Optical illusions are fun, but they can also teach us a lot about how our brains work. In particular, how our brains accomplish the incredible feat of constructing a three-dimensional reality using nothing but 2-D images from our eyes. A...

This video is about a better way to understand Penrose tilings (the famous tilings invented by Roger Penrose that never repeat themselves but still have some kind of order/pattern).

Hexagons appear all over the natural world from honeycomb to bubbles, and they even appear in organic chemistry! In this episode of Crash Course Organic Chemistry, we're learning all about cyclohexanes, including how rings pucker to...

Engineer RA Mashelkar shares three stories of ultra-low-cost design from India that use bottom-up rethinking, and some clever engineering, to bring expensive products (cars, prosthetics) into the realm of the possible for everyone.

We're enjoying the summer here in Montana, and to help celebrate we thought we'd put together a compilation of our favorite sun-related episodes from our past. Don't worry, you won't need sunglasses for this one!

Sunbeams shooting down through the clouds make for some great photographs, but what's the science behind these beautiful rays of light?

Why are most manhole covers round? Sure it makes them easy to roll, and slide into place in any alignment. But there's another, more compelling reason, involving a peculiar geometric property of circles and other shapes. Marc Chamberland...

This video, entitled "Translating Parallel Lines," demonstrates how a set of parallel lines can be translated on a coordinate plane.

Pupil outcome: I can make compound shapes by joining two polygons in different ways. Key learning points: - The same parts can create a different whole. - Lines are parallel because they are always the same distance apart. - A...

Pupil outcome: I can make and draw quadrilaterals on circular geoboards and name quadrilaterals according to their properties. Key learning points: - Join four dots on the edge of the circle to create a quadrilateral. - Use the...

Pupil outcome: I can draw polygons on isometric paper. Key learning points: - Different patterns on the paper allow you to draw polygons with different properties. - A ruler helps to draw shapes accurately. - Mark the vertices of the...

Pupil outcome: I can make and draw compound shapes with and without parallel and perpendicular sides. Key learning points: - The properties must match the shape you have created. - Lines are not perpendicular when they are not at right...

Pupil outcome: I can draw quadrilaterals and other polygons with given properties. Key learning points: - If you know the properties of a shape you can use a ruler and a grid to create it. - Lines are perpendicular when they are at right...

Pupil outcome: I can decompose a polygon in different ways and identify properties of polygons. Key learning points: - The same whole can be split into different parts. - Lines are perpendicular when they are at right angles to each...

Pupil outcome: I can apply trigonometric ratios to practical situations including angles of elevation and depression. Key learning points: - Trigonometric ratios are used in many scenarios - Trigonometric ratios are used to calculate the...

Pupil outcome: I can find a bearing between the points on a map or scaled plan. Key learning points: - If the map is to scale, then you can use a protractor to measure the bearing. - If the map is not to scale, you may need to use angle...

Pupil outcome: I can recognise and name polygons with five or more sides and recognise the difference between regular and irregular shapes. Key learning points: - The prefix is derived from Ancient Greek. - A regular polygon has sides...

Pupil outcome: I can form and solve equations using my knowledge of angles and polygons. Key learning points: - Missing angles can be found in polygons using knowledge of exterior and interior angles. - A missing angle can be represented...

Pupil outcome: I can use the properties of a rhombus to construct a perpendicular to a given line through a given point. Key learning points: - A rhombus can be constructed from two congruent isosceles triangles. - This can be used to...

Pupil outcome: I can identify different linkages within existing products. Key learning points: - Interactive books have a variety of linkages inside them. - Linkages are chosen to carry out a purpose in a product. - Analysis of existing...

Pupil outcome: I can use my knowledge of angles to solve problems. Key learning points: - Problems can be solved using parallel line angle facts. - Problems can be solved using interior and exterior angles of polygons. - Problems can be...

Pupil outcome: I can demonstrate and prove that in a triangle, the sum of the interior angles is 180°. Key learning points: - By considering a number of different triangles you can demonstrate facts about the angles in triangles. - The...

Pupil outcome: I can solve two linear simultaneous equations graphically (0 or 1 or infinitely many solutions). Key learning points: - You can use your knowledge of linear graphs to draw the graphs of both equations on the same axes. -...

Pupil outcome: I can reason mathematically using my knowledge of angle facts. Key learning points: - Alternate, corresponding and co-interior angles can be identified in diagrams containing pairs of parallel lines. - Facts about angles...