This activity has students explore the patterns that emerge when connecting midpoints of triangles. The activity includes a student worksheet, discussion questions, and an interactive fractal tool.

This interactive Flash applet helps students develop number sense and fluency with addition and subtraction facts within 10. Okta hides some bubbles under a shell, and then either adds more bubbles or takes some away. Students determine how many bubbles are left under the shell. Users can choose a specific one-digit starting number or let the applet choose randomly. Users can select addition, subtraction or both.

This lesson focuses learners on the concept of 1,000,000. It allows learners to see firsthand the sheer size of 1 million, while at the same time providing learners with an introduction to sampling and its use in mathematics. Learners use grains of rice and a balance to figure out the approximate volume and weight of 1,000,000 grains of rice. This lesson guide includes questions for learners, assessment options, extensions, and reflection questions.

In this recycling activity students conduct a poll and display data showing which type of material the survey population feels is the best for shopping bags. Students share their results in a data display of their choice and then use the data to draw conclusions and create a recycling plan. The activity includes the student worksheet, extension suggestions, and related resources.

This 2-lesson unit focuses on combinations, a subject related to probability. Students develop strategies for discovering all the possible combinations in two given situations. They learn to collect and organize data and then use the results to generalize methods for determining possible combinations. They discuss how the number of possible outcomes is affected by decisions about the order of choices, or whether choices may be repeated. The unit includes student activity sheets, questions and extensions for students, and a link to an interactive applet.

This subject explores the varied nature and practice of computation in design. We will view computation and design broadly. Computation will include both work done on the computer (digital computing) and by-hand. Design will include both the process of making designs and artifacts, as well as the designs and artifacts themselves. The aim of the course is to develop a view of computation and design beyond the specifics of techniques and tools, and a critical, self-awareness of our own approaches and metaphors for computation and design.

The applets in this Interactive Geometry Dictionary (IGD) will allow students an opportunity to explore finding the area of some common shapes. The applets demonstrate how to find the area of a triangle using the area of a parallelogram, which in turn can be found using the area of a rectangle. This tool also supports the lesson "What's My Area" cataloged separately.

This seminar will explore the difficulties of getting agreement on global definitions of sustainability; in particularly building international support for efforts to combat climate change created by greenhouse gas emissions as well as other international resource management efforts. We will focus on possible changes in the way global environmental agreements are formulated and implemented, especially on ways of shifting from the current "pollution control" approach to combating climate change to a more comprehensive strategy for taking advantage of sustainable development opportunities.

Explores, through exercises, lectures, and discussion, the nature and exercise of architectural intelligence; investigates design as processes located in individuals and in groups; seeks to understand design as argument, as claims for which reasons can be adduced, as logic in which there are explicit sets of elements and relations among them, and as experiment in which design and its results are themselves used to inform future designs or simply to inquire. Subject aims to open avenues for further research.

In this lesson students are introduced to various types of symmetry. After exploring the symmetries that exist with letters of the alphabet, they make inversions of their own name. Suggestions for implementation and support materials are provided.

In this lesson plan from Illuminations, students use relationship rods to explore fraction relationships. Relationship rods range in length from one to ten centimeters, and each rod is a different color. An activity sheet with solutions, questions for students, assessment options, and suggested extension activities are included. The lesson plan is part of a five lesson plan unit, Fun with Fractions, which is cataloged separately.

This Java interactive tool can be used to create dynamic drawings on an isometric dot grid, and to explore volume, surface area, and congruence concepts. Users can draw figures using edges, faces, or cubes and can shift, rotate, color, decompose, and view figures in 2‑D or 3‑D with this applet. Instructions on using and exploring with the tool are included on the page. A related multi-lesson unit from Illuminations for middle school students is linked to the side.

This subject investigates the special relation of women to several musical folk traditions in the British Isles and North America. Throughout, we will be examining the implications of gender in the creation, transmission, and performance of music. Because virtually all societies operate to some extent on a gendered division of labor (and of expressive roles) the music of these societies is marked by the gendering of musical repertoires, traditions of instrumentation, performance settings, and styles. This seminar will examine the gendered dimensions of the music -- the song texts, the performance styles, processes of dissemination (collection, literary representation) and issues of historiography -- with respect to selected traditions within the folk musics of North America and the British Isles, with the aim of analyzing the special contributions of women to these traditions. In addition to telling stories about women's musical lives, and studying elements of female identity and subjectivity in song texts and music, we will investigate the ways in which women's work and women's cultural roles have affected the folk traditions of these several countries.

In this math activity, learners prepare jumping jack data to send to officials on the planet Jumpalot. Learners record how many jumping jacks they can do in ten seconds and use their knowledge of time conversions to figure out how many jumping jacks they could complete in a minute all the way to a year. Learners then organize group data and explore mean, median, and mode and the effects extreme values have on these measures. Finally, learners brainstorm the advantages and disadvantages each measure offers. This lesson guide includes questions for learners, assessment options, extensions, and reflection questions.

In this lesson for grades 1 and 2, students record observations and look for patterns while exploring weights on a balance scale. They balance equal and unequal weights and record their distances from the fulcrum. Students use a crayon (as the fulcrum) and a ruler to represent the balance. A printable record keeping sheet is provided.

The activities in this four-lesson unit enable students to use their knowledge of number, measurement, and geometry to solve interesting problems. Planning and visualizing, estimating and measuring, and testing and revising are components of the ladybug activities. Students design "virtual paths" that enable a ladybug to either hide under a leaf or go through a maze. They develop navigational skills by testing their path and revising it. Two interactive Java applets (Ladybug Mazes and Hiding Ladybug, cataloged separately) support student solutions.

This lesson introduces students to the measurable attribute of length and provides practice in measuring length using non-standard units. The lesson is launched using the story Ladybug on the Move by Richard Fowler. Lesson objectives, teaching ideas, and handouts are included.

In this 6-lesson unit students develop concepts of number, relationships between numbers, and equality. They make groups of 10 to 20 objects, connect number names to the groups, compose and decompose numbers, and use numerals to record the size of a group. Each lesson includes visual, auditory, and kinesthetic activities, as well as student activity sheets, questions for teachers and students, ideas for assessment and extensions, and links to electronic applets.

In this 5-lesson unit students make groups of zero through five objects and connect number words to the groups. They develop counting strategies and use numerals to record the size of a group. Lessons include familiar nursery rhymes and songs, links to interactive applets, and visual, auditory, and kinesthetic activities. Also included are student activity sheets, questions for students and teachers, assessment and extension ideas.

This 5-lesson unit is intended to help children who already understand the meanings of addition to develop fluency with addition facts. The activities and games take advantage of commutativity, the additive identity, doubles, and number patterns to develop operation sense and foster retention. Lessons include student materials, questions for students and teachers, assessment ideas, and links to interactive applets.