Make one big triangle so the numbers that touch on the small triangles add to 10. You could use the interactivity to help you.
Imagine a pyramid which is built in square layers of small cubes. If we number the cubes from the top, starting with 1, can you picture which cubes are directly below this first cube?
Find your way through the grid starting at 2 and following these
operations. What number do you end on?
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. . . .
In a square in which the houses are evenly spaced, numbers 3 and 10
are opposite each other. What is the smallest and what is the
largest possible number of houses in the square?
A dog is looking for a good place to bury his bone. Can you work
out where he started and ended in each case? What possible routes
could he have taken?
A magician took a suit of thirteen cards and held them in his hand
face down. Every card he revealed had the same value as the one he
had just finished spelling. How did this work?
What is the smallest cuboid that you can put in this box so that
you cannot fit another that's the same into it?
This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
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.
Building up a simple Celtic knot. Try the interactivity or download
the cards or have a go on squared paper.
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
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?
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?
Use the three triangles to fill these outline shapes. Perhaps you can create some of your own shapes for a friend to fill?
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?
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?
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?
How many DIFFERENT quadrilaterals can be made by joining the dots
on the 8-point circle?
Design an arrangement of display boards in the school hall which fits the requirements of different people.
If you split the square into these two pieces, it is possible to fit the pieces together again to make a new shape. How many new shapes can you make?
Here you see the front and back views of a dodecahedron. Each
vertex has been numbered so that the numbers around each pentagonal
face add up to 65. Can you find all the missing numbers?
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?
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
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 cover the camel with these pieces?
What is the best way to shunt these carriages so that each train
can continue its journey?
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?
Cut four triangles from a square as shown in the picture. How many
different shapes can you make by fitting the four triangles back
What happens when you try and fit the triomino pieces into these
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?
How many different cuboids can you make when you use four CDs or
DVDs? How about using five, then six?
How many different triangles can you make on a circular pegboard that has nine pegs?
Can you make a 3x3 cube with these shapes made from small cubes?
This article for teachers describes how modelling number properties
involving multiplication using an array of objects not only allows
children to represent their thinking with concrete materials,. . . .
How many different ways can you find of fitting five hexagons
together? How will you know you have found all the ways?
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?
An activity centred around observations of dots and how we visualise number arrangement patterns.
One face of a regular tetrahedron is painted blue and each of the
remaining faces are painted using one of the colours red, green or
yellow. How many different possibilities are there?
This article introduces the idea of generic proof for younger children and illustrates how one example can offer a proof of a general result through unpacking its underlying structure.
A toy has a regular tetrahedron, a cube and a base with triangular
and square hollows. If you fit a shape into the correct hollow a
bell rings. How many times does the bell ring in a complete game?
Can you find ways of joining cubes together so that 28 faces are
In this town, houses are built with one room for each person. There
are some families of seven people living in the town. In how many
different ways can they build their houses?
Can you predict when you'll be clapping and when you'll be clicking
if you start this rhythm? How about when a friend begins a new
rhythm at the same time?
How can you arrange these 10 matches in four piles so that when you
move one match from three of the piles into the fourth, you end up
with the same arrangement?
Here are some arrangements of circles. How many circles would I need to make the next size up for each? Can you create your own arrangement and investigate the number of circles it needs?
In each of the pictures the invitation is for you to: Count what you see. Identify how you think the pattern would continue.
If you can post the triangle with either the blue or yellow colour face up, how many ways can it be posted altogether?
Exchange the positions of the two sets of counters in the least possible number of moves
A game for 2 players. Given a board of dots in a grid pattern, players take turns drawing a line by connecting 2 adjacent dots. Your goal is to complete more squares than your opponent.