Telling a story which poses a problem for children to solve. One of our EYFS resources designed to support you in developing the initial building blocks for mathematical thinking, reasoning and problem solving with your children.

Algebra - representing, sequences, simplifying expressions Key Stages: 3 and 4 ★★ What patterns do you notice when you enter a number into the bottom left hand corner of the pyramid? Can you explain your patterns? This problem offers students the opportunity to notice patterns, make conjectures, explain what they notice and prove their conjectures. Generalisation provokes the need to use algebraic techniques such as collecting like terms and representing number sequences algebraically. This resource has comprehensive teachers' notes and resources, linked from the problem page. This includes possible approaches and key questions, as well as possible support and extensions. The file attached is a HTML file, which, when opened, automatically redirects you to the problem on the NRICH website.

In this problem, we're going to find sets of letter shapes that go together.

This activity is accessible to a wide variety of pupils. At one level, learners can explore ways of putting the five shapes together by ‘playing’ with hexagon pieces. At a higher level, more experienced or older pupils can be expected to go about the activity in an organised, systematic way. In addition, this problem encourages learners to use visualisation and to apply their understanding of reflective and rotational symmetry. The two pdf files (hexagonal shapes) could be used to introduce the challenge by creating some hexagons to be dragged around the interactive whiteboard screen, or large shapes out of card could be cut and fixed to the board or wall.

Addition and Subtraction Key Stages: 1 and 2 ★ Have a go at this game on the numberline. Can you be the last person able to cross out the values for an addition or subtraction? This game offers an engaging context for practising addition and subtraction, but it also requires some strategic thinking. It is easily adaptable, and can be used co-operatively or competitively. This resource has comprehensive teachers' notes and resources, linked from the problem page. This includes possible approaches and key questions, as well as possible support and extensions. The file attached is a HTML file, which, when opened, automatically redirects you to the problem on the NRICH website.

Use baskets and labels for sorting activities. One of our EYFS resources designed to support you in developing the initial building blocks for mathematical thinking, reasoning and problem solving with your children.

Angles and Polygons, 2D Shapes Key Stage: 3 ★★★ In this game, you turn over two cards. You get to keep those cards if you can draw a triangle which has both properties. Otherwise the cards are returned and the next player takes their turn. The game provides a powerful and engaging context for working on properties of triangles/quadrilaterals. This resource has comprehensive teachers' notes and resources, linked from the problem page. This includes possible approaches and key questions, as well as possible support and extensions. The file attached is a HTML file, which, when opened, automatically redirects you to the problem on the NRICH website.

Angles and Polygons, 2D Shapes Key Stage: 3 ★★ Can you arrange eight of the property cards around the outside of this grid and then draw quadrilaterals in the grid which have the properties corresponding to both their row and column? This game provides an interesting context in which to consider the properties of quadrilaterals (or triangles), and has a particular focus on the combinations of properties that are possible. This resource has comprehensive teachers' notes and resources, linked from the problem page. This includes possible approaches and key questions, as well as possible support and extensions. The file attached is a HTML file, which, when opened, automatically redirects you to the problem on the NRICH website.

This problem provides a challenge when you are focusing on drawing lines and shapes accurately or finding areas either by counting squares or calculation. The problem calls on learners’ understanding of squares and right-angled triangles, and requires working systematically and visualisation as well as reasonably accurate drawing. A supporting sheet is provided with which children can draw their lines/shapes on to help with their investigations.

Our making caterpillars activity uses clay and dough to introduce measurement and comparison. One of our EYFS resources designed to support you in developing the initial building blocks for mathematical thinking, reasoning and problem solving with your children.

Try this version of Snap with a friend - do you know the order of the days of the week?

Addition, Subtraction, Multiplication, Division Key Stages: 2 and 3 ★ Can you use the four basic operations and the six numbers in order to make the target? Countdown offers a motivating context in which to practise calculation strategies. It encourages learners to estimate and to 'tinker' with solutions so as to get closer to the target number. This resource has comprehensive teachers' notes and resources, linked from the problem page. This includes possible approaches and key questions, as well as possible support and extensions. The file attached is a HTML file, which, when opened, automatically redirects you to the problem on the NRICH website.

Number Patterns/Simultaneous Equations Key Stage: 3 ★ An arithmagon is a polygon with numbers at its vertices, which determine the numbers on the edges. How do the values at the vertices determine those at the edges? Can you work out a way to work out what numbers belong on the vertices, if you're given the numbers on the edges? This resource encourages students to explore number patterns with and without symbols, and offers several routes to generality. It also asks the question as to whether it is possible to 'solve' the arithmagon. This resource has comprehensive teachers' notes and resources, linked from the problem page. This includes possible approaches and key questions, as well as possible support and extensions. The file attached is a HTML file, which, when opened, automatically redirects you to the problem on the NRICH website.

In this web page and worksheet students practice their knowledge of time-distance graphs. Four vehicles travel along a road one afternoon. Can you make sense of the graphs showing their motion?

Volume and Surface Area of Cuboids Key Stage: 3 ★★ What is the largest volume of box you can cut out from a square sheet of paper? This problem offers opportunities for visualising, and for consolidating the formula for working out the volume of a cuboid, while at the same time challenging students to conjecture, test out ideas and compare different strategies for arriving at an optimum solution. This resource has comprehensive teachers' notes and resources, linked from the problem page. This includes possible approaches and key questions, as well as possible support and extensions. The file attached is a HTML file, which, when opened, automatically redirects you to the problem on the NRICH website.

Describing Positions, Turns Key Stage: 1 ★ How many times do you have to press the turn button to make the man look the same as each of the pictures. Is there more than one answers? This problem is intended to help children who are confident about turning themselves a quarter or half turn, but find it difficult to relate this to quarter or half turns in a picture or diagram. The Turning Man is a "halfway house" between these two. This resource has comprehensive teachers' notes and resources, linked from the problem page. This includes possible approaches and key questions, as well as possible support and extensions. The file attached is a HTML file, which, when opened, automatically redirects you to the problem on the NRICH website.

Where can you draw a line on a clock face so that the numbers on both sides have the same total?

Sorting, Properties of Shapes Key Stage: 1 ★ Can you find some collections of shapes that go together? Can you think of a name for your collection? This problem provides an opportunity for children to sort and categorise, both of which are important mathematical processes. This open activity challenges children to find their own categories and then name them. This means it is a good way to introduce specific vocabulary associated with properties of shape, or to remind children of relevant mathematical language. This resource has comprehensive teachers' notes and resources, linked from the problem page. This includes possible approaches and key questions, as well as possible support and extensions. The file attached is a HTML file, which, when opened, automatically redirects you to the problem on the NRICH website.

Which of these sets of numbered balls will give the most even totals when two balls are chosen from them?

Coordinate Geometry, Squares Key Stage: 3 ★★ Can you draw some tilted squares on this grid? Can you tell when four coordinates form a square? This problem emphasises to students that squares don't just exist in their usual orientation. The context offers an ideal opportunity to challenge students to visualise relationships between coordinates. The interactivity could also be useful when introducing Pythagoras' Theorem and when working on the gradients of perpendicular lines. This resource has comprehensive teachers' notes and resources, linked from the problem page. This includes possible approaches and key questions, as well as possible support and extensions. The file attached is a HTML file, which, when opened, automatically redirects you to the problem on the NRICH website.

Symmetry Key Stage: 1 ★★ Can you colour this triangle in a symmetrical pattern with two colours. What about more colours? This problem will help children recognise reflective symmetry, but it offers more than that. By giving children the freedom to create their own symmetrical patterns, they will push their own understanding of symmetry further and may well suprise you! It also provides an opportunity for children to discuss what makes one symmetrical pattern different, or the same as, another. This resource has comprehensive teachers' notes and resources, linked from the problem page. This includes possible approaches and key questions, as well as possible support and extensions. The file attached is a HTML file, which, when opened, automatically redirects you to the problem on the NRICH website.