This short video and interactive assessment activity is designed to teach third graders about determining unknown angles in trapezoids.

This short video and interactive assessment activity is designed to teach fourth graders about determining unknown angles in trapezoids.

This short video and interactive assessment activity is designed to teach fifth graders about determining unknown angles within rectangles and squares.

This short video and interactive assessment activity is designed to teach third graders about determining unknown angles within rectangles and squares.

This short video and interactive assessment activity is designed to teach third graders about determining the unknown angle in an isosceles triangle.

This short video and interactive assessment activity is designed to give fourth graders an overview of special triangles.

'Tricks' tap into children's natural curiosity and can provide the motivation for exploring the underlying mathematics in order to unpick how they are done. This Nrich problem explores a "trick" to provide an engaging context in which to explore place value and in particular 'adding nine' as 'adding ten and subtracting one'.

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.

The Nrich problem offers opportunities to think about area, proportion and fractions, while offering an informal introduction to the mathematics of infinity and convergence which would not normally be met by younger students, to tempt their curiosity.

An interactive applet and associated web page that demonstrate how to find the perpendicular distance between a point and a line using trigonometry, given the coordinates of the point and the slope/intercept of the line. The applet has a line with sliders that adjust its slope and intercept, and a draggable point. As the line is altered or the point dragged, the distance is recalculated. The grid and coordinates can be turned on and off. The distance calculation can be turned off to permit class exercises and then turned back on the verify the answers. The applet can be printed as it appears on the screen to make handouts. The web page has a full description of the concept of the concepts, a worked example and has links to other pages relating to coordinate geometry. Applet can be enlarged to full screen size for use with a classroom projector. This resource is a component of the Math Open Reference Interactive Geometry textbook project at http://www.mathopenref.com.

Unit: Area and Surface Area
Lesson 16: Distinguishing Between Surface Area and Volume

In this optional lesson, students distinguish among measures of one-, two-, and three-dimensional attributes and take a closer look at the distinction between surface area and volume (building on students' work in earlier grades). Use this lesson to reinforce the idea that length is a one-dimensional attribute of geometric figures, surface area is a two-dimensional attribute, and volume is a three-dimensional attribute.

By building polyhedra, drawing representations of them, and calculating both surface area and volume, students see that different three-dimensional figures can have the same volume but different surface areas, and vice versa. This is analogous to the fact that two-dimensional figures can have the same area but different perimeters, and vice versa. Students must attend to units of measure throughout the lesson.

Note: Students will need to bring in a personal collection of 10–50 small objects ahead of time for the first lesson of the next unit. Examples include rocks, seashells, trading cards, or coins.

Khan Academy video describing using coordinate plane to divide a line segment into a 3:1 ratio. Interactive drag and drop for estimating point, and button for additional explanation regarding ratio is added.

This Nrich problem gives learners practice in fractions (tenths) as well as in addition and subtraction in a challenging form.

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 Nrich problem uses the idea of sequences in a very tangible form. Children will need to recognize odd and even numbers as well as be able to count fluently both backwards and forwards. They will also have opportunities to justify their answers.

The Nrich game as introduced is intended for children who are just beginning to become confident with small numbers. However there are many variations, some suggested below, that make it suitable for older children. As with many of the NRICH games, consolidation of basic number facts is combined with an element of strategic thinking.

This Nrich activity provides a context for doubling multiples of 5. The children will also be noticing and describing patterns.

This team-building task is designed to develop students' team-working skills. If you wish to learn more about these skills, and find other team-builder tasks, take a look at this article.

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.