This Nrich activity will be very useful when wishing to challenge and extend pupils' spatial awareness with 2D shapes. It can also be an exercise in perseverance.

The Mathematics Vision Project (MVP) curriculum has been developed to realize the vision and goals of the New Core Standards of Mathematics. The Comprehensive Mathematics Instruction (CMI) framework is an integral part of the materials. You can read more about the CMI framework in the Utah Mathematics Teacher Journal. (UCTM, 2009)

This task is intended to help model a concrete situation with geometry. Placing the seven pennies in a circular pattern is a concrete and fun experiment which leads to a genuine mathematical question: does the physical model with pennies give insight into what happens with seven circles in the plane?

This Nrich game can give pupils the opportunity to use their number knowledge and it can be adapted to stretch even the highest attainers. In its simplest form it can be accessed by anyone in the class who is able to connect the number of spots on a die to the numeral that represents it. Altering the rules and including operations will give the children opportunities to explore ideas about what makes a "good" game and to develop winning strategies to play their games.

The topic of music can make a good connection between science and mathematics
The nature of sound and the working of the ear are rich areas of applied mathematics.
The ratio emphasis follows from harmonics or overtones and rests on ideas like lowest common multiple.

This Nrich game will help children to understand the tens and units structure of the numbers to a hundred. It can be used as an activity for one child on his/her own or by up to three at once. If there are four, it would be more suitable to play two parallel games.

This Nrich activity engages the pupils in both a spatial and numerical context. It gives them also the freedom to choose how they go about it - visualizing in their head, using paper, string etc. that they have requested and/or making use of a spreadsheet. They can learn a lot from adopting one method and then realizing that an alternative method would be better.

This Nrich task encourages creativity in developing patterns and using shapes to create composite shapes. This task could be done with tiles, blocks, or paper shapes.

This Nrich activity can be used to build up children's confidence with the language associated with 2D shape.

This Nrich activity can be printed or used interactively. Students will write down and discuss similarities and differences they see.

This Nrich game offers an excellent opportunity to practice visualizing squares and angles on grids and also encourages students to look at strategies using systematic approaches. Describing strategies to others is always a good way to focus and clarify mathematical thought.

The whole idea of this Nrich problem is to invite children to picture something in their mind and in this instance, pupils will need to be familiar with properties of a cube. Ideally, it would be good to encourage your class to tackle this challenge purely by trying to imagine what is happening. To convince you and each other of their solutions, they will need to explain particularly carefully what they are picturing, which can be quite tricky, and you may find that they gesticulate rather a lot! In order to reach a joint conclusion, you might find it helpful to make a model of the cube from interlocking cubes.

In this Nrich activity, student will work in groups and whole group to produce a data chart based on countable classroom situations.

After geometric series, this Nrich problem is one of the simplest infinite series with finite sum, all of whose terms are positive. This geometric demonstration of the result requires students to continue a pattern and to use several steps of reasoning to deduce that the sum is bounded by 2. Summing infinite geometric series also play an important role in the this proof, so this could be used to show an application of them in a larger proof. (It would be useful for students to be able to sum 12+14+18+⋯ before tackling this problem.)

In Nrich's Twisting and Turning, the Conway Rope Trick was introduced. You'll need to take a look at the video on that page and do the rope trick for yourself before reading the rest of this article, since here we're going to take a good long look at the symmetries of the resulting tangles.

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 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?

First term of a theoretical treatment of the physics of solids. Concept of elementary excitations. Symmetry: translational, rotational, and time-reversal invariances: theory of representations. Energy bands: APW, OPW, pseudopotential and LCAO schemes. Survey of electronic structure of metals, semimetals, semiconductors, and insulators. Excitons. Critical points. Response functions. Interactions in the electron gas.