10 space travellers are waiting to board their spaceships. There are two rows of seats in the waiting room. Using the rules, where are they all sitting? Can you find all the possible ways?
What is the greatest number of counters you can place on the grid below without four of them lying at the corners of a square?
Chandra, Jane, Terry and Harry ordered their lunches from the sandwich shop. Use the information below to find out who ordered each sandwich.
Imagine that the puzzle pieces of a jigsaw are roughly a rectangular shape and all the same size. How many different puzzle pieces could there be?
Use the clues to colour each square.
Building up a simple Celtic knot. Try the interactivity or download the cards or have a go on squared paper.
The Red Express Train usually has five red carriages. How many ways can you find to add two blue carriages?
El Crico the cricket has to cross a square patio to get home. He can jump the length of one tile, two tiles and three tiles. Can you find a path that would get El Crico home in three jumps?
What happens when you try and fit the triomino pieces into these two grids?
Find your way through the grid starting at 2 and following these operations. What number do you end on?
In how many ways can you fit two of these yellow triangles together? Can you predict the number of ways two blue triangles can be fitted together?
Lorenzie was packing his bag for a school trip. He packed four shirts and three pairs of pants. "I will be able to have a different outfit each day", he said. How many days will Lorenzie be away?
What is the best way to shunt these carriages so that each train can continue its journey?
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?
An activity making various patterns with 2 x 1 rectangular tiles.
Swap the stars with the moons, using only knights' moves (as on a chess board). What is the smallest number of moves possible?
Can you shunt the trucks so that the Cattle truck and the Sheep truck change places and the Engine is back on the main line?
Can you find out in which order the children are standing in this line?
Take a rectangle of paper and fold it in half, and half again, to make four smaller rectangles. How many different ways can you fold it up?
My briefcase has a three-number combination lock, but I have forgotten the combination. I remember that there's a 3, a 5 and an 8. How many possible combinations are there to try?
This problem focuses on Dienes' Logiblocs. What is the same and what is different about these pairs of shapes? Can you describe the shapes in the picture?
The brown frog and green frog want to swap places without getting wet. They can hop onto a lily pad next to them, or hop over each other. How could they do it?
Using different numbers of sticks, how many different triangles are you able to make? Can you make any rules about the numbers of sticks that make the most triangles?
These activities focus on finding all possible solutions so if you work in a systematic way, you won't leave any out.
These activities lend themselves to systematic working in the sense that it helps if you have an ordered approach.
Take 5 cubes of one colour and 2 of another colour. How many different ways can you join them if the 5 must touch the table and the 2 must not touch the table?
These practical challenges are all about making a 'tray' and covering it with paper.
Can you work out how many cubes were used to make this open box? What size of open box could you make if you had 112 cubes?
Design an arrangement of display boards in the school hall which fits the requirements of different people.
These activities lend themselves to systematic working in the sense that it helps to have an ordered approach.
These activities focus on finding all possible solutions so working in a systematic way will ensure none are left out.
Kate has eight multilink cubes. She has two red ones, two yellow, two green and two blue. She wants to fit them together to make a cube so that each colour shows on each face just once.
Can you find all the different ways of lining up these Cuisenaire rods?
What is the smallest cuboid that you can put in this box so that you cannot fit another that's the same into it?
How many models can you find which obey these rules?
How many DIFFERENT quadrilaterals can be made by joining the dots on the 8-point circle?
A tetromino is made up of four squares joined edge to edge. Can this tetromino, together with 15 copies of itself, be used to cover an eight by eight chessboard?
How many triangles can you make on the 3 by 3 pegboard?
What is the least number of moves you can take to rearrange the bears so that no bear is next to a bear of the same colour?
Explore the different snakes that can be made using 5 cubes.
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....?
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?
Are all the possible combinations of two shapes included in this set of 27 cards? How do you know?
This task, written for the National Young Mathematicians' Award 2016, involves open-topped boxes made with interlocking cubes. Explore the number of units of paint that are needed to cover the boxes. . . .
Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.
How can you arrange the 5 cubes so that you need the smallest number of Brush Loads of paint to cover them? Try with other numbers of cubes as well.
How can you put five cereal packets together to make different shapes if you must put them face-to-face?
Use the information to describe these marbles. What colours must be on marbles that sparkle when rolling but are dark inside?
The ancient Egyptians were said to make right-angled triangles using a rope with twelve equal sections divided by knots. What other triangles could you make if you had a rope like this?