matrices to determine the nature
of the solution set of systems of
equations.
4. I can use inverses to find the
solution set of systems of
equations.
5. I can use echelon row reduction
to solve for the solution set of
systems of equations.
A Survey of Mathematics,
Angel, Abbott, Runde
(Chapter 7)
12 Days
TOTAL DAYS:
37 DAYS
3rd Nine Weeks
Standard
7. Solve problems through
investigation and application
of existence and nonexistence
of Euler paths, Euler circuits,
Hamilton paths, and Hamilton
circuits.
8. Apply algorithms, including
Kruskal’s and Prim’s, relating
to minimum weight spanning
trees, networks, flows, and
Steiner trees.
“I Can” Statements
1. I can solve problems through
investigation and application of
existence and nonexistence of Euler
paths.
2. I can solve problems through
investigation and application of
existence and nonexistence of Euler
Circuits.
3. I can solve problems through
investigation and application of
Resources
A Survey of Mathematics
– Angel, Abbott, and Runde
(Chapter 14)
Pacing
Recommendation
/ Date(s) Taught
18 days
Website:
Mathmaniacs.org/lessons/12euler/index.html
5
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.
10. Use vertex-coloring
techniques and matching
techniques to solve
application-based problems.
12. Use combinatorial
reasoning and counting
techniques to solve
application-based problems.
existence and nonexistence of Hamilton
paths
4. I can solve problems through
investigation and application of
existence and nonexistence of Hamilton
Circuits
5. I can apply algorithms, including
Kruskal’s and Prim’s.
6. I can relate minimum weight
spanning trees.
7. I can relate networks, flows, and
Steiner trees.
8. I can determine a minimum project
time using algorithms to schedule tasks
in order.
9. I can include critical path analysis.
10. I can do the list-processing
algorithm.
11. I can do a student-created
algorithms
12. I can use vertex-coloring techniques
to solve application-based problems.
13. I can use matching techniques to
solve application-based problems.
Additional topics include: bridges,
connected and disconnected graphs,
Nearest Neighbor algorithm, minimumcost spanning tree, interpret probable
life expectancy
1. I can use combinatorial reasoning to
solve application-based problems.
2. I can use counting techniques to
solve application-based problems.
Additional topics include: odds,
expected value, tree diagram, P(A and
B), P (A or B), empirical probability
A Survey of Mathematics
– Angel, Abbott, and Runde
(Chapter 12)
13 days
NMSI Lessons:
Calculating Tree Diagrams
Probability Rules
6
A Survey of Mathematics
– Angel, Abbott, and Runde
(Chapter 13)
6 days
TOTAL DAYS:
37 DAYS
4th Nine Weeks
“I Can” Statements
Standard
Resources
Pacing
Recommendation
/ Date(s) Taught
7
N/A
N/A
13. Analyze election data to
compare election methods and
voting apportionment,
including determining strength
within specific groups.
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
(Chapter 13)
A Survey of Mathematics
– Angel, Abbott, and Runde
(Chapter 15)
10 Days
10 Days
Use the lesson: Will the Best
Candidate Win? From the
websiteIlluminations.nctm.org
1. I can use the recursive process and
difference equations to create fractals.
2. I can use the recursive process and
difference equations to create
population grown models.
3. I can use the recursive process and
difference equations to create
sequences.
4. I can use the recursive process and
difference equations to create series.
5. I can use the recursive process and
difference equations to create
compound interest models.
A Survey of Mathematics
– Angel, Abbott, and Runde
(Chapter 11 with emphasis
on Section 11.3)
12 Days
TOTAL DAYS:
32 DAYS
8