Download MATH INV CCRS Standard

MATH INV
Mathematics CCRS Standards and Alabama COS
CCRS Standard
1. Critique ancient
numeration systems and
applications, including
astronomy and the
development and use of
money and calendars.
(Alabama)
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Standard ID
Modeling
Number/Quantity
MI-NM.1
Determine
relationships
among
mathematical
achievements of
ancient peoples,
including the
Sumerians,
Babylonians,
Egyptians,
Mesopotamians,
Chinese, Aztecs,
and Incas.
(Alabama)
Explain origins of
the Hindu-Arabic
numeration
system. (Alabama)
Example: Perform
addition and
subtraction in both
the Hindu-Arabic
and the Roman
numeration
systems to
compare place
value and place
holders.
Franklin County Schools
Evidence of Student
Attainment
Students:
 Create a
presentation identifying
and analyzing the
mathematical
achievements of ancient
people.
 Compare and
contrast Hindu-Arabic
and Roman numeration
systems.
Teacher Vocabulary
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Knowledge
Resources
Numeration systems
Place value/place holders
Roman Numerals
Hindu-Arabic Numerals
Click below to access
all ALEX resources
aligned to this
The significance standard.
of place value.
 ALEX Resources
Students know:
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MATH INV
Mathematics CCRS Standards and Alabama COS
2. Analyze mathematical
Modeling
relationships in music to
Number/Quantity
interpret frequencies of
MI-NM.2
musical notes and to
compare mathematical
structures of various
musical instruments.
(Alabama)
Examples: Compare
frequencies of notes
exactly one octave apart on
the musical scale; using
frequencies and wave
patterns of middle C, E
above middle C, and G
above middle C to explain
why the C major chord is
harmonious.
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Students:
 Demonstrate the
relationship between
math and music.
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Frequencies
Octaves
Pythagorean tuning
Harmonious/harmonic
tones
Students know:
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Basic fractional
concepts.
Characteristics of
periodic functions.
Click below to access
all ALEX resources
aligned to this
standard.

ALEX Resources
Determine lengths
of strings
necessary to
produce harmonic
tones as in
Pythagorean
tuning. (Alabama)
3. Use special numbers,
including e, i, π; and the
golden ratio, to solve
application-based
problems. (Alabama)
Modeling
Number/Quantity
MI-NM.3
Students:
 Solve applicationbased problems
involving e, i, π and the
golden ratio.
a. Identify transcendental
numbers.
Example: Calculate e to ten
decimal places using a
summation with 1/n!
4. Explain the development Modeling
and uses of sets of
Number/Quantity
Franklin County Schools
Students:
 Describe the
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e
i
π
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Real numbers
Rational/irrational
Transcendental numbers
Golden ratio
Summation
Complex numbers
Irrational numbers
Factorial
Students know:
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How to calculate
factorials.
The approximation
for e and π.
The definition of i.
How to perform
operations using
imaginary
numbers.
Students know:
Click below to access
all ALEX resources
aligned to this
standard.

ALEX Resources
Click below to access
all ALEX resources
MATH INV
numbers, including
complex, real, rational,
irrational, integer, whole,
and natural numbers.
(Alabama)
Mathematics CCRS Standards and Alabama COS
MI-NM.4
development and use of
sets of numbers from
natural to complex
including the
contributions of wellknown mathematicians.
numbers
 Imaginary/complex
numbers
 Gaussian plane (complex
plane
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a. Analyze contributions
to the number system by
well-known
mathematicians, including
Archimedes, John Napier,
René Descartes, Sir Isaac
Newton, Johann Carl
Friedrich Gauss, and Julius
Wilhelm Richard Dedekind.
(Alabama)
Example: Plot solutions to
the polynomial equation, x2
– 6x + 11 = 0, on the
Gaussian plane.
5. Identify beginnings of
algebraic symbolism and
structure through the
works of European
mathematicians. (Alabama)
a.
b.
Seeing Structure
in Expressions
Algebra
MI-SSE.1
Create a Fibonacci
sequence when given
two initial integers.
(Alabama)
Investigate Tartaglia’s
formula for solving
cubic equations.
(Alabama)
6. Explain the development
and applications of
logarithms, including
contributions of John
Napier, Henry Briggs, and
the Bernoulli family.
(Alabama)
Seeing Structure
in Expressions
Algebra
MI-SSE.2
Franklin County Schools
Students:
 Summarize the
works of
European
mathematicians
focusing on the
beginnings of
algebraic
symbolism and
structure.
Students:
Outline the contributions
of John Napier, Henry
Briggs, and Bernoulli
family to the
development and
application of logarithms
aligned to this
The characteristics standard.
of each of the sets
of numbers.
 ALEX Resources
How to solve
polynomial
equations.
Students know:
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Fibonacci sequence
Cubic equations
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Exponentials
Natural logarithms
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Click below to access
Characteristics of all ALEX resources
sequences.
aligned to this
How to identify a standard.
cubic equation and
that the solutions
 ALEX Resources
are real or
complex.
Students know:

Definition and
basic application
of logarithms and
exponentials.
Click below to access
all ALEX resources
aligned to this
standard.

ALEX Resources
MATH INV
7. Justify the historical
significance of the
development of multiple
perspectives in
mathematics. (Alabama)
Example: Relate the
historical development of
multiple perspectives to the
works of Sir Isaac Newton
and Gottfried Wilhelm von
Leibniz in the foundations
of calculus.
a.
b.
Mathematics CCRS Standards and Alabama COS
Seeing Structure
in Expressions
Algebra
MI-SSE.3
Students:
Cartesian coordinate system
Critique historical
significance of the
development of multiple
perspectives in
mathematics.
Click below to access
all ALEX resources
aligned to this
The basic concepts standard.
of the coordinate
system.
 ALEX Resources
Students know:

Summarize the
significance of René
Descartes’ Cartesian
coordinate system.
(Alabama)
Interpret the
foundation of analytic
geometry with regard
to geometric curves
and algebraic
relationships.
(Alabama)
8. Solve problems from
non-Euclidean geometry,
including graph theory,
networks, topology, and
fractals. (Alabama)
Math Investigation
Standard 8 Example
Expressing
Geometric
Properties with
Equations
Geometry
MI-GPE.1
Students:
Will be able to solve
problems from nonEuclidean geometry
involving:
 Graph theory
 Networks
 Topology
 Fractals
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Topology
Fractals
Networks
Non-Euclidean Geometry
Euclidean Geometry
Traversable
Sierpinski’s triangle
9. Analyze works of visual
art and architecture for
mathematical relationships.
(Alabama)
Examples: Use Leonardo da
Vinci’s Vitruvian Man to
explore the golden ratio.
Modeling with
Geometry
Geometry
MI-MG.1
Students:
 Examine works of
visual art and
architecture and identify
the mathematical
relationships within
them.
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Golden Ratio
Tessellations
Perspective
Symmetry
Franklin County Schools
Click below to access
all ALEX resources
aligned to this
The basic concepts standard.
of Euclidean
geometry.
 ALEX Resources
Students know:
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Students know:
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Basic concepts of
ratio and
proportion.
The types of
symmetry and
Click below to access
all ALEX resources
aligned to this
standard.

ALEX Resources
MATH INV
Mathematics CCRS Standards and Alabama COS
Identify mathematical
patterns in Maurits Cornelis
Escher’s drawings,
including the use of
tessellations in art, quilting,
paintings, pottery, and
architecture.
how to identify
each type.
a. Summarize the
historical development of
perspective in art and
architecture. (Alabama)
10. Determine the
mathematical impact of the
ancient Greeks, including
Archimedes, Eratosthenes,
Euclid, Hypatia,
Pythagoras, and the
Pythagorean Society.
(Alabama)
Example: Use Euclid’s
proposition to inscribe a
regular hexagon within a
circle.
Modeling with
Geometry
Geometry
MI-MG.2
Students:
 Investigate and
analyze the impact of
the ancient Greek
mathematicians.
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Pythagorean Theorem
Inscribe
Regular Polygon
Figurate Numbers
Sequence
Proofs
Hypothesis
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a. Construct multiple
proofs of the Pythagorean
Theorem. (Alabama)
b. Solve problems
involving figurate numbers,
including triangular and
pentagonal numbers.
(Alabama)
Example: Write a sequence
of the first 10 triangular
numbers and hypothesize a
formula for finding the nth
triangular number.
11. Describe the
development of
mathematical tools and
Students know:
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Modeling with
Geometry
Geometry
Franklin County Schools
Students:
Summarize the use and
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Napier’s Bones
Slide Rule
Knotted Ropes
How to construct
proofs.
The Pythagorean
Theorem.
How to generate a
sequence.
How to derive a
formula for the nth
term of a
sequence.
Students know:

How to use a
Click below to access
all ALEX resources
aligned to this
standard.

ALEX Resources
Click below to access
all ALEX resources
aligned to this
MATH INV
Mathematics CCRS Standards and Alabama COS
their applications.
MI-MG.3
(Alabama)
Examples: Use knotted
ropes for counting; Napier’s
bones for multiplication; a
slide rule for multiplying
and calculating values of
trigonometric, exponential,
and logarithmic functions;
and a graphing calculator
for analyzing functions
graphically and numerically.
development of
mathematical tools.
12. Summarize the history
of probability, including the
works of Blaise Pascal;
Pierre de Fermat; Abraham
de Moivre; and PierreSimon, marquis de Laplace.
(Alabama)
Example: Discuss the
impact of probability on
gaming, economics, and
insurance.
Students:
 Are able to describe
the historical
development of
probability.
Making
Inferences &
Justifying
Conclusions
Statistics &
Probability
MI-IC.1
Franklin County Schools
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Trigonometric Function
Exponential Function
Logarithmic Function
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Probability
Statistics
Gaming
Economics
Insurance

graphing
standard.
calculator.
Concepts involving
 ALEX Resources
trigonometric,
exponential and
logarithmic
functions.
Click below to access
all ALEX resources
aligned to this
Concepts involving standard.
simple probability.
 ALEX Resources
Students know:
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