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
Place the numbers from 1 to 9 in the squares below so that the difference between joined squares is odd. How many different ways can you do this?
Here is a chance to play a version of the classic Countdown Game.
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?
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. . . .
This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.
Imagine a wheel with different markings painted on it at regular
intervals. Can you predict the colour of the 18th mark? The 100th
What happens when you turn these cogs? Investigate the differences
between turning two cogs of different sizes and two cogs which are
An environment which simulates working with Cuisenaire rods.
If you have only four weights, where could you place them in order
to balance this equaliser?
Use the interactivities to complete these Venn diagrams.
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?
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.
Use the interactivity to create some steady rhythms. How could you
create a rhythm which sounds the same forwards as it does
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
Is it possible to place 2 counters on the 3 by 3 grid so that there
is an even number of counters in every row and every column? How
about if you have 3 counters or 4 counters or....?
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?
Starting with the number 180, take away 9 again and again, joining up the dots as you go. Watch out - don't join all the dots!
Arrange the four number cards on the grid, according to the rules,
to make a diagonal, vertical or horizontal line.
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?
How have the numbers been placed in this Carroll diagram? Which
labels would you put on each row and column?
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
Try to stop your opponent from being able to split the piles of counters into unequal numbers. Can you find a strategy?
Can you complete this jigsaw of the multiplication square?
Work out how to light up the single light. What's the rule?
In this activity, the computer chooses a times table and shifts it. Can you work out the table and the shift each time?
The idea of this game is to add or subtract the two numbers on the dice and cover the result on the grid, trying to get a line of three. Are there some numbers that are good to aim for?
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?
Triangle numbers can be represented by a triangular array of
squares. What do you notice about the sum of identical triangle
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?
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
Can you fit the tangram pieces into the outline of this telephone?
Slide the pieces to move Khun Phaen past all the guards into the position on the right from which he can escape to freedom.
Practise your diamond mining skills and your x,y coordination in this homage to Pacman.
A generic circular pegboard resource.
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
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.
Investigate how the four L-shapes fit together to make an enlarged
L-shape. You could explore this idea with other shapes too.
Choose a symbol to put into the number sentence.
Can you fit the tangram pieces into the outline of Little Fung at the table?
Use the interactivity to find all the different right-angled
triangles you can make by just moving one corner of the starting
Investigate which numbers make these lights come on. What is the smallest number you can find that lights up all the lights?
Ahmed has some wooden planks to use for three sides of a rabbit run
against the shed. What quadrilaterals would he be able to make with
the planks of different lengths?
A game for 1 or 2 people. Use the interactive version, or play with friends. Try to round up as many counters as possible.
Can you fit the tangram pieces into the outlines of Mai Ling and Chi Wing?
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?
Can you spot the similarities between this game and other games you
know? The aim is to choose 3 numbers that total 15.
Start by putting one million (1 000 000) into the display of your
calculator. Can you reduce this to 7 using just the 7 key and add,
subtract, multiply, divide and equals as many times as you like?
Use the interactivity to investigate what kinds of triangles can be
drawn on peg boards with different numbers of pegs.
An interactive game for 1 person. You are given a rectangle with 50 squares on it. Roll the dice to get a percentage between 2 and 100. How many squares is this? Keep going until you get 100. . . .