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Karen E. Spike

Department of Mathematics and Statistics

 


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                                                              (more info on 141-142)


 

MATH 141 and MATH 142

Basic Concepts of Mathematics I & II

 

 

Web Links

Why study Mathematics?   http://www.uncw.edu/math/math_why_math.html
The National Council of Teachers of Mathematics is a good source for information on teaching mathematics.  In the spring of 2000 they published Principles and Standards for School Mathematics.  Click on the link for this website, then explore what is available.  The electronic examples have many interactive activities that I think you will find interesting.    http://www.nctm.org/standards/content.aspx?id=16909
The NCTM Illuminations website has many math activities and lesson plans:  http://illuminations.nctm.org
Selected Web Links are useful mathematics education resources on the Internet. Each resource has been approved by an editorial board. They can be used to improve the teaching of mathematics:   http://illuminations.nctm.org/Weblinks.aspx
The North Carolina Council of Teachers of Mathematics:  http://www.ncctm.org/
The North Carolina Department of Public Instruction has many interesting things available on the web.  http://www.ncpublicschools.org/
The following site will provide information on the curriculum for kindergarten through 12 grade as well as instructional resources for all those grade levels.Click on the link below to see the North Carolina Standard Course of Study and Grade Level Competencies; select mathematics and grade level.    http://www.learnnc.org/scos/        
For information on End of Grade testing, click on the following link and then click on the link for "Testing"   http://www.ncpublicschools.org/curriculum/mathematics/ 
Shodor.org lists of lessons by topic and grade level:   http://www.shodor.org/interactivate/lessons/
Click on the topic you want and then explore the possible lessons.
The InterMath curriculum is meant to engage teachers and is intended to deepen teachers' understanding of mathematical concepts related to the middle school curriculumhttp://intermath.coe.uga.edu/

The Interactive Mathematics Dictionary is a dictionary for middle school students, teachers, parents, and anyone else interested in learning more about mathematical topics in the middle school curriculum. http://intermath.coe.uga.edu/dictnary/homepg.asp

Source for manipulatives for "hands-on" learning:  http://www.mathlearningcenter.org 
 
The Mathematical Moments program promotes appreciation and understanding of the role mathematics plays in science, nature, technology, and human culture. Download this series of pdf files to use as teaching resources and to promote awareness of mathematics to students, colleagues, and attendees at meetings and special events.      http://www.ams.org/mathmoments
The poster style discussions are great for classroom bulletin boards! 
The following sites are good general sites where you can find information on a variety of mathematical concepts!
 http://www.sosmath.com/wwwsites.html  -- an extensive compilation of web sites related to mathematics
 http://www.coolmath.com/  -- great site for students, teachers and parents -- fun format for lessons on a wide variety of topics
 http://www.coolmath4kids.com/ -- this is part of the "cool math" website with a colorful index to find topics in elementary mathematics
 http://www.coolmath.com/reference/online-math-dictionary.html -- This is an easy to use dictionary with lots of math concepts for elementary or middle grades students.
 http://britton.disted.camosun.bc.ca/jbfunpatt.htm  -- "selected web pages for educators, each leading to recreation-orientated learning experiences for middle school students."
 http://mathforum.org/ -- "the leading online resource for improving math learning, teaching, and communication since 1992."
 http://mathforum.org/dr.math  -- a great resource for students to find answers to their questions.
 http://mathworld.wolfram.com/ -- extensive resource for "higher level" mathematics 
 http://archives.math.utk.edu/ -- a wide range of resources for K-12 and college level mathematics
 http://www.webmath.com -- an online resource for students questions about their homework
 http://www.aaamath.com  -- links to online help and activities for many math topics
 http://www.mathexpression.com/ -- links to lessons and videos for math topics
 http://www.khanacademy.org/ -- Link to information about the Khan Academy (with additional links to videos & exercises on many educational topics).
 http://www.khanacademy.org/#arithmetic -- Link to videos that teach arithmetic concepts.
 http://www.khanacademy.org/exercisedashboard?k -- Link to exercises that begin with basic arithmetic concepts then built to other concepts.
This site for the National Library of Virtual Manipulatives is one you will want to use this semester and also when you become an elementary or middle grades teacher!  The site is setup in the form of a chart so you can pick the grade level and the concept for which you would like a manipulative.   http://nlvm.usu.edu/en/nav/vlibrary.html
It was created during a three-year NSF supported project to develop a library of uniquely interactive, web-based virtual manipulatives or concept tutorials, mostly in the form of Java applets, for mathematics instruction (K-8 emphasis).
Listed in Bold print in the table below are a variety of e-manipulatives from the chart that will be helpful with various topics this semester.  
The following are some samples of the many websites available which are related to the specific topics that we are studying in Math 141 and Math 142.  They can be used with many different textbooks, but I have classified them by the chapters in the text that I use.  
Textbook:  Mathematics for Elementary Teachers by Musser, Burger & Peterson.
Math 141     Chapter 1     Chapter 2     Chapters 3 & 4     Chapter 5     Chapter 6     Chapter 7     Chapter 8     Chapter 9

Math 142     Chapter 10 & 11     Chapter 12     Chapter 13     Chapter 14     Chapter 16
 
Math 141 topics            
Chapter 1 --  Problem Solving  
 Information about George Polya  http://www.drkhamsi.com/classe/polya.html
 http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Polya.html
 Color Patterns e-manipulative  http://nlvm.usu.edu/en/nav/frames_asid_184_g_1_t_1.html?from=category_g_1_t_1.html
Chapter 2 --  Sets & Number Systems      Return to Top of page
Venn Diagram e-manipulative  http://nlvm.usu.edu/en/nav/frames_asid_153_g_3_t_1.html?open=instructions
Fibonacci, Roman numerals, algorithms for base ten arithmetic, Fibonacci sequence  http://www.barcodesinc.com/articles/fibonacci-numbers.htm
 http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/fibBio.html
Roman numerals  http://mathforum.org/dr.math/faq/faq.roman.html
Mayan math  http://www.mayacalendar.com/f-mayamath.html
Babylonian numerals  http://www-history.mcs.st-andrews.ac.uk/history/HistTopics/Babylonian_numerals.html
other number bases  http://mathforum.org/dr.math/faq/faq.bases.html
Multi-Base blocks e-manipulative to represent numbers in various bases  http://nlvm.usu.edu/en/nav/frames_asid_152_g_2_t_1.html
 Base 5 Blocks Cut-Outs  http://mason.gmu.edu/~mmankus/Handson/base5.htm
 Base 10 Blocks Cut-Outs  http://mason.gmu.edu/~mmankus/Handson/b10blocks.htm
 Chip Abacus e-manipulative  http://nlvm.usu.edu/en/nav/frames_asid_209_g_2_t_1.html?open=activities
 binary numbers (base two)  http://britton.disted.camosun.bc.ca/jbbinflag.htm
 What are functions?
 Function Machine e-manipulative  http://nlvm.usu.edu/en/nav/frames_asid_191_g_3_t_1.html
Chapters 3 & 4 --  Whole Numbers            Go back to Math 141         Return to Top of page
"fun numbers" that are powers of ten  http://www.straightdope.com/mailbag/mgazilli.html
 Cool Math lessons on addition
 See lesson 7 for "scratch addition"
 http://www.coolmath4kids.com/addition/
 Cool Math lessons on subtraction  http://www.coolmath4kids.com/subtraction/index.html
 Cool Math lessons on multiplication
   (includes "four-fact families")
 http://www.coolmath4kids.com/times-tables/
 Cool Math lessons on long division  http://www.coolmath4kids.com/long-division/index.html
 Lattice method for multiplication   http://www.ualr.edu/lasmoller/medievalmult.html
 http://coolmath4kids.com/times-tables/times-tables-lesson-lattice-multiplication-1.html
e-manipulative for number line arithmetic for +, -, x and divide  http://nlvm.usu.edu/en/nav/frames_asid_197_g_2_t_1.html?open=activities
Number Line Bar e-manipulative  http://nlvm.usu.edu/en/nav/frames_asid_180_g_2_t_1.html?open=activities
Base blocks e-manipulative for addition  http://nlvm.usu.edu/en/nav/frames_asid_154_g_2_t_1.html
 Click on "Create a Problem" to choose a non-decimal base.
Base blocks e-manipulative for subtraction  http://nlvm.usu.edu/en/nav/frames_asid_155_g_2_t_1.html
 Click on "Create a Problem" to choose a non-decimal base.
 Understanding & practice with rules for exponents  http://www.coolmath.com/algebra/01-exponents/index.html
 Understanding rules for working with exponents  http://www.mathexpression.com/exponent-rules.html
Chapter 5 -- Number Theory                    Go back to Math 141           Return to Top of page
Sieve of Eratosthenes e-manipulative  http://nlvm.usu.edu/en/nav/frames_asid_158_g_2_t_1.html?open=instructions
Prime numbers  http://mathforum.org/dr.math/faq/faq.prime.num.html 
 http://mathworld.wolfram.com/PrimeNumber.htm/
Prime factorization  http://mathforum.org/library/drmath/sets/elem_prime_numbers.html 
 http://mathforum.org/dr.math/problems/prime.fac.html
Summary of divisibility rules
 http://mathforum.org/dr.math/faq/faq.divisibility.html
Why divisibility rules work  http://mathforum.org/k12/mathtips/division.tips.html 
 http://mathforum.org/k12/mathtips/ward.html
e-manipulative for factor trees, GCF, LCM  http://nlvm.usu.edu/en/nav/frames_asid_202_g_3_t_1.html 
(Choose the "two" tree option in order to use a Venn Diagram and find LCM and GCF.)
Chapter 6  --  Fractions                      Go back to Math 141         Return to Top of page
Understanding & Teaching fractions  http://mathforum.org/paths/fractions/e.fraclessons.html
 http://illuminations.nctm.org/LessonDetail.aspx?id=L284
 http://www.coolmath.com/prealgebra/01-p2-fractions/index.html
 e-manipulatives for fractions (below):  
      Number line - fractions  http://nlvm.usu.edu/en/nav/frames_asid_265_g_3_t_1.html?open=activities
      Fraction pieces  http://nlvm.usu.edu/en/nav/frames_asid_274_g_3_t_1.html?open=activities
      Fractions - Parts of a Whole  http://nlvm.usu.edu/en/nav/frames_asid_102_g_2_t_1.html
      Fractions - Visualizing Fractions  http://nlvm.usu.edu/en/nav/frames_asid_105_g_2_t_1.html
      Equivalent fractions  http://nlvm.usu.edu/en/nav/frames_asid_105_g_3_t_1.html
      Comparing fractions  http://nlvm.usu.edu/en/nav/frames_asid_159_g_3_t_1.html
Adding fractions  http://nlvm.usu.edu/en/nav/frames_asid_106_g_3_t_1.html
Multiplying fractions  http://nlvm.usu.edu/en/nav/frames_asid_194_g_3_t_1.html
Chapter 7  --  Decimals                          Go back to Math 141         Return to Top of page
Base Blocks for + & - decimals  http://nlvm.usu.edu/en/nav/frames_asid_264_g_3_t_1.html
Understanding decimals  http://www.coolmath.com/prealgebra/02-decimals/index.html
Chapter 8  --  Integers                     Go back to Math 141            Return to Top of page
Integers (also rational and irrational numbers)
Integer number line e-manipulative
 http://mathforum.org/dr.math/faq/faq.integers.html
 http://matti.usu.edu/nlvm/nav/frames_asid_107_g_3_t_1.html
Number Line Bar e-manipulative  http://nlvm.usu.edu/en/nav/frames_asid_180_g_2_t_1.html
Chapter 9 -- Real Numbers                   Go back to Math 141
Integers, rat'l and irat'l numbers  http://mathforum.org/dr.math/faq/faq.integers.html
 Fractional exponents to work with roots  http://www.mathexpression.com/fractional-exponent.html
Pi, π,  is an irrational number
[For more information about pi, see the links below under chapter 13.]
 http://mathforum.org/dr.math/faq/faq.pi.html
 http://mathforum.org/library/drmath/view/58288.html
 What are Functions?  http://www.coolmath.com/algebra/Algebra1/14Functions/01_whatarethey.htm
 Function Machine e-manipulative  http://nlvm.usu.edu/en/nav/frames_asid_191_g_3_t_1.html
Math 142 topics  
Chapters 10 & 11- Statistics & Probability               Go back to Math 142        Return to Top of page

Links to various e-manipulatives for data analysis and probability

 http://nlvm.usu.edu/en/nav/category_g_3_t_5.html
     histogram e-manipulative  http://nlvm.usu.edu/en/nav/frames_asid_145_g_3_t_5.html?open=instructions
     scatter-plots e-manipulative  http://nlvm.usu.edu/en/nav/frames_asid_144_g_3_t_5.html?open=activities
     box plot e-manipulative  http://nlvm.usu.edu/en/nav/frames_asid_200_g_3_t_5.html?open=instructions
 Use to introduce experimental probability  http://www.shodor.org/interactivate/activities/ExpProbability/
     coin toss e-manipulative  http://nlvm.usu.edu/en/nav/frames_asid_305_g_3_t_5.html
     simulation e-manipulative  http://nlvm.usu.edu/en/nav/frames_asid_146_g_4_t_5.html?open=instructions
     spinner e-manipulative  http://nlvm.usu.edu/en/nav/frames_asid_186_g_2_t_5.html?open=activities
 List of websites for data analysis  and probability compiled by NCTM  http://illuminations.nctm.org/WebResourceList.aspx?Ref=2&Std=4&Grd=0
 Website with lessons on a variety of topics  http://www.shodor.org/interactivate/lessons/  click on probability for appropriate lessons
Permutations quiz  http://www.glencoe.com/sec/math/studytools/cgi-bin/msgQuiz.php4?isbn=0-02-833052-8&chapter=12&lesson=2
Combinations quiz  http://www.glencoe.com/sec/math/studytools/cgi-bin/msgQuiz.php4?isbn=0-02-833052-8&chapter=12&lesson=3
Chapter 12  --  Geometric Shapes             Go back to Math 142          Return to Top of page
Lessons on geometry  http://www.aaamath.com/geo.html
Basic concepts in geometry, worth exploring  http://www.ies.co.jp/math/products/geo1/menu.html
Origami - paper folding - geometry  http://www.ams.org/ams/mm22s-origami.pdf 
 http://www.merrimack.edu/~thull/OrigamiMath.html
Polygons  http://www.math.com/tables/geometry/polygons.htm -- polygon definition, angles & names
 http://www.mathleague.com/help/geometry/polygons.htm--definitions of types of polygons with nice pictures -- a good site elementary and middle school students
 http://www.mathsisfun.com/geometry/polygons.html -- similar to site above
Understanding the relationship between rectangles and parallelograms  http://standards.nctm.org/document/eexamples/chap5/5.3/index.htm
Pentagons  http://britton.disted.camosun.bc.ca/jbpentag.htm
Symmetry - snowflakes
 http://www.snowflakebentley.com/ 
 http://www.snowflakebentley.com/snowflakes.htm  In the table of snowflake photos, click on any image to enlarge it and you will see the details in each snowflake!!
Symmetry - African symbols  http://www.welltempered.net/adinkra/htmls/adinkra_index.htm
Understanding tessellations (& vertex angles)  http://www.coolmath.com/lesson-interior-angles-of-polygons-1.htm and  
 http://www.coolmath.com/lesson-tessellations-1.htm

 http://mathforum.org/sum95/suzanne/whattess.html
Pattern block e-manipulative for tessellations  http://nlvm.usu.edu/en/nav/frames_asid_163_g_3_t_3.html?open=activities
Tessellations -- Escher Art  http://www.mcescher.net/ 
 http://www.mcescher.com/
 http://britton.disted.camosun.bc.ca/escher/jbescher.htm
Regular polyhedra e-manipulative  http://nlvm.usu.edu/en/nav/frames_asid_128_g_3_t_3.html?open=instructions
Polyhedra  http://mathforum.com/alejandre/applet.polyhedra.html
 http://illuminations.nctm.org/imath/3-5/GeometricSolids/index.html
 http://britton.disted.camosun.bc.ca/jbpolyhedra.htm
Polyhedron  http://mathworld.wolfram.com/Polyhedron.html
Prisms  http://www.mathsnet.net/geometry/solid/prisms.html
Chapter 13  --  Measurement           Go back to Math 142          Return to Top of page
Lessons on measurement  http://www.geocities.com/smilecdg/measuremtles.html
Metric measurement  http://www.nist.gov/public_affairs/kids/metric.htm
Area of a Circle (related to a parallelogram)  http://britton.disted.camosun.bc.ca/areacirc/areacirc.htm
Information about pi  http://www.joyofpi.com/pilinks.html 
 http://www.ualr.edu/~lasmoller/pi.html
Teaching about pi  http://mathforum.org/dr.math/faq/faq.pi.html
 http://mathforum.org/library/drmath/view/58288.html
Geoboard e-manipulative about perimeter & area  http://nlvm.usu.edu/en/nav/frames_asid_282_g_3_t_4.html?open=activities
Surface Area and Volume FORMULAS  http://argyll.epsb.ca/jreed/math8/strand3/3208.htm
Chapter 14  --  Congruence & Similarity           Go back to Math 142          Return to Top of page
Congruent triangle e-manipulative  http://nlvm.usu.edu/en/nav/frames_asid_165_g_3_t_3.html?open=instructions
 Congruent and similar polygons  http://www.ies.co.jp/math/products/geo1/menu.html
Congruence, similarity & transformations  http://standards.nctm.org/document/eexamples/chap6/6.4/part4.htm
Congruence and transformations  http://www.ies.co.jp/math/products/geo1/applets/cong/cong.html
Chapter 16 -- Geometric Transformations           Go back to Math 142          Return to Top of page
translation e-manipulative  http://nlvm.usu.edu/en/nav/frames_asid_301_g_3_t_3.html?open=activities
 http://illuminations.nctm.org/LessonDetail.aspx?ID=L474
reflection e-manipulative  http://nlvm.usu.edu/en/nav/frames_asid_297_g_3_t_3.html?open=activities
 http://illuminations.nctm.org/LessonDetail.aspx?ID=L473
rotation e-manipulative  http://nlvm.usu.edu/en/nav/frames_asid_299_g_3_t_3.html?open=activities
 http://illuminations.nctm.org/index_d.aspx?id=466
e-manipulative for composition of transformations  http://nlvm.usu.edu/en/nav/frames_asid_294_g_3_t_3.html?open=activities
e-manipulative for size transformation  http://nlvm.usu.edu/en/nav/frames_asid_295_g_3_t_3.html?open=activities
Congruence, similarity & transformations   http://standards.nctm.org/document/eexamples/chap6/6.4/part4.htm
Additional topic  
Logo Programming, Geometry   http://www.terrapinlogo.com/show.cgi?id=1001004165916225&file=educators/why.html

 http://www.mhhe.com/math/ltbmath/bennett_nelson/conceptual/student/logo.mhtml

 http://mckoss.com/logo/

Logo designs  http://www.geocities.com/CollegePark/Lab/2276/

You can also search the web using a key word search to find many different interesting sites that are related to teaching elementary and middle school mathematics.                Return to Top of page

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