There are **220** NRICH Mathematical resources connected to **Interactivities**, you may find related items under Physical and Digital Manipulatives.

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

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.

There are three versions of this challenge. The idea is to change the colour of all the spots on the grid. Can you do it in fewer throws of the dice?

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?

Mathmo is a revision tool for post-16 mathematics. It's great installed as a smartphone app, but it works well in pads and desktops and notebooks too. Give yourself a mathematical workout!

Investigate which numbers make these lights come on. What is the smallest number you can find that lights up all the lights?

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?

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

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

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

Use your skill and knowledge to place various scientific lengths in order of size. Can you judge the length of objects with sizes ranging from 1 Angstrom to 1 million km with no wrong attempts?

Can you work through these direct proofs, using our interactive proof sorters?

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

Place the numbers 1 to 6 in the circles so that each number is the difference between the two numbers just below it.

Can you locate these values on this interactive logarithmic scale?

Can you work out which spinners were used to generate the frequency charts?

This is a game for two players. Can you find out how to be the first to get to 12 o'clock?

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

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?

What shape is the overlap when you slide one of these shapes half way across another? Can you picture it in your head? Use the interactivity to check your visualisation.

How good are you at finding the formula for a number pattern ?

Use your mouse to move the red and green parts of this disc. Can you make images which show the turnings described?

How many different triangles can you draw on the dotty grid which each have one dot in the middle?

An environment that simulates a protractor carrying a right- angled triangle of unit hypotenuse.

Can you complete this jigsaw of the multiplication square?

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

Use the interactivity to find out how many quarter turns the man must rotate through to look like each of the pictures.

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

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?

Sort the houses in my street into different groups. Can you do it in any other ways?

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

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?

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?

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

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

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

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

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.

An environment which simulates working with Cuisenaire rods.

How many trains can you make which are the same length as Matt's and Katie's, using rods that are identical?

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

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

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

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

Use the interactivity or play this dice game yourself. How could you make it fair?

Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.