LCSS Mathematics Pacing Guide
Mathematical Investigations
Resources The suggested text is The Number Devil: A Mathematical Adventure. Extra links have been provided but should not be considered to be allinclusive. There is a blog online with activities related to The Number Devil (www.moreofamom.com) The videos may not need to be shown in their entirety.
For example, The Early History of Mathematics can be used in segments for several of the standards. The videos may be accessed through the CD provided.
1st 9 Weeks
Domain
Number
and
Quantity
Content
Standard
# and
Identifier
1
Content Standard Description
Critique ancient numeration systems and applications, including astronomy
and the development and use of money and calendars. (Alabama)
a. Determine relationships among mathematical achievements of ancient
peoples, including the Sumerians, Babylonians, Egyptians, Mesopotamians,
Chinese, Aztecs, and Incas. (Alabama)
b. 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.
1|Page
RESOURCES AND MATERIALS
The Number Devil – History of Number Systems are found
throughout the book.
Suggested Activities:
Have students write numbers using different systems.
Have students write reports on different cultures and their
development of numbers.
History of Numbers can be found at:
http://www.archimedes-lab.org/numeral.html
At the same site access Numberopedia and Ancient Puzzles
from the
Teacher Resources Tab.
Videos :Tunnel of Samos and Early History of Mathematics
ALEX Lesson Plans http://alex.state.al.us/standardAll.php?subject=MA2013&ccod
e=MI1&summary=3
LCSS Mathematics Pacing Guide
Mathematical Investigations
1st 9 Weeks
Domain
G
e
o
m
e
t
r
y
Number
and
Quantity
Content
Standard
# and
Identifier
11
Content Standard Description
Describe the development of mathematical tools and their applications.
(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.
3
Use special numbers, including e, i, π and the golden ratio, to solve
application-based problems.
a. Identify transcendental numbers. (Alabama)
Example: Calculate e to ten decimal places using a summation with 1/n!.
2|Page
RESOURCES AND MATERIALS
Websites and Activities - http://www-history.mcs.stand.ac.uk/HistTopics/Inca_mathematics.html
http://incas.homestead.com/quipu/quipu_video_elearning.ht
ml
http://agutie.homestead.com/files/Quipu_B.htm
http://alex.state.al.us/lesson_view.php?id=32277
http://alex.state.al.us/lesson_view.php?id=32266
http://www.youtube.com/watch?v=waiprjueVpQ&feature=rela
ted
http://education.ti.com/calculators/timathnspired/US/Activitie
s/?sa=5022&t=5034
http://education.ti.com/calculators/downloads/
US/Activities/Search/Subject?s=5022&sa=5022&t=5034&d=9
ALEX Lesson Plans http://alex.state.al.us/standardAll.php?subject=MA2013&ccod
e=MI1&summary=3
10.4 (ex. 4 and 5), 10.5 (ex. 5 and 6); Supplementary Materials
The Number Devil Connection – These numbers are found
in the Twelfth night of the book.
The Golden Ratio is in the tenth night.
Videos – Reference Story of Pi and show Theorem of Pythagoras
Websites - http://www.mathsisfun.com/
numbers/e-eulers-number.html
http://cuip.uchicago.edu/~dlnarain/golden/
http://illuminations.nctm.org/ActivityDetail.aspx?ID=161
http://illuminations.nctm.org/LessonDetail.aspx?id=U174
ALEX Lesson Plans http://alex.state.al.us/standardAll.php?subject=MA2013&ccod
e=MI1&summary=3
LCSS Mathematics Pacing Guide
Mathematical Investigations
2nd 9 Weeks
Domain
Number
and
Quantity
Content
Standard
# and
Identifier
4
Content Standard Description
RESOURCES AND MATERIALS
Explain the development and uses of sets of numbers, including complex,
real, rational, irrational, integer, whole, and natural numbers. (Alabama)
Website - http://www.famous-mathematicians.com/
The Number Devil connection – Number sets are found
throughout the book.
The Mathematicians are: Gauss the twelfth night,
Archimedes the twelfth night. Euler the tenth night.
Videos – Polynomials, Qudratic Formulas, and Quadratic
Roots and selected segment of Early History of Mathematics
Activities – Parabolic Food Fight and ParaBOOla
ALEX Lesson Plans http://alex.state.al.us/standardAll.php?subject=MA2013&cco
de=MI1&summary=3
The Number Devil Connection – The development of
Fibonacci Sequence is in the sixth night.
Video – Review Polynomials
Websites - Tartaglia’s formula is mentioned in the polynomial
video.
http://www.discoveryeducation.com/teachers/free-lessonplans/numbers-in-nature.cfm
http://illuminations.nctm.org/LessonDetail.aspx?id=L736
http://mathdl.maa.org/mathDL/46/?pa=content&sa=viewDo
cument&nodeId=2433&pf=1
ALEX Lesson Plans http://alex.state.al.us/standardAll.php?subject=MA2013&cco
de=MI1&summary=3
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.
A
l
g
e
b
r
a
3|Page
5
Identify beginnings of algebraic symbolism and structure through the
works of European mathematicians. (Alabama)
a. Create a Fibonacci sequence when given two initial integers.
(Alabama)
b. Investigate Tartaglia's formula for solving cubic equations. (Alabama)
LCSS Mathematics Pacing Guide
Mathematical Investigations
A
l
g
e
b
r
a
Domain
A
l
g
e
b
r
a
6
Content
Standard
# and
Identifier
7
Explain the development and applications of logarithms, including
contributions of John Napier, Henry Briggs, and the Bernoulli family.
(Alabama)
3rd 9 Weeks
Content Standard Description
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. Summarize the significance of René Descartes' Cartesian coordinate
system. (Alabama)
b. Interpret the foundation of analytic geometry with regard to geometric
curves and algebraic relationships. (Alabama)
4|Page
Websites - http://www.johnnapier.com/
http://mathdl.maa.org/mathDL/3/?pa=content&sa=viewDoc
ument&nodeId=1514
http://alex.state.al.us/lesson_view.php?id=32277
http://www.math.twsu.edu/history/men/bernoulli.html
RESOURCES AND MATERIALS
Suugested : Read the book Fly on the Ceiling by Julie Glass. (A
funny history on Descartes’ coordinate plane)
http://illuminations.nctm.org/LessonDetail.aspx?id=L777
Any activity using the coordinate plane would be appropriate.
Read and discuss: The CALCULUS
(Who actually invented it?) By E.T. Bell from Men of
Mathematics
Video – Segment of Early History of Mathematics
LCSS Mathematics Pacing Guide
Mathematical Investigations
G
e
o
m
e
t
r
y
Domain
G
e
o
m
e
t
r
y
8
Content
Standard
# and
Identifier
9
Solve problems from non-Euclidean geometry, including graph theory,
networks, topology, and fractals. (Alabama)
3rd 9 Weeks
Content Standard Description
Analyze works of visual art and architecture for mathematical
relationships. (Alabama)
Examples: Use Leonardo da Vinci's Vitruvian Man to explore the golden
ratio.
Identify mathematical patterns in Maurits Cornelis Escher's
drawings, including the use of tessellations in art, quilting, paintings,
pottery, and architecture.
a.
5|Page
Summarize the historical development of perspective in art and
architecture. (Alabama)
The Number Devil connection – The seventh night
Sierpinski’s triangle. The tenth night Networks and Fractals.
The twelfth night topology.
Websites and Activities- http://math.rice.edu/~lanius/frac/
http://www.mhhe.com/math/ltbmath/bennett_nelson/conc
eptual/netgraphs/graphs.htm
http://www.davidparker.com/janine/mathpage/topology.ht
ml#MOBIUS
http://www.cut-the-knot.org/do_you_know/moebius.shtml
http://videos.howstuffworks.com/tlc/33733-understandingfractals-video.htm
http://fractalanimation.com/
Research Project – Find examples of fractals in nature,
architecture, etc. and put together a PowerPoint with
pictures explaining fractals.
ALEX Lesson Plans http://alex.state.al.us/standardAll.php?subject=MA2013&cco
de=MI1&summary=3
RESOURCES AND MATERIALS
Websites and Activities - http://www.tessellations.org/sethtessellation-bug-motif-03.shtml
http://www.mcescher.com/
http://partner.galileo.org/tips/davinci/vitruviantask.html
ALEX Lesson Plans http://alex.state.al.us/standardAll.php?subject=MA2013&cco
de=MI1&summary=3
LCSS Mathematics Pacing Guide
Mathematical Investigations
Domain
G
e
o
m
e
t
r
y
Content
Standard #
and
Identifier
10
4th 9 Weeks
Content Standard Description
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.
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.
Statistics
and
Probability
6|Page
12
Summarize the history of probability, including the works of Blaise Pascal;
Pierre de Fermat; Abraham de Moivre; and Pierre-Simon, marquis de
Laplace. (Alabama)
Example: Discuss the impact of probability on gaming, economics, and
insurance.
RESOURCES AND MATERIALS
The Number Devil Connection The third night Eratosthenes.
The fourth night- Pythagoras, the Pythagorean Society
The fifth night- triangular numbers
The seventh night- triangular numbers
The eighth night- triangular numbers
The ninth night- series
The twelfth night – Pythagoras and the Pythagorean Society
and triangular numbers
Video – Segment of Early History of MAthematics
ALEX Lesson Plans http://alex.state.al.us/standardAll.php?subject=MA2013&ccod
e=MI1&summary=3
The Number Devil Connection – Pascal mentioned on the
Seventh Night.
Websites and Activities - There are numerous links in each of
the following:
http://www.education.ne.gov/BMIT/pdf/curric/f/insurance
/AutomobileInsuranceUnit.pdf
http://classroom.jc-schools.net/basic/math-prob.html
http://ozpk.tripod.com/000000Prob2
ALEX Lesson Plans http://alex.state.al.us/standardAll.php?subject=MA2013&ccod
e=MI1&summary=3
LCSS Mathematics Pacing Guide
Mathematical Investigations
Number
and
Quantity
2
Analyze mathematical relationships in music to interpret frequencies of
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.
a. Determine lengths of strings necessary to produce harmonic tones as in
Pythagorean tuning. (Alabama)
7|Page
Information about Math and Music can be found at:
http://library.thinkquest.org/4116/Music/music.htm
http://www.pyxidium.unet.com/Acoustics/MusicMaths/MusicMaths.html#pythag
Videos: Sines and Consines Part I and Story of Pi
The end of the Sines and Cosines Part One Video has footage
of graphs made by various musical instruments in terms of
Sine and Cosine Waves.
You might consider inviting the Band Director in to teach with
you
Check YouTube for additional informational videos.
ALEX Lesson Plans http://alex.state.al.us/standardAll.php?subject=MA2013&ccod
e=MI1&summary=3
LCSS Mathematics Pacing Guide
Mathematical Investigations
Essential Vocabulary
st
1 9 Weeks
number, numeral, numeration
system, digits
linear function, quadratic function,
parabola, vertex, axis of symmetry,
exponential function
radius, diameter, circumference, area,
pi, cylinder, sphere, surface area,
volume
8|Page
nd
2 9 Weeks
Gaussian plane, Fibonnaci sequence,
Tartaglia’s formula, cubic equation,
logarithms
3rd 9 Weeks
Elliptic geometry, Hyperbolic
geometry, fractals, tessellations
graph, vertex, edge, loop, path,
connected graph, disconnected
graph, bridge, adjacent vertices,
circuit, Euler path, Euler circuit,
Euler’s theorem, Fleury’s algorithm
4th 9 Weeks
odds, expected value, sine and
cosine waves, figurative number,
triangular number, pentagonal
numbers