Filter by: Content type: ALL Problems Articles Games Stage: All Stage 1&2 Stage 2&3 Stage 3&4 Stage 4&5 Challenge level:
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?
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?
If you have only four weights, where could you place them in order to balance this equaliser?
This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.
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?
An environment which simulates working with Cuisenaire rods.
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?
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!
Imagine a wheel with different markings painted on it at regular intervals. Can you predict the colour of the 18th mark? The 100th mark?
Try to stop your opponent from being able to split the piles of counters into unequal numbers. Can you find a strategy?
Here is a chance to play a version of the classic Countdown Game.
How have the numbers been placed in this Carroll diagram? Which labels would you put on each row and column?
Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.
Can you complete this jigsaw of the multiplication square?
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?
Work out how to light up the single light. What's the rule?
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?
Can you make a cycle of pairs that add to make a square number using all the numbers in the box below, once and once only?
Hover your mouse over the counters to see which ones will be removed. Click to remover them. The winner is the last one to remove a counter. How you can make sure you win?
You have 4 red and 5 blue counters. How many ways can they be placed on a 3 by 3 grid so that all the rows columns and diagonals have an even number of red counters?
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?
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
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?
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.
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?
Choose 13 spots on the grid. Can you work out the scoring system? What is the maximum possible score?
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....?
Use the interactivity to create some steady rhythms. How could you create a rhythm which sounds the same forwards as it does backwards?
Use the sightings of the lion to guess the location of its lair.
Choose a symbol to put into the number sentence.
Investigate which numbers make these lights come on. What is the smallest number you can find that lights up all the lights?
Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?
Use the interactivities to complete these Venn diagrams.
Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.
This problem is based on a code using two different prime numbers less than 10. You'll need to multiply them together and shift the alphabet forwards by the result. Can you decipher the code?
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?
A card pairing game involving knowledge of simple ratio.
What are the coordinates of the coloured dots that mark out the tangram? Try changing the position of the origin. What happens to the coordinates now?
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. . . .
There are nine teddies in Teddy Town - three red, three blue and three yellow. There are also nine houses, three of each colour. Can you put them on the map of Teddy Town according to the rules?
Can you find all the different triangles on these peg boards, and find their angles?
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 to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.
How can the same pieces of the tangram make this bowl before and after it was chipped? Use the interactivity to try and work out what is going on!
Use the Cuisenaire rods environment to investigate ratio. Can you find pairs of rods in the ratio 3:2? How about 9:6?
How many different triangles can you make on a circular pegboard that has nine pegs?
Find out how we can describe the "symmetries" of this triangle and investigate some combinations of rotating and flipping it.
What shaped overlaps can you make with two circles which are the same size? What shapes are 'left over'? What shapes can you make when the circles are different sizes?
A train building game for 2 players.
Find out what a "fault-free" rectangle is and try to make some of your own.