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?

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.

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.

This Nrich game is designed to get children used to moving along a number line either side of a central point adding and subtracting within 27. It can help to introduce the idea of negative numbers or practice fluency with negatives by changing the midpoint to 0.

This Nrich problem introduces an intriguing trick which provides a context for practicing manipulation of fractions. Watching the video, or perhaps trying the trick out for themselves, can engage students' curiosity, and lead to some intriguing mathematics to explore and explain.

This Nrich problem is a fantastic opportunity for learners to apply knowledge of place value and offers a context for learning and practicing the relevant vocabulary (odd, even, multiple). The interactivity will help learners satisfy their curiosity in the sense of finding a 'better' solution, as it enables them to play around with the digits without having to commit anything to paper. This act of deciding whether one solution is better than another also provides a meaningful context in which to compare and order numbers.

This Nrich investigation is one that uses the very popular multilink cubes. It gives a wonderful opportunity for pupils to explore ways of recording. This activity is also designed to nurture children's curiosity by introducing mathematics into a familiar non-mathematical context. Children might end up pursuing different ideas from each other and this freedom to explore may well encourage learners to persevere more than they might usually. In this way, they will immerse themselves in the particular number sequence they have chosen to use, which will help them gain a deep understanding of its structure. This activity lends itself to pupils posing their own questions in the form “I wonder what would happen if...?”

This Nrich activity offers free exploration which will help learners develop a deep understanding of halves and halving. The task gives a context in which to discuss the importance of the part-whole relationship of fractions so that children realise halves can be different sizes, depending on the whole.

In this Nrich activity students look for connections in an array combining colors and shapes.

At its most basic this Nrich task is an exercise in reading and recording information from a table. It also offers opportunities for children to do some elementary reasoning as they compare results with each other and work out why they differ.