There are **110** NRICH Mathematical resources connected to **Interactivities**, you may find related items under Physical and Digital Manipulatives.

Challenge Level

Use the interactivities to fill in these Carroll diagrams. How do you know where to place the numbers?

Challenge Level

Players take it in turns to choose a dot on the grid. The winner is the first to have four dots that can be joined to form a square.

Challenge Level

The computer has made a rectangle and will tell you the number of spots it uses in total. Can you find out where the rectangle is?

Challenge Level

Each light in this interactivity turns on according to a rule. What happens when you enter different numbers? Can you find the smallest number that lights up all four lights?

Challenge Level

In this activity, the computer chooses a times table and shifts it. Can you work out the table and the shift each time?

Challenge Level

Here is a chance to play a fractions version of the classic Countdown Game.

Challenge Level

This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?

Challenge Level

Here is a chance to play a version of the classic Countdown Game.

Challenge Level

Can you find a reliable strategy for choosing coordinates that will locate the treasure in the minimum number of guesses?

Challenge Level

This interactivity invites you to make conjectures and explore probabilities of outcomes related to two independent events.

Challenge Level

Add or subtract the two numbers on the spinners and try to complete a row of three. Are there some numbers that are good to aim for?

Challenge Level

Can you complete this jigsaw of the multiplication square?

Challenge Level

Investigate how the four L-shapes fit together to make an enlarged L-shape. You could explore this idea with other shapes too.

Challenge Level

A game in which players take it in turns to choose a number. Can you block your opponent?

Challenge Level

What do the numbers shaded in blue on this hundred square have in common? What do you notice about the pink numbers? How about the shaded numbers in the other squares?

Challenge Level

Find the frequency distribution for ordinary English, and use it to help you crack the code.

Challenge Level

The number of plants in Mr McGregor's magic potting shed increases overnight. He'd like to put the same number of plants in each of his gardens, planting one garden each day. How can he do it?

Challenge Level

Mr McGregor has a magic potting shed. Overnight, the number of plants in it doubles. He'd like to put the same number of plants in each of three gardens, planting one garden each day. Can he do it?

Challenge Level

Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.

Challenge Level

Semi-regular tessellations combine two or more different regular polygons to fill the plane. Can you find all the semi-regular tessellations?

Challenge Level

Experiment with the interactivity of "rolling" regular polygons, and explore how the different positions of the dot affects its vertical and horizontal movement at each stage.

Challenge Level

Experiment with the interactivity of "rolling" regular polygons, and explore how the different positions of the red dot affects its speed at each stage.

Challenge Level

Experiment with the interactivity of "rolling" regular polygons, and explore how the different positions of the red dot affects the distance it travels at each stage.

Challenge Level

An environment which simulates working with Cuisenaire rods.

Challenge Level

Six balls are shaken. You win if at least one red ball ends in a corner. What is the probability of winning?

Challenge Level

Seven balls are shaken. You win if the two blue balls end up touching. What is the probability of winning?

Challenge Level

Discs are flipped in the air. You win if all the faces show the same colour. What is the probability of winning?

Challenge Level

Choose the size of your pegboard and the shapes you can make. Can you work out the strategies needed to block your opponent?

Challenge Level

How many different triangles can you make on a circular pegboard that has nine pegs?

Challenge Level

Can you make a right-angled triangle on this peg-board by joining up three points round the edge?

Challenge Level

What is the relationship between the angle at the centre and the angles at the circumference, for angles which stand on the same arc? Can you prove it?

Challenge Level

Can you find triangles on a 9-point circle? Can you work out their angles?

Challenge Level

We can show that (x + 1)² = x² + 2x + 1 by considering the area of an (x + 1) by (x + 1) square. Show in a similar way that (x + 2)² = x² + 4x + 4

Challenge Level

Can you find the pairs that represent the same amount of money?

Challenge Level

Can you work out what step size to take to ensure you visit all the dots on the circle?

Challenge Level

A tilted square is a square with no horizontal sides. Can you devise a general instruction for the construction of a square when you are given just one of its sides?

Challenge Level

Draw some isosceles triangles with an area of $9$cm$^2$ and a vertex at (20,20). If all the vertices must have whole number coordinates, how many is it possible to draw?

Challenge Level

Players take it in turns to choose a dot on the grid. The winner is the first to have four dots that can be joined to form a square.

Challenge Level

Two engines, at opposite ends of a single track railway line, set off towards one another just as a fly, sitting on the front of one of the engines, sets off flying along the railway line...

Challenge Level

It's easy to work out the areas of most squares that we meet, but what if they were tilted?

Challenge Level

When number pyramids have a sequence on the bottom layer, some interesting patterns emerge...

Challenge Level

Try entering different sets of numbers in the number pyramids. How does the total at the top change?

Challenge Level

Triangular numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?

Challenge Level

Two circles of equal radius touch at P. One circle is fixed whilst the other moves, rolling without slipping, all the way round. How many times does the moving coin revolve before returning to P?

Challenge Level

A circle rolls around the outside edge of a square so that its circumference always touches the edge of the square. Can you describe the locus of the centre of the circle?

Challenge Level

Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?

Challenge Level

A game for two people, or play online. Given a target number, say 23, and a range of numbers to choose from, say 1-4, players take it in turns to add to the running total to hit their target.

Challenge Level

Practise your tables skills and try to beat your previous best score in this interactive game.

Challenge Level

Can you match pairs of fractions, decimals and percentages, and beat your previous scores?