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Locust Valley High School
Math Research Curriculum
Written 2010
Locust Valley Middle School
Mathematics Department
MATH RESEARCH
July 2010
Superintendent of Schools: Dr. Anna Hunderfund
Board of Education:
Jack Dolce – President
Suzanne Sgueglia – Vice President
Philip Bellisari
Erika Bruno
Dr. Yao Chu
Joseph Madsen
Ronald J. Walsh, Jr.
Principal:
Howard Hogan
Assistant Principal:
Rachel Green
Curriculum Supervisor: Robert Teseo
Written By:
Lisa McNamara
Locust Valley High School
Math Research Curriculum
Written 2010
TABLE OF CONTENTS
Philosophy…………………………………………………………………………....1
State Standards…………………………………………………………………….....2
Units of Study……………………………………………………………………….14
Daily Objectives in Each Unit……………………………………………………....15
Appendix A Sources for exploration activities………………………………………A1
Appendix B: Bibliography…………………………..………………….……………B1
Locust Valley High School
Math Research Curriculum
Written 2010
STATEMENT OF PHILOSOPHY
Thinking mathematically is a skill that is a useful tool for students of all ages. Logical
thinking and reasoning can be explored at all levels of mathematics and is a way for
students to become better thinkers. The Math Research curriculum extends, formalizes,
and builds upon students prior mathematics concepts. The New York State standards, as
well as national standards, were taken into consideration when creating the Math
Research curriculum.
The curriculum should:
 Include a broad range of content
 Emphasize the mastering of problem solving skills
 Allow for students to use conjecture to further their understanding of math topics
 Promote the development of thinking and reasoning abilities
 Include relevant applications of mathematics
 Incorporate the use math type

We recommend the classroom teacher employ the following strategies:

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Extensive use of problem solving
Student discussions of mathematical ideas
The utilization of varied methodologies
An emphasis on differentiated instruction
Small group learning
The use of manipulative tools when possible
Locust Valley High School
Math Research Curriculum
Written 2010
MATH RESEARCH
In implementing math research it is expected that students will develop skills such as
questioning, conjecture, problem solving, looking for patterns, organizing information,
generating new and innovative ideas. In this course students will be given the
opportunity to explore math topics in depth thereby making connections, reasoning and
proving, communicating and creating representations in different forms. Students will
participate in their own research and submit original research to the Long Island Math
Fair. Students will also participate in problem solving competitions such as the American
Mathematics Competition, American Scholastic Mathematics Association, Continental
Mathematics League, Sigma Mathematics, and Raytheon MATHCOUNTS. Throughout
this document the performance indicators use the words investigate, explore, discover,
conjecture, reasoning, argument, justify, explain, proof, and apply. Each of these terms
is an important component in developing a student’s mathematical reasoning ability. It is
therefore important that a clear and common definition of these terms be understood.
The order of these terms reflects different stages of the reasoning process.
Investigate/Explore - Students will be given situations in which they will be asked to
look for patterns or relationships between elements within the setting.
Discover - Students will make note of possible patterns and generalizations that result
from investigation/exploration.
Conjecture - Students will make an overall statement, thought to be true, about the new
discovery.
Reasoning - Students will engage in a process that leads to knowing something to be true
or false.
Argument - Students will communicate, in verbal or written form, the reasoning process
that leads to a conclusion. A valid argument is the end result of the conjecture/reasoning
process.
Justify/Explain - Students will provide an argument for a mathematical conjecture. It
may be an intuitive argument or a set of examples that support the conjecture. The
argument may include, but is not limited to, a written paragraph, measurement using
appropriate tools, the use of dynamic software, or a written proof.
Proof - Students will present a valid argument, expressed in written form.
Apply - Students will use a theorem or concept to solve an algebraic or numerical
problem.
Locust Valley High School
Math Research Curriculum
Written 2010
Problem Solving Strand
Students will build new mathematical knowledge through problem solving.
A.PS.1
A.PS.2
8.PS.2
Use a variety of problem solving strategies to understand
new mathematical content
Recognize and understand equivalent representations of
a problem situation or a mathematical concept
Construct appropriate extensions to problem situations
Students will solve problems that arise in mathematics and in other contexts.
A.PS.3
A.PS.4
Observe and explain patterns to formulate
generalizations and conjectures
Use multiple representations to represent and explain
problem situations (e.g., verbally, numerically,
algebraically, graphically)
Students will apply and adapt a variety of appropriate strategies to solve problems.
A.PS.5
8.PS.5
A.PS.6
A.PS.7
8.PS.7
Choose an effective approach to solve a problem from a variety
of strategies (numeric, graphic, algebraic)
Make conjectures from generalizations
Use a variety of strategies to extend solution methods to other
problems
Work in collaboration with others to propose, critique, evaluate,
and value alternative approaches to problem solving
Understand that there is no one right way to solve mathematical
problems but that different methods have advantages and
disadvantages
Students will monitor and reflect on the process of mathematical problem solving.
A.PS.8 Determine information required to solve a problem,
choose methods for obtaining the information, and define
parameters for acceptable solutions
A.PS.9 Interpret solutions within the given constraints of a
problem
A.PS.10 Evaluate the relative efficiency of different
representations and solution methods of a problem
Locust Valley High School
Math Research Curriculum
Written 2010
Reasoning and Proof Strand
Students will recognize reasoning and proof as fundamental aspects of mathematics.
A.RP.1
Recognize that mathematical ideas can be supported by
a variety of strategies
Students will make and investigate mathematical conjectures.
A.RP.2
Use mathematical strategies to reach a conclusion and
provide supportive arguments for conjecture
8.RP.3 Evaluate conjectures by distinguishing relevant from
irrelevant information to reach a conclusion or make
appropriate estimates
8.RP.16 Justify solution methods through logical argument
8.PS.17 Evaluate the efficiency of different representations of a
problem
Students will develop and evaluate mathematical arguments and proofs.
A.RP.5
A.RP.6
A.RP.7
Develop, verify, and explain an argument, using
appropriate mathematical ideas and language
Present correct mathematical arguments in a variety of
forms
Evaluate written arguments for validity
Students will select and use various types of reasoning and methods of proof.
A.RP.8
Support an argument by using a systematic approach to
test more than one case
A2.RP.9 Devise ways to verify results, using counterexamples
and informal indirect proof
A.RP.10 Extend specific results to more general cases
Locust Valley High School
Math Research Curriculum
Written 2010
Communication Strand
Students will organize and consolidate their mathematical thinking through
communication.
A.CM.1 Communicate verbally and in writing a correct,
complete, coherent, and clear design (outline) and
explanation for the steps used in solving a problem
A.CM.2 Use mathematical representations to communicate with
appropriate accuracy, including numerical tables,
formulas, functions, equations, charts, graphs, and
diagrams
Students will communicate their mathematical thinking coherently and clearly to
peers, teachers, and others.
A.CM.3 Present organized mathematical ideas with the use of
appropriate standard notations, including the use of
symbols and other representations when sharing an idea
in verbal and written form
A.CM.4 Explain relationships among different representations of
a problem
A.CM.5 Communicate logical arguments clearly, showing why a
result makes sense and why the reasoning is valid
A.CM.6 Support or reject arguments or questions raised by others
about the correctness of mathematical work
Students will analyze and evaluate the mathematical thinking and strategies of others.
A.CM.7 Read and listen for logical understanding of
mathematical thinking shared by other students
A.CM.8 Reflect on strategies of others in relation to one’s own
strategy
A.CM.9 Formulate mathematical questions that elicit, extend, or
challenge strategies, solutions, and/or conjectures of
others
Students will use the language of mathematics to express mathematical ideas precisely.
A.CM.10 Use correct mathematical language in developing mathematical
questions that elicit, extend, or challenge other students’ conjectures
8.CM.11 Draw conclusions about mathematical ideas through decoding,
comprehension, and interpretation of mathematical visuals, symbols
Locust Valley High School
Math Research Curriculum
Written 2010
Connections Strand
Students will recognize and use connections among mathematical ideas.
A.CN.1 Understand and make connections among multiple
representations of the same mathematical idea
A.CN.2 Understand the corresponding procedures for similar
problems or mathematical concepts
Students will understand how mathematical ideas interconnect and build on one
another to produce a coherent whole.
A.CN.3 Model situations mathematically, using representations
to draw conclusions and formulate new situations
A.CN.4 Understand how concepts, procedures, and mathematical
results in one area of mathematics can be used to solve
problems in other areas of mathematics
A.CN.5 Understand how quantitative models connect to various
physical models and representations
Students will recognize and apply mathematics in contexts outside of mathematics.
A.CN.6 Recognize and apply mathematics to situations in the outside
world
A.CN.7 Recognize and apply mathematical ideas to problem situations
that develop outside of mathematics
8.CN.8 Investigate the presence of mathematics in careers and areas
of interest
8.CN.9 Recognize and apply mathematics to other disciplines, areas
of interest, and societal issues
Locust Valley High School
Math Research Curriculum
Written 2010
Representation Strand
Students will create and use representations to organize, record, and communicate
mathematical ideas.
A.R.1
A.R.2
A.R.3
Use physical objects, diagrams, charts, tables, graphs,
symbols, equations, or objects created using technology
as representations of mathematical concepts
Recognize, compare, and use an array of
representational forms
Use representation as a tool for exploring and
understanding mathematical ideas
Students will select, apply, and translate among mathematical representations to solve
problems.
A.R.4
A.R.5
8.R.4
8.R.6
Select appropriate representations to solve problem situations
Investigate relationships between different representations and
their impact on a given problem
Explain how different representations express the same
relationship
Use representations to explore problem situations
Students will use representations to model and interpret physical, social, and
mathematical phenomena.
A.R.7
A.R.8
8.R.9
8.R.11
Use mathematics to show and understand social phenomena
(e.g., determine profit from student and adult ticket sales)
Use mathematics to show and understand mathematical
phenomena (e.g., compare the graphs of the functions
represented by the equations y=x and y= -x)
Use mathematics to show and understand physical phenomena
(e.g., make and interpret scale drawings of figures or scale
models of objects)
Use mathematics to show and understand mathematical
phenomena (e.g., use tables, graphs, and equations to show a
pattern underlying a function)
Locust Valley High School
Math Research Curriculum
Written 2010
Number Sense and Operations Strand
Students will understand meanings of operations and procedures, and how they relate
to one another.
Operations
A.N.1
A.N.7
A.N.8
8.N.5
8.N.6
Evaluate numerical expressions with negative and/or fractional
exponents, without the aid of a calculator (when the answers
are rational numbers)
Determine the number of possible events, using counting
techniques or the Fundamental Principle of Counting
Determine the number of possible arrangements
(permutations) of a list of items
Estimate a percent of quantity, given an application
Justify the reasonableness of answers using estimation
Algebra Strand
Students will represent and analyze algebraically a wide variety of problem solving
situations.
Equations and Inequalities
A.A.1
A.A.2
A.A.3
A.A.4
A.A.5
A.A.6
A.A.8
8.A.3
8.A.4
Translate a quantitative verbal phrase into an algebraic
expressions
Write a verbal expression that matches a given
mathematical expression
Distinguish the difference between an algebraic expression
and an algebraic equation
Translate verbal sentences into mathematical equations or
inequalities
Write algebraic equations or inequalities that represent a
situation
Analyze and solve verbal problems whose solution requires
solving a linear equation in one variable or linear inequality
in one variable
Analyze and solve verbal problems that involve quadratic
equations
Describe a situation involving relationships that matches a
given graph
Create a graph given a description or an expression for a
situation involving a linear or nonlinear relationship
Locust Valley High School
Math Research Curriculum
Written 2010
Students will perform algebraic procedures accurately.
Variables and Expressions
A.A.13
A.A.14
A.A.16
A.A.17
A.A.18
A.A.19
A.A.20
8.A.7
8.A.8
8.A.9
Add, subtract, and multiply monomials and polynomials
Divide a polynomial by a monomial or binomial, where the
quotient has no remainder
Simplify fractions with polynomials in the numerator and
denominator by factoring both and renaming them to lowest
terms
Add or subtract fractional expressions with monomial or like
binomial denominators
Multiply and divide algebraic fractions and express the product
or quotient in simplest form
Identify and factor the difference of two perfect squares
Factor algebraic expressions completely, including trinomials
with a lead coefficient of one ( after factoring a GCF)
Add and subtract polynomials (integer coefficients)
Multiply a binomial by a monomial or a binomial (integer
coefficients)
Divide a polynomial by a monomial (integer coefficients)
Equations and Inequalities
A.A.22
A.A.23
A.A.24
A.A.25
A.A.26
Solve all types of linear equations in one variable
Solve literal equations for a given variable
Solve linear inequalities in one variable
Solve equations involving fractional expressions
Solve algebraic proportions in one variable which result in linear
or quadratic equations
A8A.13 Solve multi-step inequalities and graph the solution set on the
number line
8.A.14 Solve linear inequalities by combining like terms, using the
distributive property, or moving variables to one side of the
inequality
Locust Valley High School
Math Research Curriculum
Written 2010
Students will recognize, use, and represent algebraically patterns, relations, and
functions.
Patterns, Relations, and Functions
A.A.30
A.A.31
8.A.15
8.A.19
Find the complement of a subset of a given set, within a given
Universe
Find the intersection of sets and or union of sets
Understand that numerical information can be represented in
multiple ways: arithmetically, algebraically, and graphically
Interpret multiple representations using equation, table of
values, and graph
Coordinate Geometry
A.A.32
A.A.33
A.A.34
A.A.35
A.A.36
A.A.37
A.A.38
A.A.39
A.A.40
Explain slope as a rate of change between dependent and
independent variables
Determine the slope of a line, given the coordinates of two
points on the line
Write the equation of a line, given its slope and the coordinates
of two points on the line
Write the equation of a line, given the coordinates of two points
on the line
Write the equation of a line parallel to the x- or y-axis
Determine the slope of a line, given its equation in any form
Determine if two lines are parallel, given their equations in any
form
Determine whether a given point is on a line, given the equation
of the line
Determine whether a given point is in the solution set of a
system of linear inequalities
Trigonometric Functions
A.A.42 Find sine, cosine, and tangent ratios of an angle of a right
triangle, given the lengths of the sides
A.A.43 Determine the measure of an angle of a right triangle,
given the length of any tow sides of the triangle
A.A.44 Find the measure of a side of a right triangle, given an
acute angle and the length of another side
A.A.45 Determine the measure of a third side of a right triangle
using the Pythagorean theorem, given the lengths of any
two sides
Locust Valley High School
Math Research Curriculum
Written 2010
Geometry Strand
Students will use visualization and spatial reasoning to analyze characteristics and
properties of geometric shapes.
Shapes
A.G.1
A.G.2
Find the area and/or perimeter of figures composed of polygons
and circles or sectors of a circle.
Use of formulas to calculate volume and surface area of regular
solids and cylinders
Students will apply coordinate geometry to analyze problem solving situations.
Coordinate Geometry
A.G.5
A.G.5
Investigate and generalize how changing the coefficients of a
function affects its graph
Use of formulas to calculate volume and surface area of regular
solids and cylinders
Measurement Strand
Students will determine what can be measured and how, using appropriate methods
and formulas.
Units of Measurement1
A.M.1
A.M.2
Calculate rates using appropriate units
Solve problems involving conversions within measurement
systems, given the relationship between the units
Locust Valley High School
Math Research Curriculum
Written 2010
Statistics and Probability Strand
Students will collect, organize, display, and analyze data.
Organization and Display of Data
A.S.4
Compare and contrast the appropriateness of different
measures of central tendency for a given data set
A.S.5
Construct a histogram, cumulative frequency histogram,
and box-and-whisker plot, given a set of data
A.S.6
Understand how the five statistical summary (minimum,
maximum, and the three quartiles) is used to construct a
box-and-whisker plot
A.S.7
Create a scatter plot of bivariate data
A.S.8
Construct manually a reasonable line of best fit for a
scatter plot and determine the equation of that line
Analysis of Data
A.S.9
Analyze and interpret a frequency distribution table or
histogram, a cumulative frequency distribution table or
histogram, or a box-and-whisker plot
A.S.10 Evaluate published reports and graphs that are based on
data by considering: experimental design, appropriateness
of the data analysis and the soundness of the conclusions
A.S.12 Identify the relationship between the independent and
dependent variables from a scatter plot (positive, negative,
or none)
A.S.13 Understand the difference between correlation and
causation
A.S.14 Identify variables that might have a correlation but not a
causal relationship
Students will make predictions that are based upon data analysis.
Predictions from Data
A.S.15
A.S.16
Identify and describe sources of bias and its effect, drawing
conclusions from data
Recognize how linear transformations of one-variable data
affect the data’s mean, median, mode, and range
A.S.17
Locust Valley High School
Math Research Curriculum
Written 2010
Use a reasonable line of best fit to make a prediction involving
interpolation or extrapolation
Students will understand and apply concepts of probability.
Probability
A.S.18
A.S.19
A.S.20
A.S.21
A.S.22
A.S.23
Know the definition of conditional probability and use it to
solve for probabilities in finite sample space
Determine the number of elements in a sample space and the
number of favorable events
Calculate the probability of an event and its complement
Determine empirical probabilities based on specific sample
data
Determine, based on calculated probability of a set of events,
if: some or all are equally likely to occur, one is more likely to
occur than another, whether or not an event is certain to
happen or not to happen
Calculate the probability of: a series of independent events,
two mutually exclusive events
Locust Valley High School
Math Research Curriculum
Written 2010
Units of Study
1
Introduction to math research
a. Define math research
b. Reading mathematical papers
2
Independent research
a. Choosing a math fair topic
b. Research math fair topic
c. Creating an outline
d. Writing mathematically
e. Presenting math fair project
3
Problem Solving
a. Strategies to problem solve
b. Practice for math competitions
4.
Math Investigations
a. Problem solving activities
b. Patterns and numeration activities
c. Measurement activities
d. Probability and Statistic activities
e. Real World math activities
f. Geometric activities
Locust Valley High School
Math Research Curriculum
Written 2010
Daily Topic
#
Days
Introduction to Math Research
Exploration activity: Trains: investigation of patterns
Problem Solving strategies: Using Picture Pattern
Problems Solving Strategies: Using list and tables
Problems Solving Strategies: Using trial and error and
simplifying problem
Problem Solving Strategies: Using experiment, working
backwards
Problem Solving Strategies: Using prediction and changing
point of view
Reading Math Research articles
How to find your own math research topic.
What are components of your research paper?
Creating a math research paper outline
Writing mathematically with Mathtype.
Problem solving for Math Competitions.
Exploration activity : Pick a Pattern
Independent work on Research paper for LI math fair
Problem solving for Math Competitions.
Exploration activity: What’s the number?
Problem solving for Math Competition
Exploration activity: Platonic Solids
Problem solving for Math Competition
Exploration activity: Adding a La Gauss
Exploration activity: Fibonacci beautiful patterns beautiful
mathematics
1
2
2
2
2
Exploration activity: What’s so special about 11?
Problem Solving for Math Competitions
Exploration activity: Pascal’s Triangle
Problem Solving for math competitions
Exploration activity: Getting a “Bee” in Mathematics Class
Problem Solving for math competitions
Exploration activity: Building Mathematically Powerful
Students Through Connections
Presentations for LI Math Fair
Exploration activity: How does your Doughnut Measure up?
Exploration activity: Networks: Service Woes at Speedy
Delivery: Finding the Shortest Route
Problem Solving for Math Competitions
2
3
4
1
2
4
2
2
2
4
12
2
4
4
7
2
8
4
2
2
2
1
2
4
8
2
3
4
Locust Valley High School
Math Research Curriculum
Written 2010
Exploration activity: What’s Your Mileage?
Exploration activity: The Giants Project
Exploration activity: Mean, Median or Mode: Which one is
My Pencil? And Antics of statistics
Exploration activity: Amazing Profit
Problem Solving for math competitions
Exploration activity: As the Ball Rolls: A Quadratic
Investigation Using Multiple Representations
Exploration activity: Wind sail Design
Problems Solving for math competitions
Exploration activity: Building Bridges
Exploration activity: Water Geometry
Problem Solving for Math Competitions
Exploration activity: A Treasure Hunt: Reflecting,
Translating, and Rotating Points on a Coordinate Map
Exploration activity: Geometric review I have…Who has
Exploration activity: What’s the Fastest way to get Rich?
Exploration activity: Classic Middle-Grades Problems for
the Classroom
Problem Solving for Math Competitions
Exploration activity: Check that Digit
Exploration activity: What are my Chances?
Problems Solving for Math Competitions
Exploration activity: Bean Counting and Ratios
Exploration activity: Probability Experiments with Shared
Spreadsheets
Problem Solving for Math Competitions
Exploration activity: To Replace or Not to Replace? That is
the Question?
Exploration activity: The Other Life of Florence Nightingale
Exploration activity: Let’s Count the Ways
Exploration activity: Heart rate and scatter plots
Exploration activity: Ages of Famous Personalities
Exploration activity: Bouncing Tennis Balls
Exploration activity: Like Moths Around a Flame
Exploration activity: Testing Wing Designs in Aircraft
Exploration activity: Serving up Sierpinski!
Exploration activity: The Mathematics of Native American
Star Quilts
Exploration activity: Heptades and Heptagons: the
Historical Roots
2
4
2
2
1
2
2
1
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
3
2
Locust Valley High School
Math Research Curriculum
Written 2010
APPENDIX A:
SOURCES FOR EXPLORATION ACTIVITIES
1. “Counting the Trains”, NCTM Illuminations Resources for Teaching Math.
Retrieved from http://illuminations.nctm.org/LessonDetail.aspx?id=L736.
2. “Pick a Pattern”, John C. Wetzel, CAPT Resources, 1997.
3. “How Many Toothpicks?’ NYS Core Curriculum Manual for grade 8.
Retrieved from http://www.emsc.nysed.gov/ciai/mst/mathcompanion.pdf
4. “What’s the Number?” NYS Core Curriculum Manual for grade 8. Retrieved
from http://www.emsc.nysed.gov/ciai/mst/mathcompanion.pdf
5. “Exploring Platonic Solids”, David Parker. Retrieved from
http://www.davidparker.com/janine/mathpage/platonic.html
6. “Adding a la Gauss”, Armando M. Martinez-Cruz and Ellen c. Barger,
Mathematics Teaching in the Middle School, Vol. 10, No 3 October 2004.
7. “Fibonacci: Beautiful Patterns, Beautiful Mathematics, Catherine B. Miller and
Tamara B. Veenstra, Mathematics Teaching in the Middle School, Vol, 7,
No. 5, January 2002.
8. “What’s So Special about 11?”, Getting Started: TI-30xs multiview TI-34xs
multiview Activities, Texas Instruments Incorporated.2008.
9. “Pascal’s Triangle Poster” , Dale Seymore Publications, 1986.
10. “Getting a “Bee” in Mathematics Class”, Brian Sharp, Mathematics Teaching in
the Middle School, Vol 14, No 3, October 2008.
11. “Building Mathematically Powerful Students through Connections”, Christine
D. Thomas and Carmelita Santiago, Mathematics Teaching in the Middle
School, Vol. 7, No. 9, May 2002.
12. “How Does Your Doughnut Measure up?”, Paula Maida and Michael Maida,
Mathematics Teaching in the Middle School, Vol. 11, No. 5, Dec 2005/Jan
2006.
Locust Valley High School
Math Research Curriculum
Written 2010
13. “Service Woes at Speedy Delivery: Finding the Shortest Route”, Mathematics
for Decision Making in Industry and Government, High School Operations
Research , retrieved from
Http://www.hsor.org/modules.cmf?name=Speedy_Delivery.
14. “What’s Your Mileage?” Getting Started: TI-30xs multiview TI-34xs
multiview Activities, Texas Instruments Incorporated.2008.
15. “The Giants Project”, Suzanne Levin Weinberg, Penny L. Hammrich, Matthew
H. Bruce, Mathematics Teaching in the Middle School, Vol. 8, No.8, April
2003.
16. “Mean, Median, or Mode: Which One is My Pencil?”, Kathleen Cage Mittag,
Sharon E. Taylor, and David Fies, Mathematics Teaching in the Middle School,
Vol. 15, No. 9, May 2010.
17. “The Antics of Statistics”, Getting Started: TI-30xs multiview TI-34xs
multiview Activities, Texas Instruments Incorporated.2008.
18. “Amazing Profit”, NCTM Illuminations Resources for Teaching Math,
Retrieved from http://illuminations.nctm.org/LessonDetail.aspx?id=L799.
19. “As the Ball Rolls: A Quadratic Investigation Using Multiple Representations”,
Kathleen Cage Mittag and Sharon Taylor, Mathematics Teacher, Vol. 103,
No.1, August 2009.
20. “Windsail Design”, Futures Channel, retrieved from
http://www.thefutureschannel.com/algebra/windsail_design.php.
21. “Building Bridges”, NCTM, Illuminations Resources for Teaching Math,
Retrieved from http://illuminations.nctm.org/LessonDetail.aspx?id=L247.
22. “Water Geometry”, Futures Channel , Retrieved from
http://www.thefutureschannel.com/hands-on_math/water_geometry.php
23. “A Treasure Hunt: Reflecting, Translating, and Rotating Points on a Coodinate
Map, Carryn Bellomo, Mathematics Teaching in the Middle School, Vol.13, No.
5, Dec 2007/Jan 2008.
Locust Valley High School
Math Research Curriculum
Written 2010
24. “What’s the Fastest Way to Get Rich?”, Getting Started: TI-30xs multiview TI34xs multiview Activities, Texas Instruments Incorporated.2008.
25. “Classic Middle-Grades Problems for the Classroom”, NCTM Illuminations
Resources for Teaching Math , Retrieved from
http://illuminations.nctm.org/LessonDetail.aspx?id=L264.
26. “Check That Digit”, NCTM Illuminations Resources for Teaching Math,
Retrieved from http://illuminations.nctm.org/LessonDetail.aspx?id=L693.
27. “What Are My Chances?”, NYS Core Curriculum Manual for grade 8,
Retrieved from http://www.emsc.nysed.gov/ciai/mst/mathcompanion.pdf.
28. “Bean Counting an Ratios”, NCTM Illuminations Resources for Teaching Math,
Retrieved from http://illuminations.nctm.org/LessonDetail.aspx?id=L722.
29. “Probability Experiments with Shared Spreadsheets”, Darin Beigie,
Mathematics Teaching in the Middle School, Vol. 15, No.8, April 2010.
30. “To Replace or Not to Replace? That is the Question”, Exploration, Texas
Instruments, 2004.
31. “The Other Life of Florence Nightingale”, Christine Annette Franklin,
Mathematics Teaching in the Middle School, Vol. 7, No. 6, February 2002.
32. “Let’s Count the Ways”, Getting Started: TI-30xs multiview TI-34xs multiview
Activities, Texas Instruments Incorporated.2008.
33. “Picturing Data: Scatter Plots and Line Graph – Heart Rate”, More than Graphs,
Key Curriculum Press, 2000.
34. “Ages of Famous Personalities”, Mathbits.com, Retrieved from
http://mathbits.com/mathbits/ppt/EstimateAge.htm.
35. “Bouncing Tennis Balls”, NCTM Illuminations Resources for Teaching Math,
Retrieved from http://illuminations.nctm.org/lessondetail.aspx?ID=L246.
36. “Like Moths Around a Flame”, Sample Activities: TI84 plus and TI-83 Plus
families Math, Texas Instruments, 2005.
Locust Valley High School
Math Research Curriculum
Written 2010
37. “Testing Wing Design in Aircraft”, David K Puglalee, Chuck Nusinov, Chris
Giersch, David Royster, and Thomas E. Pinelli, Mathemathics Teaching in the
Middle School, Vol. 10 No. 5, Dec 2004/Jam 2005.
38. “Serving Up Sierpinski!”, Thomasenai Lott Adams and Fatma Aslan-Tutak,
Mathematics Teaching in the Middle School, Vol. 11, No. 5, Dec 2005/ Jan
2006.
39. “The Mathematics of Native American Star Quilts”, Marueen D. Neumann,
Mathematics Teaching in the Middle School, Vol. 9, No. 4, December 2003.
40. “Heptades and Heptagons: The Historical Roots”, Charles P. Funkhourser,
Mathematics Teaching in the Middle School, Vol. 9, No. 2, Cotober 2003.
Locust Valley High School
Math Research Curriculum
Written 2010
APPENDIX B
BIBLIOGRAPHY
1. Writing Math Research Papers A Guide for Students and Instructors, Robert
Gerver, Key Curriculum Press, 2004.
2. Creative Problem Solving in School Mathematics, George Lenchner, Glenwood
Publishing Inc, 1983.
3. Competition Math for Middle School, J. Batterson, AGMATH, 2009.
4. About Teaching Mathematics a k-8 Resource, Marilyn Burns, Math Solutions
Publications 2007.
5. The Art of Problem Solving Volume 1: The Basics, Sandor Lehoczky and
Richard Rusczyk,, AoPS Incorporated, 2006.