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?

Can you find a relationship between the number of dots on the circle and the number of steps that will ensure that all points are hit?

Work out how to light up the single light. What's the rule?

A collection of resources to support work on Factors and Multiples at Secondary level.

A and B are two interlocking cogwheels having p teeth and q teeth respectively. One tooth on B is painted red. Find the values of p and q for which the red tooth on B contacts every gap on the. . . .

Interactive game. Set your own level of challenge, practise your table skills and beat your previous best score.

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

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...

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.

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

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?

This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.

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.

Learn how to use the Shuffles interactivity by running through these tutorial demonstrations.

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?

Practise your diamond mining skills and your x,y coordination in this homage to Pacman.

Can you locate the lost giraffe? Input coordinates to help you search and find the giraffe in the fewest guesses.

Can you spot the similarities between this game and other games you know? The aim is to choose 3 numbers that total 15.

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

Meg and Mo still need to hang their marbles so that they balance, but this time the constraints are different. Use the interactivity to experiment and find out what they need to do.

Place a red counter in the top left corner of a 4x4 array, which is covered by 14 other smaller counters, leaving a gap in the bottom right hand corner (HOME). What is the smallest number of moves. . . .

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

How many different triangles can you make which consist of the centre point and two of the points on the edge? Can you work out each of their angles?

Mo has left, but Meg is still experimenting. Use the interactivity to help you find out how she can alter her pouch of marbles and still keep the two pouches balanced.

Six balls of various colours are randomly shaken into a trianglular arrangement. What is the probability of having at least one red in the corner?

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

Carry out some time trials and gather some data to help you decide on the best training regime for your rowing crew.

Imagine picking up a bow and some arrows and attempting to hit the target a few times. Can you work out the settings for the sight that give you the best chance of gaining a high score?

This game challenges you to locate hidden triangles in The White Box by firing rays and observing where the rays exit the Box.

This resource contains interactive problems to support work on number sequences at Key Stage 4.

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

7 balls are shaken in a container. You win if the two blue balls touch. What is the probability of winning?

Meg and Mo need to hang their marbles so that they balance. Use the interactivity to experiment and find out what they need to do.

A game for 1 person to play on screen. Practise your number bonds whilst improving your memory

Start with any number of counters in any number of piles. 2 players take it in turns to remove any number of counters from a single pile. The winner is the player to take the last counter.

You have 27 small cubes, 3 each of nine colours. Use the small cubes to make a 3 by 3 by 3 cube so that each face of the bigger cube contains one of every colour.

These formulae are often quoted, but rarely proved. In this article, we derive the formulae for the volumes of a square-based pyramid and a cone, using relatively simple mathematical concepts.

First Connect Three game for an adult and child. Use the dice numbers and either addition or subtraction to get three numbers in a straight line.

Can you beat Piggy in this simple dice game? Can you figure out Piggy's strategy, and is there a better one?

Slide the pieces to move Khun Phaen past all the guards into the position on the right from which he can escape to freedom.

Square It game for an adult and child. Can you come up with a way of always winning this game?

What can you say about the values of n that make $7^n + 3^n$ a multiple of 10? Are there other pairs of integers between 1 and 10 which have similar properties?

Do you know how to find the area of a triangle? You can count the squares. What happens if we turn the triangle on end? Press the button and see. Try counting the number of units in the triangle now. . . .

The opposite vertices of a square have coordinates (a,b) and (c,d). What are the coordinates of the other vertices?

Use Excel to explore multiplication of fractions.

Can you put the 25 coloured tiles into the 5 x 5 square so that no column, no row and no diagonal line have tiles of the same colour in them?

A right-angled isosceles triangle is rotated about the centre point of a square. What can you say about the area of the part of the square covered by the triangle as it rotates?

You can move the 4 pieces of the jigsaw and fit them into both outlines. Explain what has happened to the missing one unit of area.