**General Resources**
**Center for Comprehensive School Reform and Improvement (Learning Point Associates)**
http://www.centerforcsri.org
Sponsored by the U.S. Department of Education this website provides education research and strategies through free resources and technical assistance. Resources include: a searchable online database with thousands of abstracts of school improvement studies, research reports, and articles; webcast discussions with national experts and local practitioners on various education topics; published materials on topics pertinent to school improvement; online and telephone FAQ services; and research-based guides, tools, and information to help schools increase academic achievement for all students. Click here for mathematics-specific resources.
**National Council of Teachers of Mathematics**
http://www.nctm.org
Here you can find all about NCTM, its belief statements, and positions on important topics. Also find an overview of *Principles and Standards *and free access to interactive applets (see Standards—Electronic), the *Curriculum Focal Points*, the *Illuminations* website, membership and conference information, publications catalog, links to related sites, and much more. Members have access to even more information.
**NCTM’s Position Statements**
http://www.nctm.org/positionstatements.aspx
NCTM’s position statements define the Council's views related to mathematics education on such topics as: closing the achievement gap, algebra, assessment, early childhood, equity, teacher quality and retention, and technology. The NCTM Board of Directors approves position statements.
**NCTM’s Research Clips and Briefs**
http://www.nctm.org/news/content.aspx?id=8468
These are research-based responses to questions of practice such as research on homework, student learning, effective instruction, formative assessment and more. Clips are short and provide only the findings. Briefs include more information and list related research.
**NCTM’s Tips for Teachers**
http://www.nctm.org/teachingtips.aspx?linkidentifier=id&itemid=9584
Provides tips on motivating learners, grading, communicating with parents, using tools and technology, etc.
**National Mathematics Advisory Panel (NMAP)**
http://www.ed.gov/about/bdscomm/list/mathpanel/reports.html
March 2008 reports of the U.S. National Mathematics Advisory Panel, including Task Groups and subcommittees.
**Equity**
**Benjamin Banneker Association, Inc.**
http://www.bannekermath.org
A national non-profit organization dedicated to mathematics education advocacy, leadership, and professional development to support teachers in providing for mathematics learning of the highest quality for African-American students.
Ethnomathematics Digital Library (EDL)
**http://www.ethnomath.org/index.asp**
The EDL provides access to online resources worldwide. There are about 700 items in the collection, and is a resource network and interactive learning community for ethnomathematics, with emphasis on the indigenous mathematics of the Pacific region.
**EQUALS program (UCB)**
http://lawrencehallofscience.org/equals/aboutEQ.html
The University of California at Berkeley, supporters of the EQUALS program for equal opportunities for females in mathematics and science, provides information about gender equity and parental involvement.
**International Children's Digital Library (University of Maryland)**
http://en.childrenslibrary.org/index.shtml
The ICDL provides a collection of books that represents oustanding historical and contemporary books from throughout the world. Numerous cultures and languages are represented so that every child can know and appreciate the riches of children's literature from the worldwide community.
**LD Online**
http://www.ldonline.org/indepth/math
A collection of informative resources here for both parents and educators regarding learning disabilities in the area of mathematics.
**Multilingual Mathematics Glossary (Holt, Rinehart and Winston)**
http://my.hrw.com/math06_07/nsmedia/tools/glossary/msm/glossary.html
A glossary of mathematics terms, translated in the following languages: Arabic, Armenian, Chinese, Hmong, Khmer, Korean, Punjabi, Russian, Spanish, Tagalog, Urdu, and Vietnamese.
**National Association for Gifted Children (NAGC)**
http://www.nagc.org
NAGC, which has been in existence for over 50 years, is dedicated to serving professionals who work on behalf of gifted children. The site has a “Tools for Educators” section that includes online articles and resources.
**TODOS: Mathematics for All**
http://www.todos-math.org/mc/page.do
An organization that provides information and resources in support of the mathematics education of Hispanics/Latinos.
**Women on Mathematics Education**
http://www.wme-usa.org
Provides resources that promote the mathematics education of girls and women.
**Curriculum**
**Center for the Study of Mathematics Curriculum - State Mathematics Standards Database**
http://mathcurriculumcenter.org/states.php
This website from The Center for the Study of Mathematics Curriculum (CSMC) has the complete set of hotlinks to current state-level K–12 mathematics curriculum standards. In some cases states provide multiple documents, including their standards for assessment or other important information for teachers of mathematics.
*Curriculum Focal Points for Prekindergarten through Grade 8 Mathematics: A Quest for Coherence ***(NCTM)**
**http://www.nctm.org/standards/content.aspx?id=270**
The *Focal Points* are organized by grade level and NCTM content strands, emphasizing for each grade three essential areas (Focal Points) as the primary focus of that year’s instruction. The *Curriculum Focal Points *are, in fact, a stimulus for conversations among teachers, administrators, families, and other interested stakeholders about the emphasis, depth, and sequence of key ideas for their child, classroom, school, or state.
**Curriki.org**
http://www.curriki.org/xwiki/bin/view/Demo/nrocCourses
A global resource that encourages the collaboration and sharing of high-quality lessons, modules and full courses developed by exemplary teachers from all over the world.
*Principles and Standards for School Mathematics ***(NCTM)**
http://standards.nctm.org
NCTM document that articulates the ideals, processes, and content that should be emphasized in pre-K through grade 12 classrooms and programs.
**Show-Me Center **
http://www.showmecenter.missouri.edu
This website will provide information and direct links to the exemplary middle school math programs via the Show-Me Center's website. The programs include the Connected Mathematics (CMP 6-8), Mathematics in Context (MIC 5-8), MathScape (6-8), Middle School Mathematics Through Applications Project (MMAP 6-8), Middle Grades Math Thematics (STEM 6-8).
** ****Teaching**
**Annenberg Media Learner.org**
http://www.learner.org
A unit of the Annenberg Foundation, Annenberg/CPB offers professional development information and useful information for teachers who want to learn about and teach mathematics.
**Doing What Works**
http://dww.ed.gov
Doing What Works (DWW) is a website sponsored by the U.S. Department of Education and dedicated to helping educators identify and make use of effective teaching practices. The Math and Science section explores topics such as “Critical Foundations for Algebra” and “Encouraging Girls in Math and Science.”
**ENC Online (Eisenhower National Clearinghouse)**
http://www.goenc.com
The ENC site is full of useful information for teachers who are planning lessons and activities or searching for professional development resources.
**The Futures Channel**
http://www.thefutureschannel.com
This site provides teacher professional development, career-related lessons, classroom resources, and engaging video clips.
**NCTM’s e-Examples**
http://standards.nctm.org/document/eexamples/index.htm
Online activities to illuminate the NCTM’s *Principles and Standards for School Mathematics.*
** ****Learning**
**Adding It Up: Helping Children Learn Mathematics**
http://www.nap.edu/catalog.php?record_id=9822
This free online version of the book by Jeremy Kilpatrick, Jane Swafford, and Bradford Findell (Editors; Mathematics Learning Study Committee, National Research Council) explores how students in prekindergarten through grade 8 learn mathematics and recommends how teaching, curricula, and teacher education should change to improve mathematics learning during these critical years.
**Ask Dr. Math (Math Forum)**
http://mathforum.org/dr.math
Ask Dr. Math is a great homework resource for families, students, and teachers. Dr. Math has answers to all the classic math questions students have, like why a negative times a negative is a positive.
**The Math Forum**
http://mathforum.org
Along with the NCTM sites, this may contain some of the most important source of information and links to useful sites. The forum has resources (Math Tools) for both teachers and students. There are suggestions for lessons, puzzles, and activities, plus links to other sites with similar information. There are forums where teachers can talk with other teachers. Two pages accept questions about mathematics from students or teachers (Ask Dr. Math) and about teaching mathematics from teachers (Teacher 2 Teacher). Problems are regularly posted, and solutions can be entered via the Internet.
** ****Assessment**
**NAEP (National Assessment of Educational Progress, “The Nation’s Report Card”)**
http://nces.ed.gov/nationsreportcard/mathematics
Past and current data and reports related to NAEP assessments.
**Trends in International Mathematics and Science Study (TIMSS)**
http://nces.ed.gov/timss
Also, published by the National Center for Education Statistics, this page is the home page for reading about the background of the Trends in International Mathematics and Science Study (TIMSS). Provides many links to actual questions and data generated by student responses to questions.
** ****Technology**
**Apple’s Learning Interchange **
http://edcommunity.apple.com/ali/search.php?collectionID=2407
A collection of teacher created, innovative lessons that can be viewed by topic, subject or technology. These are presented in a videocast format. Teachers can create post their own innovative teaching ideas.
**Arcytech**
http://arcytech.org/java
This site includes tool applets for base-ten blocks, pattern blocks, Cuisenaire rods, fraction bars, and integer bars. There is also an extended interactive lesson developing the Pythagorean theorem.
**Center for Implementing Technology in Education (CITEd): Tech Matrix**
http://www.techmatrix.org
CITEd’s Tech Matrix is useful database of technology products that supports instruction in mathematics for students with special needs. Each product evaluation includes a link to the supplier’s website.
**Illuminations (NCTM)**
http://illuminations.nctm.org
This is an incredible site developed by NCTM to provide Internet resources for teaching and learning intended to “illuminate” *Principles and Standards for School Mathematics. *You can find resources from lesson ideas to “math-lets” (applets designed to provide tools for developing understanding in mathematics). Also at this site are multimedia investigations for students and links to video vignettes designed to promote professional reflection. The Illuminations website continues to be updated with the addition of many new lessons. In addition the Illuminations Game Room Project allows students to explore mathematics topics while playing mathematics games with one another over the Web.
**Interactivate (Shodor Education Foundation)**
http://www.shodor.org/interactivate
The site contains a huge list of applets that continues to grow. In addition, there are lessons and activities. Applets (referred to as “activities”) are arranged by content rather than grade level, so be sure to look through the full list. This is a valuable site, especially for teachers in the upper grades and middle school.
**The National Library for Virtual Manipulatives and eNLVM**
http://nlvm.usu.edu/en/nav/vlibrary.html
This NSF-funded site located at Utah State University contains a huge collection of applets organized by the five content strands of the *Standards *and also by the same four grade bands. The eNVLM section contains online units, customizable student activities, and tools to help teachers develop activities collaboratively.
**Scott Foresman eTools**
http://www.kyrene.org/mathtools
The eTools software provides several applets, including one that will allow the creation of a rectangle up to 50 by 100 that can be filled in with base-ten blocks the same as would be done with physical blocks (Similar to Rectangle Multiplication).
**Texas Instruments**
http://education.ti.com/educationportal/sites/US/sectionHome/pd.html
This page is the main education page of Texas Instruments. The site contains a plethora of information for math educators interested in using calculators in the classroom.
**Thinkport (PBS)**
http://www.thinkport.org/classroom/mathresources/default.tp
Thinkport is the product of a partnership between Maryland Public Television and the Johns Hopkins Center for Technology in Education. Four distinct “channels” of the site include Think Classroom delivers lesson plans, member features and online resources correlated to state standards. Think Technology provides online video clips, virtual field trips, and online professional development courses.
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Standards
Based Mathematics
**Adding It Up: Helping Children Learn Mathematics**
**http://www.nap.edu/catalog.php?record_id=9822**
This free online version of the book by Jeremy Kilpatrick, Jane Swafford, and Bradford Findell (Editors; Mathematics Learning Study Committee, National Research Council) explores how students in prekindergarten through grade 8 learn mathematics and recommends how teaching, curricula, and teacher education should change to improve mathematics learning during these critical years.
**ARC Center**
**http://www.comap.com/elementary/projects/arc/**
The ARC Center promotes the implementation of standards-based mathematics curricula by providing schools and districts and provides with information and resources to support teacher professional development, leadership development, and public awareness of mathematics.
**Association for Supervision and Curriculum Development (ASCD)**
**http://www.ascd.org**
The ASCD website includes articles, information about its publications, plus articles and other publications related to learning.
*Before It's Too Late: A Report to the Nation from The National Commission on Mathematics and Science Teaching for the 21st Century*
**http://www.ed.gov/inits/Math/glenn/report.doc**
The complete 2001 report, headed by Senator John Glenn, that found that schools are not producing “graduates with the kinds of skills our economy needs to remain on the competitive cutting edge.”
**Common Core State Standards Initiative for K-12 Mathematics**
http://www.corestandards.org
This state-led effort coordinated by the National Governors Association for Best Practices (NGA Center) and the Council of Chief State School Officers (CCSSO) is an initiative that developed a common core of state standards in English-language arts and mathematics for grades K-12.
*Curriculum Focal Points for Prekindergarten through Grade 8 Mathematics: A Quest for Coherence *(NCTM)
http://www.nctm.org/standards/content.aspx?id=270
The *Focal Points* are organized by grade level and NCTM content strands, emphasizing for each grade three essential areas (Focal Points) as the primary focus of that year’s instruction. The *Curriculum Focal Points *are, in fact, a stimulus for conversations among teachers, administrators, families, and other interested stakeholders about the emphasis, depth, and sequence of key ideas for their child, classroom, school, or state.
**Educating Teachers of Science, Mathematics, and Technology: New Practices for the New Millennium**
**http://www.nap.edu/openbook.php?isbn=0309070333**
This free online versions of the 205 page book by the Center for Science, Mathematics, and Engineering Education gives recommendations for exemplary professional development practices for science, mathematics, and technology educators.
**Everyday Mathematics (UCSMP)**
**http://everydaymath.uchicago.edu**
Everyday Mathematics is a comprehensive pre-kindergarten through 6th grade mathematics curriculum developed by the University of Chicago School Mathematics Project.
**goENC**
**http://www.goenc.com**
This is the new site for the Eisenhower National clearinghouse, an organization dealing with many issues in math education, and education in general.
**Illuminations (NCTM)**
**http://illuminations.nctm.org**
A companion website to NCTM sponsored by NCTM and Marcopolo. Provides lessons, interactive applets, and links to websites for learning and teaching mathematics.
**Inside Mathematics (Noyce Foundation)**
**http://www.insidemathematics.org/index.php**
This site features classroom examples of innovative teaching methods and insights into student learning, tools for mathematics instruction that teachers can use immediately, and video tours of the ideas and materials on the site.
Investigations in Number, Data, and Space®
**http://investigations.terc.edu**
Investigations in Number, Data, and Space® is a complete mathematics program. It is designed to help all elementary children understand the fundamental ideas underlying number and arithmetic, geometry, data, measurement, and algebraic thinking.
**Key Issues in Math (Math Forum)**
**http://www.mathforum.org/social/index.html**
Part of the Math Forum at Drexel University, this page lists numerous questions concerning issues in mathematics education with answers supplied by experts in short articles or excerpts.
**Mathematically Sane **
**http://mathematicallysane.com/faq.asp**
This website is one within the larger "Mathematically Sane" website. This link answers frequently answered questions (FAQ's) regarding math reform. Within the answers are links to research supporting the implementation of math reform.
**Math Trailblazers: A Mathematical Journey Using Science and Language Arts**
**http://www.math.uic.edu/~imse/IMSE/MTB/mtb.html**
Math Trailblazers is a full mathematics curriculum for grades K 5. This project was funded by the National Science Foundation to develop a comprehensive, elementary, reform mathematics curriculums.
**NAEP (National Assessment of Educational Progress, “The Nation’s Report Card”)**
**http://nces.ed.gov/nationsreportcard/mathematics**
Past and current data and reports related to NAEP assessments.
**National Center for Education Statistics**
**http://nces.ed.gov **
This website contains general information regarding the Nation's Report Card, as well as opportunities to see actual National Assessment of Education Progress (NAEP) questions as well as student answers and data resulting from actual test administrations.
**National Council of Teachers of Mathematics**
**http://www.nctm.org**
Here you can find all about NCTM, its belief statements, and positions on important topics. Also find an overview of *Principles and Standards *and free access to interactive applets (see Standards—Electronic), the *Curriculum Focal Points*, the *Illuminations* website, membership and conference information, publications catalog, links to related sites, and much more. Members have access to even more information.
**No Child Left Behind (U.S. Dept. of Ed.)**
http://www.ed.gov/nclb
The 2001 the legislation commonly known as No Child Left Behind (NCLB) was enacted, requiring highly qualified teachers in every classroom, proficiency from all students by 2014, incremental annual achievement based on assessments of adequate yearly progress (AYP), and development by states of content standards that are rigorous and specific.
**Phi Delta Kappa International Free Online Articles**
http://www.pdkintl.org/kappan/index.htm
The debate between reform and the basics is both important and interesting. For an engaging discussion of the reform movement in light of the “back to basics” outcry, read the three free online articles from the February 1999 edition
*Principles and Standards for School Mathematics ***(NCTM)**
**http://standards.nctm.org**
NCTM document that articulates the ideals, processes, and content that should be emphasized in pre-K through grade 12 classrooms and programs.
**Show-Me Center **
**http://www.showmecenter.missouri.edu**
This website will provide information and direct links to the exemplary middle school math programs via the Show-Me Center's website. The programs include the Connected Mathematics (CMP 6-8), Mathematics in Context (MIC 5-8), MathScape (6-8), Middle School Mathematics Through Applications Project (MMAP 6-8), Middle Grades Math Thematics (STEM 6-8).
**State Mathematics Standards Database (CSMC)**
**http://mathcurriculumcenter.org/states.php**
This website from The Center for the Study of Mathematics Curriculum (CSMC) has the complete set of hotlinks to current state-level K–12 mathematics curriculum standards. In some cases states provide multiple documents, including their standards for assessment or other important information for teachers of mathematics.
**Teachers.net**
**http://teachers.net**
This website contains many different kinds of resources for teachers including lesson plans, chat rooms and curriculum resources.
**Trends in International Mathematics and Science Study (TIMSS)**
http://nces.ed.gov/timss
Also, published by the National Center for Education Statistics, this page is the home page for reading about the background of the Trends in International Mathematics and Science Study (TIMSS). Provides many links to actual questions and data generated by student responses to questions.
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Problem Solving Resources
**Activities in Mathematics and Science (AIMS)**
**http://www.aimsedu.org**
A non-profit organization that provides resources for mathematics and science teaching.** **
**Annenberg/CPB**
**http://www.learner.org/index.html**
A unit of the Annenberg Foundation, Annenberg/CPB offers professional development information and useful information for teachers who want to learn about and teach mathematics.
**ENC Online (Eisenhower National Clearinghouse)**
**http://www.goenc.com**
Click on Digital Dozen, Lessons and Activities, or Web Links. The ENC site is full of useful information for teachers who are planning lessons and activities or searching for professional development resources.
**Illuminations (NCTM)**
**http://illuminations.nctm.org**
Illuminations, the resource website of NCTM, is perhaps the best portal for finding high-quality lessons on the internet. Besides over 100 activities posted that use engaging applets, there are more than 500 full lesson plans as well as links to many high-quality websites, searchable by content and by grade band.
**Internet based lessons **
**http://math.rice.edu/~lanius/Lessons/index.html**
A web page that offers excellent internet based lessons and hints that lead to some interesting solutions to mathematical problems.
**MathCounts**
**http://mathcounts.org**
MATHCOUNTS® is an enrichment and competition program that promotes middle school mathematics achievement through the U.S.
**MathSolutions Lessons from the Classroom**
**http://www.mathsolutions.com/index.cfm?page=wp9&crid=56**
This is a great collection of lessons for teaching through problem solving.
**NCTM's Problem DataBase **
http://nctm.org/resources/content.aspx?id=16387
Free for all NCTM members, this resource contains thousands of problems, sorted by level and topic, from articles published in past issues of *Teaching Children Mathematics, Mathematics Teaching in the Middle School, Student Math Notes, and Figure This!*
Non-routine problems
**http://www.stfx.ca/special/mathproblems**
This site is dedicated to allowing teachers and students to practice non-routine problems in a fun way. The site includes sets of problems for grades 5 through 12, and they are quite challenging!
**Problem Solving with a Point**
http://www2.edc.org/mathproblems
A searchable database of problems for grades 6-12 that can be sorted by topic, habits of mind, math background, technology use, duration or keyword. The site contains many useful teacher resources.
**Problem Solving Strategies**
http://pred.boun.edu.tr/ps/index.htm
Contains a list of common problem solving strategies and suggestions for helping students use them.
**Synthesis of Research on Problem Solving**
http://jwilson.coe.uga.edu/emt725/PSsyn/Pssyn.html
A review of the research on problem solving from the University of Georgia.
**Writing and Communication in Mathematics (Math Forum)**
**http://mathforum.org/library/ed_topics/writing_in_math**
This Math Forum page lists numerous articles and Web links concerning the value of writing in mathematics at all levels.
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Planning
for Problem-Based Teaching and Learning
**Ask Dr. Math (Math Forum)**
**http://mathforum.org/dr.math**
Ask Dr. Math is a great homework resource for families, students, and teachers. Dr. Math has answers to all the classic math questions students have, like why a negative times a negative is a positive.
**Cooperative Groups and the Learning Disabled **
**http://www.ldonline.org/indepth/math_skills/coopmath.html**
A good article linking the use of cooperative groups to learning disabled students in math classrooms. Acts as a good guide for implementing cooperative groups.
**Drill and Practice **
**http://olc.spsd.sk.ca/DE/PD/instr/strats/drill/index.html**
This page includes an article on what "drill and practice" means in the math classroom, and effective ways it can be used and adapted. The article also includes links to some on-line resources for teachers, as well as on-line practice for students.
**Illuminations (NCTM)**
**http://illuminations.nctm.org**
This is a favorite of many math teachers. Click on “Lessons” and you can then select grade band and content to search for lessons—all of them excellent!
**International Children's Digital Library (University of Maryland)**
http://en.childrenslibrary.org/index.shtml
The ICDL provides a collection of books that represents oustanding historical and contemporary books from throughout the world. Numerous cultures and languages are represented so that every child can know and appreciate the riches of children's literature from the worldwide community.
**Math in Daily Life**
**http://www.learner.org/interactives/dailymath**
Hosted by Annenberg/CPB, investigate six interesting examples of how mathematics is used in daily life.
*Team Building Games on a Shoestring *
**http://www.teachmeteamwork.com**
A free downloadable e-book by Tom Heck that has eight, fun team building activities, all done with shoestrings.
**The Fraction Game (NCTM)**
**http://illuminations.nctm.org/ActivityDetail.aspx?ID=18**
A good task for a station activity is one that can be profitably repeated several times. The “Fraction Game” in the NCTM Illuminations Lessons can be played repeatedly, each time strengthening students’ understanding of fractions.
**The Math Forum: Internet Mathematics Library (Math Forum)**
**http://mathforum.org/library**
Here you will find links to all sorts of information that will be useful in both planning and assessment in a problem-based classroom.
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Effective
Assessment
**Dare to Compare – NCES Kids’ Zone**
**http://nces.ed.gov/nceskids/eyk/index.asp?flash=false**
This site, provided by the National Center for Educational Statistics, gives students an opportunity to answer math and science questions from the Trends in International Mathematics and Science Study (TIMSS). The students can choose the 4th or 8th grade level, can choose the type and number of questions they would like to receive, and can them see how their answers ranked among the world.
**Mathematics Attitude Survey (OSU)**
**http://oregonstate.edu/~schorir/ocept/survey.html**
A questionnaire that gives ideas for types of questions that can be used in an open-ended student survey.
**Position Statement—High-Stakes Tests (NCTM, Jan. 2006)**
**http://nctm.org/about/content.aspx?id=6356**
This position statement provides information about NCTM’s position on the role of high-stakes testing in making decisions for schools, students, and instruction.
**Research Clips and Briefs—Formative Assessment (NCTM)**
**http://www.nctm.org/news/content.aspx?id=8468**
NCTM provides information on the definition of formative assessment and Five Key Strategies for effective formative assessment, including an example of a task for a diagnostic interview. They also include an excellent set of references for further investigation.
**The Math Forum: Internet Mathematics Library – Assessment**
**http://mathforum.org/library/ed_topics/assessment**
Here you will find links to all orts of information that will be useful in both planning and assessment.
**The Nation's Report Card (NCES)**
**http://nces.ed.gov/nationsreportcard**
The general location of the website of the National Center for Educational Statistics. This location directs you to the report, The Nation's Report Card, which resulted from the 8th National Assessment of Educational Progress (NAEP).
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Equity
in Mathematics
**A Modern History of Blacks in Mathematics**
**http://www.math.buffalo.edu/mad/madhist.html**
A website dedicated to the significant influence of the African American population in mathematics.
**Benjamin Banneker Association, Inc.**
**http://www.bannekermath.org**
A national non-profit organization dedicated to mathematics education advocacy, leadership, and professional development to support teachers in providing for mathematics learning of the highest quality for African-American students.
**Biographies of Women Mathematicians**
**http://www.agnesscott.edu/Lriddle/women/women.htm**
This website was developed by Agnes Scott College in Atlanta, Georgia, and focuses on the numerous achievements of women in the field of mathematics.
**Culturally Responsive Teaching (Brown University)**
**http://www.alliance.brown.edu/tdl/tl-strategies/crt-principles.shtml**
This site defines, explains, and gives examples of the principles of culturally responsive teaching.
**EQUALS program (UCB)**
**http://lawrencehallofscience.org/equals/aboutEQ.html**
The University of California at Berkeley, supporters of the EQUALS program for equal opportunities for females in mathematics and science, provides information about gender equity and parental involvement.
**Equity in Mathematics Classrooms (NCTM)**
**http://www.nctm.org/equity.aspx**
Dozens of resources provided by the NCTM that focus on creating a culture of equity.
**Gender issues**
**http://www.woodrow.org/teachers/math/gender**
An excellent resource for teachers to learn more about gender issues in math classrooms. The site has many links, including one to math attitude scales that can indicate how a teacher or students feels about math.
**Gifted Students**
**http://www.hoagiesgifted.org/math_gifted.htm**
This page provides many links to articles and presentations regarding gifted or highly-talented students in math education. Many articles can relate to parents or teachers.
**LDOnline**
**http://www.ldonline.org**
This site offers identification and assessment tools, teaching strategies, recommended readings, and interesting articles on mathematical disabilities in the “LD in Depth” section.
**Multiculturalism**
**http://sln.fi.edu/school/math3/**
This page is an excellent resource for relating multiculturalism to math classrooms. Teachers or students can select a country and then work on math problems relating specifically to the chosen culture.
**Multilingual Mathematics Glossary (Holt, Rinehart and Winston)**
**http://my.hrw.com/math06_07/nsmedia/tools/glossary/msm/glossary.html**
A glossary of mathematics terms, translated in the following languages: Arabic, Armenian, Chinese, Hmong, Khmer, Korean, Punjabi, Russian, Spanish, Tagalog, Urdu, and Vietnamese.
**National Association for Gifted Children (NAGC)**
**http://www.nagc.org**
NAGC, which has been in existence for over 50 years, is dedicated to serving professionals who work on behalf of gifted children. The site has a “Tools for Educators” section that includes online articles and resources.
**National Center on Response to Intervention (RTI)**
**http://www.rti4success.org**
RTI is a three-tiered student support system that focuses on the results of implementing instructional interventions in a model of prevention. Each tier represents a level of intervention with corresponding monitoring of results and outcomes.
**Special Education Resources on the Internet**
**http://seriweb.com**
SERI is a collection of Internet-accessible information and resources of interest to those involved in fields related to special education.
**Teaching Mathematics to Gifted Students in a Mixed-Ability Classroom**
**http://www.teachervision.fen.com/gifted-education/teaching-methods/3778.html**
A free TeacherVision article written by Dana T. Johnson.
**Teachers of English to Speakers of Other Languages, Inc.**
**http://www.tesol.org/s_tesol/index.asp**
Provides advocacy, resources, workshops and publications related to the field of English language teaching.
**The International Study Group on Ethnomathematics**
**http://www.rpi.edu/~eglash/isgem.htm**
The ISGEm is dedicated to the understanding of the cultural diversity of mathematical practices and to applying this knowledge to education and development. Its webpage provides links to other useful sites.
**The Society for Advancement of Chicanos and Native Americans in Science (SACNAS) Biography Project**
**http://www.sacnas.org**
An online resource for K-12 educators who are interested in teaching their students about the accomplishments of Chicano/Latino and Native American scientists.
**TODOS: Mathematics for All**
**http://www.todos-math.org/mc/page.do**
An organization that provides information and resources in support of the mathematics education of Hispanics/Latinos.
**Women on Mathematics Education**
**http://www.wme-usa.org**
Provides resources that promote the mathematics education of girls and women.
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Technology and Mathematics
**Annenberg/CPB Projects**
**http://www.learner.org**
The tremendous resource lists free online learning activities, including information about all sorts of interesting uses of mathematics and science in the real world, resources for free and inexpensive materials from Annenberg, and information about funding opportunities.
**Apple’s Learning Interchange **
**http://edcommunity.apple.com/ali/search.php?collectionID=2407**
A collection of teacher created, innovative lessons that can be viewed by topic, subject or technology. These are presented in a videocast format. Teachers can create post their own innovative teaching ideas.
**Arcytech**
**http://arcytech.org/java**
This site includes tool applets for base-ten blocks, pattern blocks, Cuisenaire rods, fraction bars, and integer bars. There is also an extended interactive lesson developing the Pythagorean theorem.
**Center for Implementing Technology in Education (CITEd): Tech Matrix**
**http://www.techmatrix.org**
CITEd’s Tech Matrix is useful database of technology products that supports instruction in mathematics for students with special needs. Each product evaluation includes a link to the supplier’s website.
**Concord Consortium’s Technology Enhanced Elementary and Middle School Science (TEEMSS II) CBL Project **
**http://teemss.concord.org**
This project blends science and mathematics inquiry for grades 3–8. Through curriculum and software (free after registration) they share investigations in which real-time data in physical science, life science, earth science, technology, and engineering are collected, analyzed, and shared.
**Curriki.org**
http://www.curriki.org/xwiki/bin/view/Demo/nrocCourses
A global resource that encourages the collaboration and sharing of high-quality lessons, modules and full courses developed by exemplary teachers from all over the world.
**The Future’s Channel**
http://www.thefutureschannel.com
The Future’s Channel provides online videos and mathematic lessons connected to science, engineering and technology related careers.
**Glencoe Virtual Manipulatives**
http://www.glencoe.com/sites/common_assets/mathematics/ebook_assets/vmf/VMF-Interface.html
Choose the grade level, background, and tool to use these custom virtual resources.
**goENC**
**http://www.goenc.com**
This is a site of links to information about standards-based curriculum materials for K-12 mathematics and science, information and articles on standards-based issues, information about TIMSS, and ideas for classroom use.
**Illuminations (NCTM)**
**http://illuminations.nctm.org**
This is an incredible site developed by NCTM to provide Internet resources for teaching and learning intended to “illuminate” *Principles and Standards for School Mathematics. *You can find resources from lesson ideas to “math-lets” (applets designed to provide tools for developing understanding in mathematics). Also at this site are multimedia investigations for students and links to video vignettes designed to promote professional reflection. The Illuminations website continues to be updated with the addition of many new lessons. In addition the Illuminations Game Room Project allows students to explore mathematics topics while playing mathematics games with one another over the Web.
**International Society of Technology in Education (ISTE)**
**http://www.iste.org**
ISTE provides leadership and service to improve teaching, learning, and school leadership by advancing the effective use of technology in PK–12 and teacher education. ISTE sponsors the National Educational Technology Standards (NETS) and Center for Applied Research in Educational Technology (CARET).
**Lure of the Labyrinth (MPT)**
**http://labyrinth.thinkport.org**
Created by Maryland Public Television’s *Thinkport*, the “Labyrinth” engages students in a storyline designed to develop critical thinking on the topics of proportionality, variables and equations, and number and operations. Gamers learn from experience and are the “experts” in charge of their own failure or success. As the game keeps track of progress, students can get help “just in time” when they need it.
**Make it Happen**
**http://www2.edc.org/FSC/MIH/**
An approach that improves middle school education for students with diverse learning abilities. In the Make It Happen! approach, interdisciplinary teams of teachers design and implement inquiry-based I-Search Units and integrate technology into these units in meaningful ways to benefit students.
**Math by Design**
http://mathbydesign.thinkport.org
Math by Design (grades 6-8) provides students the opportunity to learn geometry and measurement concepts in a virtual environment. As junior architects of a community park and environmental center, students are tasked with building a skateboard ramp, planning a picnic area and other fun, interactive challenges.
The Math Forum
**http://mathforum.org**
Along with the NCTM sites, this may be your most important source of information and links to useful sites. The forum has resources (Math Tools) for both teachers and students. There are suggestions for lessons, puzzles, and activities, plus links to other sites with similar information. There are forums where teachers can talk with other teachers. Two pages accept questions about mathematics from students or teachers (Ask
Dr. Math) and about teaching mathematics from teachers (Teacher 2 Teacher). Problems are regularly posted, and solutions can be entered via the Internet.
**MathMovesU**
http://www.mathmovesu.com
This website helps connect middle school students to math through engaging content ( sports, music, and fashion, etc.) while delivering math subject matter using technology to engage students in games, polls, and fun math facts, all set within a ‘virtual world.’
**National Council of Teachers of Mathematics e-Examples**
**http://standards.nctm.org/document/eexamples/index.htm**
Many of these applets are referenced in and directly support the text of *Principles and Standards for School Mathematics. *They are also available on the CD version of the Standards. Most are also available on the Illuminations site.
**The National Library for Virtual Manipulatives and eNLVM**
**http://nlvm.usu.edu/en/nav/vlibrary.html**
This NSF-funded site located at Utah State University contains a huge collection of applets organized by the five content strands of the *Standards *and also by the same four grade bands. The eNVLM section contains online units, customizable student activities, and tools to help teachers develop activities collaboratively.
**NCTM’s ON-Math Journal**
**http://www.nctm.org/publications/content.aspx?id=8598**
ON-Math, the Online Journal of School Mathematics, is a peer-reviewed journal developed and designed exclusively for the Internet.
**Project Interactivate (Shodor Education Foundation)**
**http://www.shodor.org/interactivate**
The site contains a huge list of applets that continues to grow. In addition, there are lessons and activities. Applets (referred to as “activities”) are arranged by content rather than grade level, so be sure to look through the full list. This is a valuable site, especially for teachers in the upper grades and middle school.
**Texas Instruments**
**http://education.ti.com/educationportal/sites/US/sectionHome/pd.html**
This page is the main education page of Texas Instruments. The site contains a plethora of information for math educators interested in using calculators in the classroom.
**The World Factbook (CIA)**
**https://www.cia.gov/library/publications/the-world-factbook/index.html**
Provided by the Central Intelligence Agency, this page provides demographic information for every nation in the world, including population, age distributions, death and birth rates, and information on the economy, government, transportation, and geography. Maps are included as well.
**U.S. Census Data**
**http://www.census.gov**
Copious statistical information by state, county, or voting district.
**Villainy, Inc. (MPT’s Thinkport)**
http://villainyinc.thinkport.org
A website containing two interactive missions designed to assist the user in exploring a variety of topics in upper elementary and middle school mathematics, including algebra and geometry. During their involvement in a Mission, students have to draw on a wide assortment of math skills to find an answer, thinking critically and trying various methods to come up with a logical answer.
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Early
Number Concepts and Number Sense
**Counting Game (LearningPlanet)**
http://members.learningplanet.com/act/count/free.asp
This game is designed to help children practice skip counting. Finish before time runs out and you get bonus points.** **
Counting to 100 in 22 Different Languages
http://www.marijn.org/everything-is-4/counting-0-to-100/all-languages
Count to 100 in Chinese, Croatian, Czech, Danish, Dutch, English, Estonian, Finnish, French, German, Hebrew, Hungarian, Italian, Japanese, Nowegian, Polish, Portuguese, Romanian, Spanish, Swedish, Turkish, and Welsh
Count Us In
**http://www.abc.net.au/countusin/default.htm**
A site full of downloadable activities and games for early number development.
**Count Your Chickens (PBS Kids)**
**http://pbskids.org/curiousgeorge/games/count_your_chickens/count_your_chickens.html**
Kids help Curious George count chickens in a pen, reinforcing their counting and estimation skills.
**Early Childhood Mathematics: Promoting Good Beginnings**
**http://www.naeyc.org/positionstatements/mathematics**
The full position statement of the National Association for the Education of Young Children (NAEYC) and the National Council of Teachers of Mathematics (NCTM) is found at this location.
**Fishy Count (PrimaryGames)**
**http://www.primarygames.com/math/fishycount/index.htm**
Young children explore cardinality by counting fish and selecting the correct number of fish displayed from three choices.
**Five-Frame (Illuminations)**
http://illuminations.nctm.org/ActivityDetail.aspx?ID=74
A nice manipulative version of the five-frame. Four games that help students develop counting and addition skills are included in this activity.
Full Screen Calculator (Onlinecalculator.com)
http://www.online-calculator.com/full-screen-calculator
A large, four-function calculator.
**Hundred Chart/Square (Crickweb)**
http://www.crickweb.co.uk/ks1numeracy.html
An interactive and customizable hundred chart. Both small and large versions can be found here.
**"Math Buddies" (Annenberg Media)**
http://learner.org/resources/series32.html
The following video from Annenberg Media provides a glimpse into a classroom where students are building numbers 1-50, making connections tonumbers a variety of contexts, skip counting, etc.
**Let’s Count to 5 (NCTM, Grades K–2)**
**http://illuminations.nctm.org/LessonDetail.aspx?id=U57**
This site contains seven lessons with links to resources and downloads for student recording sheets. Children can make sets of zero through five objects and connect number words or numerals to the sets. Familiar songs, rhymes, and a variety of activities that appeal to visual, auditory, and kinesthetic learners are included. In a similar fashion see the following site for higher numbers.
**Let’s Count to 10 (NCTM, Grades K–2)**
**http://illuminations.nctm.org/LessonDetail.aspx?id=U147**
**Let’s Count to 20 (NCTM, Grades K–2)**
**http://illuminations.nctm.org/LessonDetail.aspx?id=U153**
These lessons emphasize the process standards of Communication and Reasoning.
**Math Tools: Math 1, Number Sense (Math Forum)**
**http://mathforum.org/mathtools/cell/m1,3.2,ALL,ALL**
On this one page of the Math Tools website you will find activities and lessons appropriate for first-grade number sense. Explore other options on the site as well.
**Representing Data—Baby Weight (NCTM, Grades K–8)**
**http://illuminations.nctm.org/LessonDetail.aspx?ID=L170**
In this grades 1–2 lesson, students work with data to complete an organized chart by doubling or halving numbers and compare data using bar graphs.
**Scott Foresman’s eTools**
**http://www.kyrene.org/mathtools**
Scott Foresman’s *eTools *(Pearson Education, 2004) includes a variety of background screens for counters. In the hands of a teacher, this program offers a great deal of diversity and challenge for both part-part-whole and missing-part activities.
**Speed Pictures 1 and 2 (Freudenthal Institute)**
**http://www.fi.uu.nl/rekenweb/en/**
The Freudenthal Institute’s Speed Pictures 1 and 2 are designed to help students practice subitizing using flashed images of fingers, number cubes, beads, eggs, or money.
**Ten Frame (NCTM)**
**http://illuminations.nctm.org/activitydetail.aspx?id=75**
A nice manipulative version of the ten-frame. Four games that help students develop counting and addition skills are included in this activity.
**Toy Shop Numbers (NCTM, Grades K–2)**
**http://illuminations.nctm.org/LessonDetail.aspx?id=L216**
Using the setting of a toy shop, these activities focus on finding numbers in the real world.
**"Whatcha' Gonna' Do? (Count by 2's, 5's, 10's)**"
http://www.schooltube.com/video/590a251b31b3db7a9995/Whatcha-Gonna-Do-Count-by-2s-5s-10s
This Schooltube video is a music rap video connection to skip counting
by 2s, 5s, and 10s.
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Mathematical
Operations
**All About Multiplication (NCTM, Grades 3–5)**
**http://illuminations.nctm.org/LessonDetail.aspx?id=U109**
Four lessons with links to other activities and student recording sheets highlight the models of the number line, equal groups, arrays, and balanced equations. Lesson 3 explores the order property, the zero property, and the identity property. Lesson 4 has an engaging applet called the Product Game.
**Begin with Buttons (NCTM, Grades K-2) **
**http://illuminations.nctm.org/LessonDetail.aspx?id=U31**
These lessons help students use buttons to explore logical and numerical relationships. The unit begins with two lessons that focus on the two basic logical thinking skills, classification and seriation, which are the foundation for understanding numbers and number relationships and form the basis for understanding addition and subtraction.
**Broken Calculators (NCTM)**
**http://my.nctm.org/eresources/view_article.asp?article_id=7457&page=11&add=Y**
**http://www.fi.uu.nl/toepassingen/00014/toepassing_wisweb.en.html**
These two applets demonstrate the broken calculator activity. The first allows for problems at any level, whereas the second is more appropriate for intermediate or middle grades students, as it includes a problem-solving feature.
**Comparing Connecting Cubes (NCTM, Grades K-2)**
http://illuminations.nctm.org/LessonDetail.aspx?id=U41
These lessons help students explore the five models of subtraction (counting, sets, number line, balanced equations, and inverse of addition) using connecting cubes.
**Do It with Dominoes (NCTM, ****Grades K-2)**
**http://illuminations.nctm.org/LessonDetail.aspx?id=U47**
These lessons help student explore the four models of addition (counting, sets, number line, and balanced equations) using dominoes. They also learn about the order property, the relation between addition and subtraction, and the result of adding 0.
**The Factor Game (NCTM)**
**http://illuminations.nctm.org/ActivityDetail.aspx?ID=12**
This game puts two players into competition to collect the factors for given numbers.
**Factorize (NCTM)**
**http://illuminations.nctm.org/ActivityDetail.aspx?ID=64**
With this applet, the connection between factors and dimensions of a rectangle is made as students build rectangles to match a factorization of a number.
**Figure This! Math Challenges for Families**
**http://figurethis.org**
A wonderful collection of exploration that is available for free. The 80 challenges are designed for middle grades students. Although not simple story problems, many involve an understanding of the operations. Each problem has interesting follow-up questions and all are designed to engage students in real-world applications of mathematics.
**FunBrain.com**
**http://www.funbrain.com**
This site provides many games and opportunities for children to learn and practice the operations at all grades and ability levels. Once the appropriate difficulty and grade levels are set, most children can work on the activities independently.
**How Many More Fish? (NCTM, ****Grades K-2)**
**http://illuminations.nctm.org/LessonDetail.aspx?id=U51**
These lessons focus on comparative subtraction as students explore all five meanings for the operations of subtraction (counting, sets, number line, balance, and inverse of addition).
**Kidport.com **
**http://www.kidport.com/default.htm**
This site is excellent for very young students developing what it means to do addition. The colorful representations, using part-part-whole problems, can help the most basic math student begin to understand what adding means.
**Macaroni Math (NCTM, Grades K-2)**
http://illuminations.nctm.org/LessonDetail.aspx?id=U65
These lessons help students explore subtraction in several different contexts (counting, sets, number line, balanced equations, and inverse of addition) using pasta shapes. They also decompose numbers and explore both the zero property and the relationship between addition and subtraction.
**Number Line Arithmetic (NLVM)**
**http://nlvm.usu.edu/en/nav/frames_asid_156_g_1_t_1.html**
This number-line applet can be used to model whole-number operations in addition, subtraction, multiplication and division.
**Rectangle Division (NLVM)**
**http://nlvm.usu.edu/en/nav/frames_asid_193_g_2_t_1.html**
An excellent interactive illustration of division with remembers. A division problem is presented with an array showing the number of squares in the product. The dimensions of the array and can be modified by the number of squares stays constant.
**Take Away (NCTM, ****Grades K-2)**
**http://illuminations.nctm.org/LessonDetail.aspx?id=L192**
An activity designed to introduce elementary students to subtraction and create a link between students' experiences and mathematics.
**Thinking Blocks: Addition and Subtraction**
**http://www.thinkingblocks.com/ThinkingBlocks_AS/TB_AS_Main.html**
**Thinking Blocks: Multiplication and Division**
**http://www.thinkingblocks.com/ThinkingBlocks_MD/TB_MD_Main.html**
This teacher-developed tool links to the various types of problems discussed earlier in the chapter. The difference is the use of two-digit numbers and problems with multiple steps, including compare, part-part-whole, and change examples. There is an emphasis on identifying and solving for an unknown quantity. Because the ideas are presented in game formats, you should view the introduction to be able to play.
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Mastering
the Basic Facts
**ArithmAttack **
**http://www.dep.anl.gov/aattack.htm**
A very straightforward fact drill program that can be used online or downloaded free of charge (Department of Energy's Argonne National Laboratory).
**Arithmetic Four (Shodor)**
**http://www.shodor.org/interactivate/activities/ArithmeticFour/index.html**
The game is like “Connect Four.” Players must answer an arithmetic fact to be able to enter a piece of their color on the board. Operations can be selected and timer set for answering each fact.
**Cross the Swamp (BBC)**
**http://www.bbc.co.uk/schools/starship/maths/crosstheswamp.shtml**
This British applet asks students to supply a missing operation and a number to complete an equation. There are five questions in a set, each with three levels of difficulty.
**Diffy (NLVM)**
**http://nlvm.usu.edu/en/nav/frames_asid_326_g_1_t_1.html**
Diffy is a classic mathematics puzzle that involves finding the differences of given numbers.
**Let’s Learn Those Facts (NCTM, Grades 1–2)**
**http://illuminations.nctm.org/LessonDetail.aspx?id=U58**
These six lessons, including links to resources and student recording sheets, target addition facts.
**Math Forum **
**http://mathforum.org/library/drmath/drmath.elem.html**
This is a part of the Math Forum website that lists interesting questions and answers on many number operations as well as online flash cards.
**Multiplication: It’s in the Cards (NCTM, Grades 3–5)**
**http://illuminations.nctm.org/LessonDetail.aspx?id=U110**
These four lessons, including links to resources and student recording sheets, use the properties of multiplication to help students master the multiplication facts. See also “Six” and Seven as Factors” (NCTM’s Illuminations—Lessons, Grades 3–5), two lessons on products where 6 or 7 is a factor (http://illuminations.nctm.org/LessonDetail.aspx?ID=U150).
**Number Invaders**
**http://www.mathplayground.com/balloon_invaders.html**
This game is like “Space Invaders.” Players choose an operation and a factor, and use the space bar and arrow keys to launch the “number (product) popper.”
**Number Puzzles (NLVM)**
**http://nlvm.usu.edu/en/nav/frames_asid_157_g_3_t_1.html**
In this applet, students are required to arrange numbers in positions in a diagram so that all numbers in a line add up to a given value.
**The Product Game (NCTM, ****Grades 3-8)**
**http://illuminations.nctm.org/LessonDetail.aspx?id=U100**
Students start with factors and multiply to find the product. This game works well with the Factor Game because they help students to see the relationship between products and factors.
**Six and Seven as Factors (NCTM, ****Grades 3-5)**
**http://illuminations.nctm.org/LessonDetail.aspx?ID=U150**
Students who have previously studied the meanings of **multiplication** will use its properties to help them master the products where 6 or 7 is a factor.
**The Product Game (NCTM, Grades 3–8)**
**http://illuminations.nctm.org/LessonDetail.aspx?id=U100**
These four lessons use the engaging and effective games “Factor Game” and “Product Game” to help students see the relationship between products and factors.
**SpeedMath Deluxe (Jefferson Lab)**
**http://education.jlab.org/smdeluxe/index.html**
Players are given four numbers between which they must enter one of the four operation signs so that the resulting expression equals a given number. Requires an understanding of order of operations and occasionally integers.
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Whole-Number
Place-Value Concepts
**Ask Dr.Math (Math Forum)**
**http://mathforum.org/library/drmath/sets/elem_place_value.html**
This link leads to part of Math Forum's "Ask Dr. Math" feature within their web site. It contains a list of interesting questions about place value, sent in by students, which have been answered by Dr. Math.
**Base-Ten Blocks (NLVM)**
**http://nlvm.usu.edu/en/nav/topic_t_1.html**
There are several variations of the basic base-ten blocks applet here. Blocks appear on a place-value chart and can be grouped or broken apart. The addition and subtraction versions pose problems and allow blocks in two colors to model two separate numbers.
**Comparison Estimator (Shodor)**
**http://www.shodor.org/interactivate/activities/estim2/index.html**
Two sets of small objects are shown and the task is to decide which set has more. The actual counts are then given. The same applet also allows for comparisons of length and areas.
**Hundreds Board and Calculator (NCTM)**
**http://standards.nctm.org/document/eexamples/chap4/4.5/index.htm**
A calculator is used to create skip-counting patterns on a hundreds chart. You can start the pattern on any number and skip by any number. The chart extends to 1000. A second pattern will show with red dots on top of the first pattern.
**The 100th Day of School **
**http://www.siec.k12.in.us/~west/proj/100th/**
The book, The 100th Day of School, is a popular one to help young students begin to understand place value. This site was posted by the illustrator of the book, Joan Holub, and contains hundreds of ideas and links for celebrating the 100th day of school in the primary grades.
**Key Concepts in Place Value **
**http://www.math.com/school/subject1/lessons/S1U1L1GL.html**
This site acts as an entire independent lesson on place value. It begins with a "First Glance" tutorial, then moves to a more "In-Depth" explanation of key concepts in place value, and concludes with an interactive "Practice" session for students.
**Lots of Dots and a Million Dots on One Page**
**http://www.vendian.org/envelope**
These explorations of big numbers are only a hint at the array of ideas found on this website. A lot is beyond the elementary school, but anyone interested in big numbers and measures will certainly be intrigued. See a dot for every second of the day!
**The MegaPenny Project**
**http://www.kokogiak.com/megapenny/default.asp**
A fascinating look at large numbers in terms of stacks of pennies. Stacks from 1 penny to a trillion pennies are shown with visual referents, value, weight, height if stacked, and more. Great for large-number concepts.
**The Place Value Game (Jefferson Lab)**
**http://education.jlab.org/placevalue/index.html**
The goal is to make the largest possible number from the digits the computer gives you. Digits are presented one at a time. The player must place the digit in the number without knowing what the next digits will be. It’s fun and also good for understanding ordering of numbers.
**Printable Activities Relating to Place Value**
**http://www.abcteach.com/directory/basics/math/place_value/**
For elementary teachers, this link provides several printable activities relating to place value. The activities would be appropriate for second through fifth graders.
**Scott Foresman’s eTools**
**http://www.kyrene.org/mathtools**
Choose “Place Value Blocks” and if you wish under “workspaces” on the bottom left, select the two-part mat as in Figure 11.5. Then select the base-ten pieces of your choice and add ones, tens, or hundreds. With the *eTools *“Number Blocks”, place-value columns can be turned off, and up to three different numbers can be modeled separately.
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**
**Whole-Number Computation Strategies
**Base Blocks Addition (NLVM)**
**http://nlvm.usu.edu/en/nav/frames_asid_154_g_2_t_1.html**
**Base Blocks Subtraction (NLVM)**
**http://nlvm.usu.edu/en/nav/frames_asid_155_g_2_t_1.html**
These two similar applets use base-ten blocks on a place-value chart. You can form any problem you wish up to four digits. The subtraction model shows the bottom number in red instead of blue. When the top blocks are dragged onto the red blocks, they disappear. Although you can begin in any column, the model forces a regrouping strategy as well as a take-away model for subtraction. Good for reinforcing the traditional algorithms.
**Geometric Perspective (GMU)**
**http://mason.gmu.edu/~mmankus/whole/base10/asmdb10.htm**
The purpose of this website is to assist the user in looking at addition, subtraction, multiplication and division of whole numbers from a geometric, "hands-on" perspective and an algorithmic perspective. The site uses explanations with manipulatives to demonstrate the different algorithms. The site is intended for teachers, but also states that parents and students are welcome.
**Math Forum (Math Forum)**
**http://mathforum.org/library/drmath/drmath.elem.html**
A part of the Math Forum web site that features numerous resources on the computation of whole numbers as well as alternate algorithms such as lattice multiplication.
**Rectangle Division (NLVM)**
**http://nlvm.usu.edu/en/nav/frames_asid_193_g_1_t_1.html**
This applet uses an array model to represent any two digit number as a product of two numbers. Remainders are included.
**Rectangle Multiplication (NLVM)**
**http://nlvm.usu.edu/en/nav/frames_asid_192_g_1_t_1.html**
This applet nicely models two-digit by two-digit products up to 30 x 30.
**Scott Foresman eTools**
**http://www.kyrene.org/mathtools/**
The eTools software provides several applets, including one that will allow the creation of a rectangle up to 50 by 100 that can be filled in with base-ten blocks the same as would be done with physical blocks (Similar to Rectangle Multiplication).
**Whole Number Algorithms and a Bit of Algebra! (GMU)**
**http://mason.gmu.edu/~mmankus/whole/base10/asmdb10.htm**
The purpose of this website is to assist the user in looking at addition, subtraction, multiplication and division of whole numbers connecting the conceptual and procedural understandings. The site uses explanations with manipulatives to demonstrate the different algorithms.
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Computational
Estimation - Whole Numbers
*Adding It Up: Helping Children Learn Mathematics ***(NRC)**
**http://www.nap.edu/openbook.php?record_id=9822&page=214**
*Adding It Up *(NRC, 2001) devotes less than five pages to the topics of mental arithmetic and estimation (pp. 214–218). Read these few pages with special attention to the discussion of estimation and the related skills that are needed for estimation.
**Beat the Calculator (Math Forum)**
**http://mathforum.org/k12/mathtips/beatcalc.html**
This site contains an enormous list of "tricks" for getting an exact computation for very specific types of problems. For example, adding two consecutive numbers, multiplying a two--digit number by 51, dividing a two-digit number by 15, squaring various types of number, finding percentages, and more. The patterns include an example and an explanation.
**Count on Math (NCTM, Grades 6–8)**
**http://illuminations.nctm.org/LessonDetail.aspx?id=U96**
The two lessons here provide activities for older students to estimate and develop number sense through data collection activities.
**Estimate!**
**http://www.fi.uu.nl/toepassingen/00062/schatten/welcome_en.html**
This is a fun fast-paced estimation applet for all four operations (go to “options” to select the ones you want to do). You click on start and a timer records how long until you get your answer entered. After ten problems you get a score, based on speed and accuracy.
**Estimate Sums**
**http://www.ixl.com/math/practice/grade-2-estimate-sums**
IXL is a site with various applets to practice skills for pre-K–3 students. There is a range of rounding and estimating activities for grades 2 and 3.
**Estimation—Hundreds (Quia)**
**http://www.quia.com/mc/65924.html**
Players select squares on a board that round to the same hundred. A concentration version is also available.
**Estimation -- K thru 8 **
**http://www.aaamath.com/est.html**
These pages teach estimation and rounding skills covered in Kindergarten through eighth grade math courses. Each page has an explanation, interactive practice and challenge games about estimation. Some topics include front-end estimation, estimating sums and differences, and rounding.
**Estimator Four (Shodor)**
**http://www.shodor.org/interactivate/activities/EstimatorFour/**
Two players must enter an acceptable estimate to a computation within a time limit to be able to place game piece on the board.
**Estimator Quiz (Shodor)**
**http://www.shodor.org/interactivate/activities/EstimatorQuiz**
Similar to Estimate!, this applet allows a student to practice estimation for addition, multiplication, and percentage problems, getting instant feedback, but this site gives one problem at a time. A timer and instant feedback allow for independent practice and reinforcement.
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Algebra,
Patterns, and Functions
**Algebra Balance Scales and Algebra Balance Scales—Negative (NLVM)**
**http://nlvm.usu.edu/en/nav/frames_asid_324_g_3_t_2.html**
Linear equations are presented on a two-pan balance with variables on each side. The user can solve equations in the same way as described in the text. The Negative version uses balloons for negative values and negative variables.
**Apple Learning Interchange**
http://edcommunity.apple.com/ali/collection.php?collection=2407
This site, published by Apple Learning Exchange, contains elementary lesson plans for many content areas. Within the math section, there are several lesson plans including algebraic topics for grades 2 and up. The lesson plans sometimes include links to interactive sites for practice.
**Function Machine (NLVM)**
**http://nlvm.usu.edu/en/nav/frames_asid_191_g_3_t_1.html**
**Function Machine (Math Playground)**
**http://www.mathplayground.com/functionmachine.html**
This is a nice, Flash-based tool.
**Function Machine (Shodor)**
**http://www.shodor.org/interactivate/activities/FunctionMachine**
The functions on this site have one of the following forms: y = x x __, y = x + __, y = x - __, where the underline can be any integer between -10 and 10.
**Graph Sketcher (Shodor)**
**http://www.shodor.org/interactivate/activities/GraphSketcher/**
Works very much like a graphing calculator for graphing functions of any type. A good demonstration tool for making graphs of equations.
**Learning about Rate of Change (NCTM e-Examples)**
**http://standards.nctm.org/document/eexamples/chap6/6.2/index.htm**
An interactive lesson in which the cost per minute to make a phone call (the slope) can be adjusted and then the graph of the cost can be displayed. A slider helps connect points on the two graphs.
**Linear Function Machine (Shodor)**
**http://www.shodor.org/interactivate/activities/LinearFunctMachine**
**Pan Balance – Shapes (NCTM)**
**http://illuminations.nctm.org/ActivityDetail.aspx?ID=33**
With each problem, four shapes are assigned unknown values. By stacking shapes on the two balance pans, the user attempts to balance the scale and then create additional balances. A numbers version and an expressions version are extensions of this applet.
**Patterns, Relations and Functions (eNLVM)**
**http://enlvm.usu.edu/ma/nav/toc.jsp?sid=__shared&cid=emready@patterns_relations_functions&bb=course**
This module encourages students to generate rules and functions for geometric sequences, describing relationships between the pattern number and characteristics of the pattern.
**PurpleMath.com **
**http://www.purplemath.com/modules/index.htm**
An excellent resource for reinforcing algebraic thinking, from elementary to high school. Each topic has thorough background notes, with interactive features. All topics include examples worked out on the page, along with practice opportunities for students.
**Slope Slider (Shodor)**
**http://www.shodor.org/interactivate/activities/slopeslider**
A good interactive tool for illustrating the meaning of slope and the *y*-intercept for a linear equation of the form *y *= *mx *+ *b*. The user can use a slider to change the value of *m *or *b *and see the graph change dynamically.
**Stop That Creature! (PBS Kids Cyberchase)**
**http://pbskids.org/cyberchase/games/functions/functions.html**
In this fun game, figure out the rule that runs the game to shut down the creature cloning machine.
**Teaching Functions (Shodor)**
**http://www.shodor.org/interactivate/Search/?ss=functions**
This Project Interactivate site contains a list of activities relating to teaching functions. The activities include a very basic introduction to functions, as well as teaching linear functions, graphing and functions, and others. All activities relate the NCTM standards to the objectives being taught.
**Understanding Distance, Speed, and Time Relationships Using Simulation Software (NCTM)**
**http://standards.nctm.org/document/eexamples/chap5/5.2/index.htm**
The speed and starting position of two runners can be set. Runners can even go in opposite directions. Graphs of each runner are created dynamically as the runners are set in motion.
**Video-based courses **
**http://www.learner.org/resources/series140.html**
This page describes video-based courses available for teaching algebra and functions to middle school students. The courses can provide the teacher with graduate course credits.
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Fraction
Concepts
**Fraction Tools (Conceptua™ Math)**
**http://www.conceptuamath.com**
These tools are designed for teacher-facilitated instruction, and include sample problems to give teachers instructional suggestions. For each tool you will find a short instructional video, standards alignment, key vocabulary, and IEP goals.
**Cuisenaire Rods (Arcytech)**
**http://arcytech.org/java/integers/**
These brightly colored, perfectly proportioned blocks can be used to teach a variety of math concepts including basic operations, fractions, decimals, percentages, algebraic reasoning and geometry.
**Cyberchase (PBS)**
**http://pbskids.org/cyberchase**
Cyberchase is a very popular television series targeting important mathematics. The site offers videos that model fractions with real world connections. Also offered are activities such as “Make a Match” (http://pbskids.org/cyberchase/games/equivalentfractions/index.html), in which students examine the concept of equivalent fractions and match a fraction with a graphic representation of that fraction. Another activity is “Thirteen Ways of Looking at a Half” (http://pbskids.org/cyberchase/games/fractions/index.html), in which students explore fractions of geometric shapes—in particular, the thirteen ways half of an eight-piece square can be arranged.
**Dynamic Paper (NCTM)**
**http://illuminations.nctm.org/ActivityDetail.aspx?ID=205**
This multi-purpose tool creates custom graph paper, number grids, number lines, shapes (including pattern blocks and color tiles), and spinners that can be exported in .jpeg and/or .pdf formats.
**Fraction Bars (Math Playground)**
**http://mathplayground.com/Fraction_bars.html**
The user sets the total parts and then the shaded parts for each bar. Explore fractional parts, the concept of numerator and denominator, and equivalency. The user can turn the numbers on or off.
**Fraction Bars (NLVM)**
**http://nlvm.usu.edu/en/nav/frames_asid_203_g_1_t_1.html**
A very versatile model that is similar to the use of Cuisenaire rods except that bars are segmented. Students can create bars of any size from 1 to 10 in any color and place them anywhere on the screen. Multiple bars are easily made. There are no numbers or evaluation of what is being done.
**Fraction Concepts (eNLVM)**
**http://enlvm.usu.edu/ma/nav/toc.jsp?sid=__shared&cid=emready@fraction_concepts&bb=published**
These part-whole activities provide practice in writing and comparing fractions. A full lesson plan with NCTM standards correlations and worksheets is provided, and the teacher can log in to see how students performed.
**Fractions – Comparing (NLVM)**
**http://nlvm.usu.edu/en/nav/frames_asid_159_g_2_t_1.html**
Students use models to find common denominators in order to compare two fractions and then locate both fractions on the number line and a new fraction between the first two.
**Fractions – Equivalent (NLVM)**
**http://nlvm.usu.edu/en/nav/frames_asid_105_g_2_t_1.html**
A tool for exploring equivalent fractions. Proper fractions are presented randomly in either square or circular formats. Students can slice the model in as many parts as they wish to see which slicings create equivalent fractions. Students enter an equivalent fraction and then click a button to check their response.
**Fractions – Visualizing (NLVM)**
**http://nlvm.usu.edu/en/nav/frames_asid_103_g_1_t_1.html**
Users are given a fraction and a model that can be subdivided into as many sections as desired. By clicking on sections the fraction model is shaded to match the given fraction. Two even simpler versions are also available.
**Fraction Pointer (Shodor)**
**http://www.shodor.org/interactivate/activities/FractionPointer**
A good applet for connecting an area model with the number line. After creating area models for two fractions, the user must then create a new fraction between the first two.
Similar to the *Illuminations *applet, “Equivalent Fractions.”
**Fraction Track (NCTM)**
**http://standards.nctm.org/document/eexamples/chap5/5.1/index.htm**
Players position fractions on number lines with different denominators. Fractions can be split into parts. A challenging game involving equivalent-fraction concepts.
**Fun with Fractions Lessons (NCTM)**
Students explore relationships among fractions through work with the set, region, and length models. These lessons help students make sense of basic fraction concepts, comparing and ordering fractions, and working with equivalency.
**Developing the Set Model**
http://illuminations.nctm.org/LessonDetail.aspx?id=U112
**Developing the Region Model**
http://illuminations.nctm.org/LessonDetail.aspx?id=U113
**Developing the Length Model**
http://illuminations.nctm.org/LessonDetail.aspx?id=U152
**Math Forum **
**http://www.mathforum.org/library/drmath/sets/elem_fractions.html**
Part of the Math Forum web page that provides lessons and activities as well as answers about fractions and decimals.
**National Library of Virtual Virtual Manipulatives (NLVM)**
**http://nlvm.usu.edu**
This site offers numerous models for exploring fractions, including fraction bars and fraction pieces. Also there is an applet for comparing and visualizing fractions.
**Teaching, Learning and Communicating About Fractions (NCTM)**
**http://illuminations.nctm.org/Reflections_3-5.html**
As part of the NCTM's Illuminations site, this 4-part website provides and introduction and video-based activities on fractions. This particular activity is geared for grades 3 -5, and promotes conceptual thinking regarding fractions.
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Fractions
and Computation
**Diffy (NLVM)**
**http://nlvm.usu.edu/en/nav/frames_asid_326_g_3_t_1.html**
The goal in a Diffy puzzle is to find differences between the numbers on the corners of the square, working to a desired difference in the center. When working with fractions, the difference of two fractions is a fraction that can be written in many different ways and students must recognize equivalent forms.
**Fraction Bars (NLVM)**
**http://nlvm.usu.edu/en/nav/frames_asid_203_g_2_t_1.html**
Much like Cuisenaire rods, this applet places bars over a number line on which the step size can be adjusted, providing a flexible model that can be used for all four operations.
**Fractions—Adding (NLVM)**
**http://nlvm.usu.edu/en/nav/frames_asid_106_g_2_t_1.html**
Two fractions and an area model for each are given. The user must find a common denominator to rename and add the fractions.
**Fractions - Rectangle Multiplication (NLVM)**
**http://nlvm.usu.edu/en/nav/frames_asid_194_g_2_t_1.html**
An easily adjusted area model for multiplication of two fractions up to 2 x 2. You cannot set your own problems but the presentation is quite good.
**Math Forum (Math Forum)**
**http://www.mathforum.org/library/drmath/sets/elem_fractions.html**
This is a part of the Math Forum web site that lists interesting questions and answers on fraction computation. Be sure to examine the library to locate lots of information on mathematics.
**Number Line Bars—Fractions (NLVM)**
http://nlvm.usu.edu/en/nav/frames_asid_265_g_1_t_1.html
Much like Cuisenaire rods, this applet encourages students to think in a good way. Bars are placed over a number line on which the step size can be adjusted. A flexible model that can be used for all four operations.
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Decimal and Percent
Concepts
**Base Blocks—Decimals (NLVM)**
**http://nlvm.usu.edu/en/nav/frames_asid_264_g_3_t_1.html**
Base-ten blocks can be placed on a place-value chart. The number of decimal places can be selected, thus designating any of the four blocks as the unit. Addition and subtraction problems can be created or can be generated randomly.
**Circle 3 (NLVM)**
**http://nlvm.usu.edu/en/nav/frames_asid_187_g_3_t_1.html**
This game challenges students to use logic as they combine decimals to add to 3. Not as easy as it sounds.
**Concentration (NCTM)**
**http://illuminations.nctm.org/ActivityDetail.aspx?ID=73**
This is an engaging matching game using representations of percents, fractions, and a regional model.
**Fractions Bars (Archytech)**
**http://arcytech.org/java/fractions**
This applet develops the relationships among fractions, decimals, and percents. Bars for one whole are displayed and can be partitioned according to selected fraction, decimal, or percent values and then labeled in any of these representations. This makes equivalencies easy to explore.
**Fraction Model—Version 3 (NCTM)**
**http://illuminations.nctm.org/tools/tool_detail.aspx?id=45**
The equivalence of fraction, decimal, and percent representations in a circle, set, or rectangle model is demonstrated.
**Percentages (NLVM)**
**http://nlvm.usu.edu/en/nav/frames_asid_160_g_3_t_1.html?open=activities**
The user enters any two of the values—whole, part, and percent—and clicks on Compute. Although the computer does the work, the applet nicely models percent problems.
**Railroad Repair (PBS)**
**http://pbskids.org/cyberchase/games/decimals/decimals.html**
This fun activity has students repairing a railroad by choosing and combining different sized decimal pieces of railroad tracks to help get Cybertrain back to the station.
**Savings Calculator (NLVM)**
http://nlvm.usu.edu/en/nav/frames_asid_320_g_3_t_5.html
This applet calculates the interest and total savings balance for a wide variety of savings possibilities. Students can explore what happens with a single deposit or with regular deposits, for any specified time, at different interest rates, and with varying compounding intervals
**Sequencer (Shodor)**
http://www.shodor.org/interactivate/activities/Sequencer
A nice extension tool. Students investigate the effect of multiplying a number by a decimal or mixed number. Allows the user to explore sequences by inputting a starting number, a multiplier and an add-on.
**Sock**
**http://www.interactivestuff.org/sums4fun/sock.html**
Click on directional arrows to guide the sphere into pushing the green cubes into holes that contain the decimals that will make the target number.
**Teaching Ideas **
**http://www.teachingideas.co.uk/maths/contents08fracdecperratprop.htm**
This site provides teachers with links to ideas for teaching decimals to intermediate and upper elementary students. The user can select a topic and an age range, and then is provided with ideas for teaching techniques. The information includes a good visual that could be used with students.
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Ratios
and Proportional Reasoning
**Ameba (The Math Forum’s Teacher Exchange)**
**http://mathforum.org/te/exchange/hosted/ameba**
In this game, students select a total number of pellets to eat that is equal to the target ratio given at the top of the board, then return to the start/finish location.
**Fibonacci Numbers **
**http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/fib.html**
This web site contains a detailed amount of information on Fibonacci numbers and the Golden Section, which could be used to demonstrate ratio concepts. Provides links as to how these concepts relate to nature, and also provides opportunities for the user to practice ratio calculations.
**Fibonacci Sequence (NLVM)**
**http://nlvm.usu.edu/en/nav/frames_asid_315_g_3_t_1.html**
The applet simply computes successive terms of the Fibonacci sequence and shows in both fraction and decimal forms the ratio of successive terms of the sequence. This ratio converges to the *golden ratio. *For what may be the most information assembled anywhere on the Fibonacci sequence, go to http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci.
**Fish Simulation Applet I (Math Forum)**
**http://mathforum.org/escotpow/puzzles/fish/applet.html**
A collection of two colors of fish is to be placed into three ponds to create specified ratios within each pond. Students should find out if there is more than one solution and then make up similar problems for their classmates.
**The Futures Channel**
**http://www.thefutureschannel.com**
This site provides lessons and includes video clips. Two related to proportional reasoning are “How Tall?,” which engages students in finding the heights of people and objects using proportional thinking, and “Snow,” which explores the ratio of inches of snowfall to liquid snowfall.
**Learning about Length, Area, Volume, Surface Area of Similar Objects (NCTM e-Example 6.3)**
**http://standards.nctm.org/document/eexamples/chap6/6.3/index.htm**
A two-part exploration complete with extensive teacher notes. The applets compare two rectangles or two prisms showing ratios of measures in both numeric and graphical form.
**Math Forum**
**http://mathforum.org/library/problems/sets/elem_ratio-proportion.html **
Part of the Math Forum web site, this link takes teachers directly to links of elementary activities for teaching ratio and proportion in elementary school. Many of the ideas are set up in a problem of the day format, and even include samples of some student responses.
**Understanding Ratios of Inscribed Figures (NCTM e-Example 7.3)**
**http://standards.nctm.org/document/eexamples/chap7/7.3/index.htm**
A nice geometry/measurement link to ratio. The user explores the ratio of figures inscribed in polygons formed by joining midpoints of sides. These points can also be adjusted. The supporting lesson and activity suggestions are quite good.
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Measurement
**Area Tool (NCTM)**
http://illuminations.nctm.org/ActivityDetail.aspx?ID=108
This tool can be used to determine how the length of the base and the height of a figure can be used to determine its area. Explore the similarities and differences between the area formulas for trapezoids, parallelograms, and triangles.
**Clock Wise (Shodor)**
**http://www.shodor.org/interactivate/activities/clockwise**
A clock face is shown and the user enters the digital time. Four difficulty levels.
**Cubes (NCTM)**
**http://illuminations.nctm.org/ActivityDetail.aspx?ID=6**
An excellent interactive applet that illustrates the volume of a rectangular prism (box). Units of single cubes, rows of cubes, or layers of cubes can be used to fill a prism.
**Elapsed Time (Shodor)**
http://www.shodor.org/interactivate/activities/ElapsedTime
This activity can be used to practice calculating elapsed time between a starting and an ending time.
**Exploring Angle Sums (NCTM)**
http://illuminations.nctm.org/ActivityDetail.aspx?ID=9
In this investigation, you will explore the sum of the interior angles of triangles, quadrilaterals and other polygons using rotations of 180° about a midpoint.
**Fill and Pour (NLVM)**
http://nlvm.usu.edu/en/nav/frames_asid_273_g_3_t_4.html
Fill one container with the required amount of liquid by filling, emptying, and pouring between the two containers.
**Geoboard (NLVM)**
**http://nlvm.usu.edu/en/nav/frames_asid_279_g_4_t_3.html**
This electronic geoboard measures the area and perimeter of any shape made. What is nice is that the measures are not shown until the user clicks the Measure button. Students can be challenged to make shapes with specified areas and/or perimeters.
**How High? (NLVM)**
**http://nlvm.usu.edu/en/nav/frames_asid_275_g_3_t_4.html**
Two cylinders are shown along with the area of the base shown as a grid of squares. One cylinder is filled to a specified height. The task is to determine the height of this same liquid when it is poured into the second container.
**Image Tool (Shodor)**
**http://www.shodor.org/interactivate/activities/imagetool/index.html**
The user can measure angles, distances, and areas in several different images (choices include maps, aerial photos, and others). A scale feature allows the user to set the scale used for measuring distances and areas. Unique!
**Isometric Drawing Tool (NCTM)**
http://illuminations.nctm.org/ActivityDetail.aspx?ID=125
Create dynamic drawings on isometric dot paper. Draw figures using edges, faces, or cubes, and then shift, rotate, color, decompose or view them in 2-D or 3-D.
**It Takes Ten (PBS)**
http://www.pbs.org/teachers/mathline/lessonplans/esmp/ittakesten/ittakesten_procedure.shtm
As part of PBS's Mathline program, this site provides excellent lessons and materials for a primary unit on measurement. Once on the main page, there is a link to a PDF document that provides everything you would need for the unit.
**Match Clocks (NLVM)**
**http://nlvm.usu.edu/en/nav/frames_asid_317_g_2_t_4.html**
The user matches either a digital time to an analog or the reverse. Problems are posed randomly and there are no controls for difficulty.
**Math Forum **
**http://mathforum.org/library/drmath/sets/elem_measurement_terms.html**
As part of the Math Forum site, this page deals directly with children's commonly asked questions surrounding measurement issues. The site also provides a good list of terms, which could be a beneficial resource for students during a measurement unit.
**Money (NLVM)**
**http://nlvm.usu.edu/en/nav/frames_asid_325_g_2_t_4.html**
This site gives students an opportunity to make a dollar, find an exact amount, or fill in how much money is shown.
**Perimeter and Area (eNLVM)**
http://enlvm.usu.edu/ma/nav/toc.jsp?sid=__shared&cid=emready@perimeter_and_area&bb=course
This eModule uses geoboards to help students develop understanding of the concepts perimeter and area of rectangles, triangles, and irregular polygons.
**Perimeter Explorer (Shodor)**
**http://www.shodor.org/interactivate/activities/PerimeterExplorer**
The user sets a fixed number of square units and the applet randomly creates shapes on a grid with this area. The object is to determine the perimeter. There is also an *Area Explorer *(fixes the perimeter) and a *Shape Explorer, *which asks the user for both the area and perimeter of the randomly produced shapes.
**Shape Explorer (Shodor)**
http://www.shodor.org/interactivate/activities/ShapeExplorer
Explore the relationships between perimeter and area by calculating the area and perimeter of different figures.
**Tangrams (PBS)**
http://pbskids.org/cyberchase/games/area/tangram.html
Try to use the 7 pieces to create the shapes displayed in the upper right corner without overlapping any others.
**What Time Will It Be? (NLVM)**
**http://nlvm.usu.edu/en/nav/frames_asid_318_g_2_t_4.html**
Elapsed-time problems are presented in word format. Two clocks are shown, one with the start time and the other to be set. Some problems are digital, others analog.
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Geometry
**Cube Nets (NCTM)**
**http://illuminations.nctm.org/ActivityDetail.aspx?ID=84**
Great visualization challenge! Shows arrangements of squares. The challenge is to find the 11 arrangements that will fold into a cube.
**Cut Out Nets**
**http://www.fi.uu.nl/toepassingen/00297/toepassing_wisweb.en.html**
Nets of the Platonic solids can be folded one side at a time and the shape rotated freely at any point in three dimensions. Fascinating!
**Cutting Corners (NCTM)**
**http://illuminations.nctm.org/tools/CutTool/CutTool.asp**
A cutting tool allows any one of three simple shapes to be sliced into parts along any straight line. Shapes can be rearranged, rotated, and flipped.
**Dynamic Paper (NCTM)**
**http://illuminations.nctm.org/ActivityDetail.aspx?ID=205**
This multi-purpose tool creates custom graph paper, number grids, nets, number lines, shapes, spinners, and tessellations that can be exported in .jpeg and/or .pdf formats.
**Geoboards (NLVM)**
**http://nlvm.usu.edu/en/nav/category_g_2_t_3.html**
The NLVM library has four geoboards. The first measures areas and perimeters. The circular board has pins in a circular arrangement. The isometric board has pins in a triangular arrangement (like isometric dot paper). The coordinate board shows coordinates for each peg when the cursor is on it. It measures the slope and distance between two points joined by a band and then the perimeter and area of banded shapes.
**GeoGebra**
**http://www.geogebra.org/cms**
This is a free downloadable dynamic geometry software that emphasizes geometry and algebra. Like *Geometer’s Sketchpad*, you can construct with points, segments, and lines.
**Math Forum**
**http://mathforum.org/library/drmath/sets/elem_geom.html**
As part of the Math Forum website, this page nicely divides into different sub-categories of elementary geometry. These links can be an excellent resource for students to review earlier geometry concepts, or to use as a reference when just beginning a new concept.
**Maze Game (Shodor)**
**http://www.shodor.org/interactivate/activities/coords/index.html**
Provides practice with coordinates. The user plots points to guide a robot through a mine field.
**Mirror Tool (NCTM)**
**http://illuminations.nctm.org/ActivityDetail.aspx?ID=24**
A nice tool for early investigations of mirror or line symmetry.
**Platonic Solids (NLVM)**
**http://nlvm.usu.edu/en/nav/frames_asid_128_g_3_t_3.html**
This applet allows you to display, rotate, and resize different Platonic solids. It also allows you to select vertices, edges, and faces, and observe that the number of vertices minus the number of edges plus the number of faces is always equal to 2 (Euler's formula).
**Pythagorean Relationship (NCTM)**
**http://standards.nctm.org/document/eexamples/chap6/6.5/index.htm**
This compelling, dynamic proof of the Pythagorean relationship uses the idea that rectangles and parallelograms with the same height and base have the same area.
**Shape Tool (NCTM)**
http://illuminations.nctm.org/ActivityDetail.aspx?ID=35
Draw, color, paste, slice, rotate, reflect, expand, and contract any shapes that you can create.
**Slicing Platonic Solids (NLVM)**
**http://nlvm.usu.edu/en/nav/frames_asid_126_g_3_t_3.html**
Any one of five Platonic solids can be shown in a window that is a plane of intersection with the solid. As the solid is rotated freely, the portion above and below the plane changes. The plane intersection shape is always shown in a second window. this is a virtual version of "Water Slices," Activity 21.37.
**Space Blocks (NLVM)**
**http://nlvm.usu.edu/en/nav/frames_asid_195_g_3_t_3.html?open=activities**
This applet allows the user to create “buildings” made of cubic blocks rather easily. Explore surface area.
**Tangrams (NLVM)**
**http://nlvm.usu.edu/en/nav/frames_asid_268_g_1_t_3.html?open=activities**
These virtual tangrams can be manipulated freely. Plus, there are 14 puzzle shapes to fill in with all 7 tangrams.
**Turtle Geometry (NLVM)**
http://nlvm.usu.edu/en/nav/frames_asid_178_g_3_t_3.html
This involves the same process used in logo programming and is a little more sophisticated than the than other primary level logo activities.
**Visualizing Transformations (NCTM)**
**http://standards.nctm.org/document/eexamples/chap6/6.4/index.htm**
This four-part applet provides an excellent exploration of the three rigid-motion transformations including composition of two transformations.
**The World of M.C. Escher**
**http://www.worldofescher.com**
A tribute to M.C. Escher’s work, this website provides discussion forums, resources and items for sale.
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Data
Analysis
**Bar Chart (NLVM)**
http://nlvm.usu.edu/en/nav/frames_asid_323_g_1_t_5.html
This bar graph can be fully customized. Add each element of a bar graph indicating whether you want totals of percentages displayed.
**Bar Graph (Shodor)**
**http://www.shodor.org/interactivate/activities/BarGraph**
The user of this applet can enter data as well as manipulate the *y*-axis values to create a bar graph. The ability to manipulate the *y*-axis values allows the creation of potentially misleading graphs, a good source of discussion.
**Bar Grapher (NCTM)**
http://illuminations.nctm.org/ActivityDetail.aspx?ID=63
Graph data sets using your own data or pre-made data sets. The color, thickness and scale of the graph are adjustable.
**Box Plotter (NCTM)**
**http://illuminations.nctm.org/ActivityDetail.aspx?ID=77**
**Box Plot (Shodor)**
**http://www.shodor.org/interactivate/activities/boxplot/**
The user can enter data and create box and whisker plots.
**Canada Data Map (NCTM)**
http://illuminations.nctm.org/ActivityDetail.aspx?ID=175
Use color-coding to represent data about the Canadian provinces and territories, including population, land area, and gas usage. Displays data using box and whisker plot.
**Circle Grapher (NCTM)**
**http://illuminations.nctm.org/ActivityDetail.aspx?ID=60**
Make your own circle graph with your own data, or display a circle graph from a given set of data.
**Collecting, Representing, and Interpreting Data Using Spreadsheets and Graphing Software (NCTM)**
**http://standards.nctm.org/document/eexamples/chap5/5.5/index.htm**
Data are provided in a spreadsheet. The data can be changed and/or ordered in different ways with simple buttons. Scatter plots and bar graphs are also easily made with various combinations of data. Lesson suggestions are provided.
**Comparing Properties of the Mean and the Median (NCTM)**
**http://standards.nctm.org/document/eexamples/chap6/6.6/index.htm**
This activity shows seven data points that can be dragged back and forth along a number line with the mean and median updated instantly. The applet allows students to see how stable the median is and how changing one point can affect the mean.
**Economic Research Service (USDA)**
**http://www.ers.usda.gov**
Here you can find wonderful data sets on the availability and consumption of hundreds of foods. Per capita estimates on a yearly basis often go back as far as 1909.
**Histograms**
**NLVM - http://nlvm.usu.edu/en/nav/frames_asid_174_g_2_t_5.html**
**Illuminations - http://illuminations.nctm.org/ActivityDetail.aspx?ID=78**
Each of these sites offers an interactive applet designed to assist the user in creating and manipulating data to display histograms.
**Internet Movie Database (IMDB)**
**http://www.imdb.com**
This website offers information about movies of all genres.
**Line of Best Fit (NCTM)**
http://illuminations.nctm.org/ActivityDetail.aspx?ID=146
This activity allows students to enter a set of data, plot the data on a coordinate grid, and determine the equation for a line of best fit.
**Mean and Median (NCTM)**
http://illuminations.nctm.org/ActivityDetail.aspx?ID=160
Investigate the mean and median from a box-and-whisker plot for a set of data.
**Multi (Double) Bar Graph (Shodor)**
http://shodor.org/interactivate/activities/MultiBarGraph
Create a double bar graph and manipulate the graph's maximum and minimum values.
**Pie Chart (NLVM)**
http://nlvm.usu.edu/en/nav/frames_asid_183_g_1_t_5.html
Use this tool to create a circle graph.
**Plop It! (Shodor)**
**http://www.shodor.org/interactivate/activities/PlopIt/**
The user can experiment with the concepts of mean, median, and mode by using a bar graph. The applet allows you to visually see the difference between these measures.
**Population Education Training **
**http://www.populationeducation.org/index.php**
This is the home page for the Population Education Training organization, a group that provides workshops to teachers interested in using population themes as a context for teaching math lessons using data. The site has links to materials, as well as information on how to receive training, or even how to become a trainer.
**Scatterplot (NLVM)**
http://nlvm.usu.edu/en/nav/frames_asid_144_g_3_t_5.html
Plot multiple data points in two dimensions and determine correlation.
**State Data Map (NCTM)**
http://illuminations.nctm.org/ActivityDetail.aspx?ID=151
Use color-coding to represent state information, such as population, area, and gasoline usage.
**Stem-and-Leaf Plot (Shodor)**
**http://www.shodor.org/interactivate/activities/StemAndLeafPlotter**
Enter data and calculate mean, median, and mode.
**U.S. Census Bureau**
**http://www.census.gov**
A site that provides statistical information sorted by state, country or voting districts.
**The World Factbook (CIA)**
**https://www.cia.gov/library/publications/the-world-factbook/index.html**
This website provides demographic information for every nation in the world, including population, age distribution, death and birth rates, and information on the economy, government, transportation, and geography. Maps are included as well.
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Probability
**Adjustable Spinner (Shodor)**
**http://www.shodor.org/interactivate/activities/AdjustableSpinner**
A virtual spinner can be adjusted to have any number of sections of any size. It can then be spun any number of times in increments of 100,000.
**A Better Fire! (Shodor)**
**http://www.shodor.org/interactivate/activities/ABetterFire/**
This site offers a realistic simulation of actual forest fires, with controls for wind speed and direction to add more realism. The simulation uses virtual “die” to see if a tree should be planted for each square.
**Box Model (NLVM)**
**http://nlvm.usu.edu/en/nav/frames_asid_146_g_3_t_5.html**
The applet permits creating a box of up to 16 colored cubes, including the possibility of duplicates. Cubes can then be drawn at random (with replacement). A bar graph shows the results that can be compared to the theoretical results.
**Coin Tossing (NLVM)**
**http://nlvm.usu.edu/en/nav/frames_asid_305_g_3_t_5.html**
A single coin can be “tossed” any number of times. The results are shown in order, which can help with the concept of randomness. A bar graph shows results.
**Dynamic Paper (NCTM)**
**http://illuminations.nctm.org/ActivityDetail.aspx?ID=205**
This multi-purpose tool creates custom graph paper, number grids, nets, number lines, shapes, spinners, and tessellations that can be exported in .jpeg and/or .pdf formats.
**Experimental Probability (Shodor)**
**http://www.shodor.org/interactivate/activities/ExpProbability/**
A spinner can be created with up to four regions or two like dice can be made with each side adjustable from 1 to 6. The devices can then be used in experiments.
**Marble Mania**
**http://www.sciencenetlinks.com/interactives/marble/marblemania.html**
This applet explores randomness and probability. You’ll be able to control how many and what color marbles to place in virtual marble bag. An advantage of this applet is that you can run a large number of different trials in a short amount of time.
**Probability (Shodor)**
**http://www.shodor.org/interactivate/activities/ExpProbability/index.html**
A spinner can be created with up to four regions or two like dice can be made with each side adjustable from 1 to 6. The devices can then be used in experiments.
**Probability Resources (Math Forum)**
**http://mathforum.org/library/topics/probability**
Links to hundreds of articles, lessons, and applets related to probability.
**Spinners (NLVM)**
**http://nlvm.usu.edu/en/nav/frames_asid_186_g_1_t_1.html**
This site provides a spinner that can be customized and used for experiments.
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Exponents,
Integers, and Real Numbers
**Color Chips – Addition (NLVM)**
**http://nlvm.usu.edu/en/nav/frames_asid_161_g_1_t_1.html**
Use color chips to illustrate addition of integers.
**Color Chips – Subtraction (NLVM)**
http://nlvm.usu.edu/en/nav/frames_asid_162_g_2_t_1.html
Use color chips to illustrate subtraction of integers.
**The Evolution of the Real Numbers**
**http://www.themathpage.com/areal/real-numbers.htm**
This is an interesting description of many topics related to the real number system. Although mostly text, the pages are filled with interactive questions.
**Exponential Growth (Otherwise)**
http://www.otherwise.com/population/exponent.html
If a population has a constant birth rate through time and is never limited by food or disease, it has what is known as exponential growth. Click the button to run the applet to simulate exponential growth of fish.
**Integer Arithmetic (eNLVM)**
**http://enlvm.usu.edu/ma/nav/toc.jsp?sid=__shared&cid=emready@integers&bb=course**
This investigation uses number lines, color chips, and a variety of scenarios to help students understand what an integer is and how to do signed addition, subtraction and multiplication.
**National Library of Virtual Manipulatives (NLVM)**
**http://nlvm.usu.edu**
Among the many applets on this site are “Color Chips—Addition,” “Color Chips Subtraction,” “Rectangle Multiplication of Integers,” and “Integer Arithmetic.” These applets focus on using models for integer computation.
**The Next Billion (NCTM)**
**http://illuminations.nctm.org/LessonDetail.aspx?id=L715**
In 1999 the world population passed 6 billion. In this lesson, students predict when it will reach 7 billion. Students discuss their predictions, past trends in population growth, and social factors—a good interdisciplinary opportunity.
**Rectangle Multiplication of Integers (NLVM)**
http://nlvm.usu.edu/en/nav/frames_asid_322_g_1_t_1.html
Practice multiplying integers using an area model.
**Tic-Tac-Go Negative Numbers (Freudenthal Institute)**
**http://www.fi.uu.nl/toepassingen/03088/toepassing_wisweb.en.html**
In this game, students pick addition, subtraction, or multiplication and find the equation to match an answer, trying to get three in a row.
**Volt Meter (NCTM)**
**http://illuminations.nctm.org/ActivityDetail.aspx?ID=152**
Click and drag batteries with negative and positive voltage to explore integer addition and subtraction.
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