i-Math Investigations are ready-to-use, online, interactive, multimedia math lessons. Complete i-Maths include student investigations, teacher notes, answers, and related professional development activities. Not every i-Math is currently complete, but they are all ready to be used.

Student i-Maths: For each i-Math Investigation, there is a specially-formatted student version that is classroom-ready. Student versions contain no irrelevant links and all teacher notes, answers, and professional development activities have been removed. All student i-Maths are listed on the Student i-Math page. This is the only page that needs to be bookmarked for classroom use.

	Simulating Probability Situations Using Box Models Investigations that allow students to explore the relationship between theoretical and experimental probabilities are important in the study of probability and statistics. A "box model" can help students in such investigations. This i-Math investigation contains an interactive tool that simulates a statistical "box model" as well as ideas for activities.
	Exploring Histograms A histogram is a standard way of representing a collection of data. The interactive tool contained in this i-Math investigation allows students to create their own sets of data and examine how various statistical functions such as mean, median, and standard deviation depend on the choice of data. WARNING: This i-Math Investigation currently runs too slowly with the Macintosh version of Netscape Navigator . Use Internet Explorer for Mac 4.0 or later.
	Gathering Evidence About Students' Understanding of Volume This i-Math Investigation is coming soon. You can see the related Reflection on Teaching activity now.

Reflections on Teaching are activities designed to encourage thinking and discussion about teaching and learning mathematics. Most of these Reflection activities are centered around video vignettes of teachers teaching math or students learning math.

	Gathering Evidence About Students' Understanding of Volume There are many options available to teachers for assessing mathematics learning. Teachers can learn a great deal about their students' level of conceptual understanding and reasoning skills by monitoring small group and whole class discussion. This video example focuses on assessing students knowledge as an ongoing part of instruction.
	Learning about Area, Perimeter, and Fractions with and from Peers When students work in small groups they are given the opportunity to communicate with their peers about mathematics. The video clips and supporting questions in this i-Math investigation support teachers as they reflect on mathematical understanding as students learn with and from peers.

In this section you will find links to exemplary mathematics education resources on the internet. These Selected Web Resources can be used to improve the teaching and learning of mathematics for all students. They can help you understand and apply the NCTM Principles and Standards for School Mathematics. Each of these web resources has been carefully reviewed and approved by a panel of experts. This collection will grow and be modified based on review by the NCTM Illuminations Advisory Panel.

See the Selection Criteria and a list of the review panel members. You can nominate a site using this Application Form.

Click on a link below to see a summary page which briefly summarizes the content and purpose of the site. Click again to go to the site. Close the window of the external site and you're back at Illuminations.

	Math Forum (All topics / All grades): The Math Forum has information, challenges, and activities in mathematics across all grade levels. Contains resources for all grades, including grades 6-8.
	Figure This - Math Challenges for Families - (All topics / Grades 6-8) Exciting, out-of-school learning activities that illustrate the worldclass mathematics that students should be doing in middle school.
	Eisenhower National Clearinghouse For Mathematics and Science Education (All topics / All grades): This site gives teachers a plethora of educational information, resources, and activities across all grade levels. Contains resources for all grades, including grades 6-8.
	The Guide to Math and Science Reform (All topics / All grades): One-stop directory for organizations, projects, and resources in the field of math reform. Contains resources for all grades, including grades 6-8.
	Mathnotes English to Spanish Math Glossary (All topics / All grades): An invaluable resource for bilingual math students. Contains resources for all grades, including grades 6-8.
	BBC Education Web Guide, Math (All topics / All grades): A superior collection of well-annotated links. Contains resources for all grades, including grades 6-8.
	The MacTutor History of Mathematics Archive (All topics / All grades): The MacTutor History of Mathematics Archive will help students appreciate the human side of math by becoming acquainted with the actual men and women who have created it over the centuries. Contains resources for all grades, including grades 6-8.
	Interactive Mathematics Miscellany and Puzzles (All topics / All grades): Alex Bogomolny's Interactive Mathematics Miscellany and Puzzles (also called Cut the Knot, in honor of another noteworthy Alexander) is an irresistible collection of puzzles, problems, and paradoxes. Contains resources for all grades, including grades 6-8.
	New York Times Mathematics Lessons (All topics / Grades 6-12): These well-constructed lessons let students see for themselves how math skills can improve their understanding of current events. Contains resources for grades 6 - 12.
	Project Interactivate (All topics / Grades 6-8): Excellent online lesson plans, activities, and discussions for middle school math.

The internet is a vast storehouse of information and resources. Effective mathematics lessons can be created by tapping into the internet. For example, internet links can provide real-world data that can be analyzed or used to develop mathematical concepts. Other links may provide detailed information about areas in which mathematics is applied. Some websites provide tools that can be used to graph, visualize, or compute. The lessons plans in this section of the Illuminations site are examples of how internet links can be used to create effective Standards-based mathematics lessons.

The Next Billion - Students predict when the world population will reach 7 billion. To do so, they use an on-line counter that simulates the changing world population. Students discuss the reliability of their predictions, compare them to past trends, and discuss social factors that can affect population growth. Five's a Crowd: A Game of Population Density - Students play a game in which they try to list 5 countries or states in order from most crowded to least crowded. Using area and population data from a web site, they estimate quotients to make their list. They determine whose list is closest to the actual order by applying a mathematical model (scoring system), which they later evaluate.

Clicking on the main link below will take you to Chapter 6: Grades 6-8 in Principles and Standards for School Mathematics (PSSM). Using this link will open another browser window in which you can navigate through the PSSM. To return to the Illuminations site, simply close the browser window that you are using to view the PSSM. Clicking on the other links will take you to specific standards for this grade band.

Standards for Grades 6-8
Number and Operations	Problem Solving
Algebra	Reasoning and Proof
Geometry	Communication
Measurement	Connections
Data Analysis and Probability	Representations