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
Which dilutions can you make using 10ml pipettes and 100ml
Can you fill in the mixed up numbers in this dilution calculation?
Can you break down this conversion process into logical steps?
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 resource contains interactive problems to support work on
number sequences at Key Stage 4.
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.
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. . . .
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?
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?
Have you seen this way of doing multiplication ?
A game in which players take it in turns to choose a number. Can you block your opponent?
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
When number pyramids have a sequence on the bottom layer, some interesting patterns emerge...
If you continue the pattern, can you predict what each of the following areas will be? Try to explain your prediction.
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?
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?
There are thirteen axes of rotational symmetry of a unit cube. Describe them all. What is the average length of the parts of the axes of symmetry which lie inside the cube?
Show how this pentagonal tile can be used to tile the plane and
describe the transformations which map this pentagon to its images
in the tiling.
Euler discussed whether or not it was possible to stroll around Koenigsberg crossing each of its seven bridges exactly once. Experiment with different numbers of islands and bridges.
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
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
What are the areas of these triangles? What do you notice? Can you generalise to other "families" of triangles?
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. . . .
The aim of the game is to slide the green square from the top right
hand corner to the bottom left hand corner in the least number of
It's easy to work out the areas of most squares that we meet, but
what if they were tilted?
Triangle numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?
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.
A counter is placed in the bottom right hand corner of a grid. You
toss a coin and move the star according to the following rules: ...
What is the probability that you end up in the top left-hand. . . .
A game for 2 players that can be played online. Players take it in turns to select a word from the 9 words given. The aim is to select all the occurrences of the same letter.
Four cards are shuffled and placed into two piles of two. Starting with the first pile of cards - turn a card over...
You win if all your cards end up in the trays before you run out of cards in. . . .
Slide the pieces to move Khun Phaen past all the guards into the position on the right from which he can escape to freedom.
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.
Can you beat Piggy in this simple dice game? Can you figure out
Piggy's strategy, and is there a better one?
A game for 2 players. Can be played online. One player has 1 red
counter, the other has 4 blue. The red counter needs to reach the
other side, and the blue needs to trap the red.
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 red square and a blue square overlap so that the corner of the red square rests on the centre of the blue square. Show that, whatever the orientation of the red square, it covers a quarter of the. . . .
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.
This problem is about investigating whether it is possible to start at one vertex of a platonic solid and visit every other vertex once only returning to the vertex you started at.
To avoid losing think of another very well known game where the
patterns of play are similar.
Can you spot the similarities between this game and other games you know? The aim is to choose 3 numbers that total 15.
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...
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. . . .
Match the cards of the same value.
Cellular is an animation that helps you make geometric sequences composed of square cells.
Here is a chance to play a version of the classic Countdown Game.
Here is a chance to play a fractions version of the classic
Practice your skills of measurement and estimation using this interactive measurement tool based around fascinating images from biology.
Practise your skills of proportional reasoning with this interactive haemocytometer.