The construction of the tangent line to a circle from a point outside of the circle requires knowledge of a couple of facts about circles and triangles. First, students must know, for part (a), that a triangle inscribed in a circle with one side a diameter is a right triangle. This material is presented in the tasks ''Right triangles inscribed in circles I.'' For part (b) students must know that the tangent line to a circle at a point is characterized by meeting the radius of the circle at that point in a right angle: more about this can be found in ''Tangent lines and the radius of a circle.''

Doing this Nrich problem is an excellent way to work at problem solving with learners. The problem lends itself to small group work, and provides an engaging context for pupils to use the skills of trial and error, and working systematically.

This Nrich problem offers an excellent opportunity for students to practice converting fractions into decimals, while also investigating a wider question that connects their knowledge of prime factors and place value.

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

This short video and interactive assessment activity is designed to teach third graders an overview of tessellations.

This short video and interactive assessment activity is designed to give fifth graders an overview of tessellations.

This Nrich activity gives children the opportunity to use, reinforce and extend their knowledge of place value, multiples and times tables. It enables them to use their understanding of pattern and possibly their visualizing skills. This activity also offers an opportunity to discuss the strategies the children come up with - what is a good strategy for putting the number tiles back in the correct places as quickly as possible? What makes one strategy 'smarter' than another?

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

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

Students explore combinations in this Nrich activity. There is a simulator to help students with visualizing the possible outcomes. Discussion is a key element.

This Nrich problem encourages children to explain observations and to generalize. It requires a good understanding of multiplication. It may also introduce the idea that opposite faces of a dice add to seven, if that is something with which learners are not already familiar

This Nrich problem supports the development of the idea of generic proof with the children. This is a tricky concept to grasp but it draws attention to mathematical structures that are not often addressed at primary school level.

ile patterns will be familiar with students both from working with geometry tiles and from the many tiles they encounter in the world. Here one of the most important examples of a tiling, with regular hexagons, is studied in detail. This provides students an opportunity to use what they know about the sum of the angles in a triangle and also the sum of angles which make a line.

ile patterns will be familiar with students both from working with geometry tiles and from the many tiles they encounter in the world. Here one of the most important examples of a tiling, with regular hexagons, is studied in detail. This provides students an opportunity to use what they know about the sum of the angles in a triangle and also the sum of angles which make a line.

This task aims at explaining why four regular octagons can be placed around a central square, applying student knowledge of triangles and sums of angles in both triangles and more general polygons.

Reasoning to Find Area: Lesson 1

Students start the first lesson of the school year by recalling what they know about area (note that students studied the areas of rectangles with whole-number side lengths in grade 3 and with fractional side lengths in grade 5). The mathematics they explore is not complicated, so it offers a low threshold for entry. The lesson does, however, uncover two important ideas:

If two figures can be placed one on top of the other so that they match up exactly, then they have the same area.
The area of a region does not change when the region is decomposed and rearranged.
At the end of this lesson, students are asked to write their best definition of area.

There are fascinating patterns to be found in recurring decimals. This Nrich problem explores the relationship between fraction and decimal representations. It's a great opportunity to practice converting fractions to decimals with and without a calculator.

The purpose of this task is to engage students in geometric modeling, and in particular to deduce algebraic relationships between variables stemming from geometric constraints. The modelling process is a challenging one, and will likely elicit a variety of attempts from the students.

Informational text about reflections, image of reflected figure with hot spots, images of special reflections (x-axis, y-axis, x=y), interactive drag and drop reflected points of triangle.