The purpose of this series of tasks is to build in a natural way from accessible, concrete problems involving volume to a more abstract understanding of volume. Here, we are given the volume and are asked to find the height.

The purpose of this series of tasks is to build in a natural way from accessible, concrete problems involving volume to a more abstract understanding of volume. This problem is based on ArchimedesŐ Principle that the volume of an immersed object is equivalent to the volume of the displaced water.

In this video segment you’ll discover how using concentric circles can help you determine how much paint is needed to cover the deck of a carousel.

This task is designed to give students insight into the effects of translations, rotations, and reflections on geometric figures in the context of showing that two figures are congruent.

Students' first experience with transformations is likely to be with specific shapes like triangles, quadrilaterals, circles, and figures with symmetry. Exhibiting a sequence of transformations that shows that two generic line segments of the same length are congruent is a good way for students to begin thinking about transformations in greater generality.

This task has two goals: first to develop student understanding of rigid motions in the context of demonstrating congruence. Secondly, student knowledge of reflections is refined by considering the notion of orientation in part (b).

The construction of the perpendicular bisector of a line segment is one of the most common in plane geometry and it is undertaken here. In addition to giving students a chance to work with straightedge and compass, the problem uses triangle congruence both to show that the constructed line is perpendicular to AB and to show that it bisects AB.

This task is for instruction purposes. Part (b) is subtle and the solution presented here uses a "dynamic" view of triangles with two side lengths fixed. This helps pave the way toward what students will see later in trigonometry but some guidance will likely be needed in order to get students started on this path.

This challenging problem and brainteaser gives first graders an opportunity to compose and decompose squares.

In these lessons students will explore the paintings of Horace Pippin and Wayne Thiebaud and the mobiles of Alexander Calder to discover and practice math and visual art concepts. Background and biographical information about the work of art and artist, guided looking with class discussion, and activities with worksheets using mathematical formulas and studio art provide the framework for each lesson.

In this video segment from Cyberchase, the CyberSquad must get into a vault before Hacker, Buzz and Delete by cracking a code of shapes and numbers.

This problem requires some visualization and knowledge of 3D shapes. It gives children experience of identifying shapes from pictures of them in different positions and orientations. Ideas for implementation, extension and support are included along with a printable sheet of shape cards.

The Word documents linked on this web page identify resources from the NRICH collection that have been mapped to the strands (Number, Algebra, Shape and Space, and Handling Data) of the framework for teaching mathematics in the United Kingdom. These resources promote the development of content knowledge as well as mathematical thinking and problem-solving (process) skills. The stage 1 mapping is most useful for K-2, while the stage 2 document is for grades 3-6.

This activity asks students to recognize differences in shapes and sort them. They are given a set of 15 shape cards that they can sort by the criteria of color, size and shape. Ideas for implementation, extension and support are included along with a printable sheet of the cards.

This article helps educators answer questions about geometric thinking and the activities that develop it. It outlines the 3 levels of thinking about shape and space and the 5 phases of activities known as the van Hiele model. The tangram puzzle provides a vehicle for describing these phases and the types of thinking students achieve in each one. The article concludes with a suggestion about followup activity.

This task gives students the opportunity to verify that a dilation takes a line that does not pass through the center to a line parallel to the original line, and to verify that a dilation of a line segment (whether it passes through the center or not) is longer or shorter by the scale factor.

Using circumference, this segment measures the total distant traveled by two carousel riders after the carousel has rotated 10 times.

The purpose of the task is to analyze a plausible real-life scenario using a geometric model. The task requires knowledge of volume formulas for cylinders and cones, some geometric reasoning involving similar triangles, and pays attention to reasonable approximations and maintaining reasonable levels of accuracy throughout.

This task would be especially well-suited for instructional purposes. Students will benefit from a class discussion about the slope, y-intercept, x-intercept, and implications of the restricted domain for interpreting more precisely what the equation is modeling.

Seminar on a selected topic from Renaissance architecture. Requires original research and presentation of a report. The aim of this course is to highlight some technical aspects of the classical tradition in architecture that have so far received only sporadic attention. It is well known that quantification has always been an essential component of classical design: proportional systems in particular have been keenly investigated. But the actual technical tools whereby quantitative precision was conceived, represented, transmitted, and implemented in pre-modern architecture remain mostly unexplored. By showing that a dialectical relationship between architectural theory and data-processing technologies was as crucial in the past as it is today, this course hopes to promote a more historically aware understanding of the current computer-induced transformations in architectural design.