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There are **173** NRICH Mathematical resources connected to **Interactivities**, you may find related items under Physical and digital manipulatives.

Problem
Primary curriculum
Secondary curriculum
### More Transformations on a Pegboard

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

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Semi-regular Tessellations

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

Age 11 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Up and Across

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.

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Speeding Up, Slowing Down

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

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### How Far Does it Move?

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.

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Take Your Dog for a Walk

Use the interactivity to move Pat. Can you reproduce the graphs and tell their story?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Are You Well Balanced?

Can you work out how to make each side of this balance equally balanced? You can put more than one weight on a hook.

Age 5 to 7

Challenge Level

Interactive
Primary curriculum
Secondary curriculum
### Cuisenaire Environment

An environment which simulates working with Cuisenaire rods.

Age 5 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Same Length Trains

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

Age 5 to 7

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Cosy Corner

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

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Two's Company

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

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Flippin' Discs

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

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Board Block Challenge

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

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Three Ball Line Up

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

Age 5 to 7

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Nine-pin Triangles

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

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Triangles All Around

Can you find all the different triangles on these peg boards, and find their angles?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Right Angles

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

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Subtended Angles

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?

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Triangles in Circles

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

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Partitioning Revisited

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

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Fractions and Percentages Card Game

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

Age 11 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Cuisenaire Counting

Here are some rods that are different colours. How could I make a yellow rod using white and red rods?

Age 5 to 7

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Stars

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

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Square Coordinates

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?

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Isosceles Triangles

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?

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Square It

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.

Age 11 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Robot Monsters

Use these head, body and leg pieces to make Robot Monsters which are different heights.

Age 5 to 7

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### An Unhappy End

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...

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Tilted Squares

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

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### More Number Pyramids

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

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Number Pyramids

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

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Picturing Triangular Numbers

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

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Guesswork

Ask a friend to choose a number between 1 and 63. By identifying which of the six cards contains the number they are thinking of it is easy to tell them what the number is.

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Rollin' Rollin' Rollin'

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?

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Rolling Around

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?

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### A Square of Numbers

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

Age 7 to 11

Challenge Level

Interactive
Primary curriculum
Secondary curriculum
### Proof Sorter - Sum of an Arithmetic Sequence

Put the steps of this proof in order to find the formula for the sum of an arithmetic sequence

Age 16 to 18

Challenge Level

Interactive
Primary curriculum
Secondary curriculum
### Proof Sorter - Quadratic Equation

This is an interactivity in which you have to sort the steps in the completion of the square into the correct order to prove the formula for the solutions of quadratic equations.

Age 14 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Got It

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.

Age 7 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Multiplication Tables - Matching Cards

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

Age 5 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Matching Fractions, Decimals and Percentages

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

Age 7 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Factor Lines

Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.

Age 7 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Attractive Tablecloths

Charlie likes tablecloths that use as many colours as possible, but insists that his tablecloths have some symmetry. Can you work out how many colours he needs for different tablecloth designs?

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Nine Colours

Can you use small coloured cubes to make a 3 by 3 by 3 cube so that each face of the bigger cube contains one of each colour?

Age 11 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Have You Got It?

Can you explain the strategy for winning this game with any target?

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Number Round Up

Arrange the numbers 1 to 6 in each set of circles below. The sum of each side of the triangle should equal the number in its centre.

Age 5 to 7

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Three Squares

What is the greatest number of squares you can make by overlapping three squares?

Age 5 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Four Triangles Puzzle

Cut four triangles from a square as shown in the picture. How many different shapes can you make by fitting the four triangles back together?

Age 5 to 11

Challenge Level