How many different triangles can you make on a circular pegboard that has nine pegs?
How many different triangles can you draw on the dotty grid which each have one dot in the middle?
Can you find all the different triangles on these peg boards, and
find their angles?
How many triangles can you make on the 3 by 3 pegboard?
How many triangles can you make using sticks that are 3cm, 4cm and 5cm long?
Ben and his mum are planting garlic. Use the interactivity to help
you find out how many cloves of garlic they might have had.
Place the numbers 1 to 10 in the circles so that each number is the
difference between the two numbers just below it.
Use the clues to colour each square.
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?
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
What happens when you try and fit the triomino pieces into these
Can you cover the camel with these pieces?
Place the numbers 1 to 6 in the circles so that each number is the
difference between the two numbers just below it.
How many different ways can you find to join three equilateral
triangles together? Can you convince us that you have found them
Can you find all the different ways of lining up these Cuisenaire
Here are some rods that are different colours. How could I make a dark green rod using yellow and white rods?
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....?
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?
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?
Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.
Cut four triangles from a square as shown in the picture. How many
different shapes can you make by fitting the four triangles back
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 trains can you make which are the same length as Matt's, using rods that are identical?
Can you work out how to balance this equaliser? You can put more
than one weight on a hook.
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?
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
How many different rhythms can you make by putting two drums on the
Can you put the numbers from 1 to 15 on the circles so that no
consecutive numbers lie anywhere along a continuous straight line?
How many DIFFERENT quadrilaterals can be made by joining the dots
on the 8-point circle?
Suppose we allow ourselves to use three numbers less than 10 and
multiply them together. How many different products can you find?
How do you know you've got them all?
Investigate the different ways you could split up these rooms so
that you have double the number.
The Vikings communicated in writing by making simple scratches on
wood or stones called runes. Can you work out how their code works
using the table of the alphabet?
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?
Arrange the four number cards on the grid, according to the rules,
to make a diagonal, vertical or horizontal line.
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.
You cannot choose a selection of ice cream flavours that includes
totally what someone has already chosen. Have a go and find all the
different ways in which seven children can have ice cream.
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?
Place the numbers 1 to 8 in the circles so that no consecutive
numbers are joined by a line.
There are 4 jugs which hold 9 litres, 7 litres, 4 litres and 2
litres. Find a way to pour 9 litres of drink from one jug to
another until you are left with exactly 3 litres in three of the
Can you put plus signs in so this is true? 1 2 3 4 5 6 7 8 9 = 99
How many ways can you do it?
I was in my car when I noticed a line of four cars on the lane next
to me with number plates starting and ending with J, K, L and M.
What order were they in?
Systematically explore the range of symmetric designs that can be
created by shading parts of the motif below. Use normal square
lattice paper to record your results.
Investigate all the different squares you can make on this 5 by 5
grid by making your starting side go from the bottom left hand
point. Can you find out the areas of all these squares?
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?
Place eight queens on an chessboard (an 8 by 8 grid) so that none
can capture any of the others.
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?
There are seven pots of plants in a greenhouse. They have lost their labels. Perhaps you can help re-label them.
These are the faces of Will, Lil, Bill, Phil and Jill. Use the clues to work out which name goes with each face.
An activity making various patterns with 2 x 1 rectangular tiles.