Ben and his mum are planting garlic. Use the interactivity to help
you find out how many cloves of garlic they might have had.
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
Place eight dots on this diagram, so that there are only two dots
on each straight line and only two dots on each circle.
How many different triangles can you draw on the dotty grid which each have one dot in the middle?
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
Can you put the numbers from 1 to 15 on the circles so that no
consecutive numbers lie anywhere along a continuous straight line?
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?
Put 10 counters in a row. Find a way to arrange the counters into
five pairs, evenly spaced in a row, in just 5 moves, using the
Only one side of a two-slice toaster is working. What is the
quickest way to toast both sides of three slices of bread?
Use the clues to colour each square.
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?
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?
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?
A game for 2 people. Take turns placing a counter on the star. You
win when you have completed a line of 3 in your colour.
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?
Place eight queens on an chessboard (an 8 by 8 grid) so that none
can capture any of the others.
What happens when you try and fit the triomino pieces into these
Find out what a "fault-free" rectangle is and try to make some of
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.
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 ways can you find to do up all four buttons on my coat?
How about if I had five buttons? Six ...?
In a bowl there are 4 Chocolates, 3 Jellies and 5 Mints. Find a way
to share the sweets between the three children so they each get the
kind they like. Is there more than one way to do it?
Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.
How many different triangles can you make on a circular pegboard that has nine pegs?
How many different ways can you find to join three equilateral
triangles together? Can you convince us that you have found them
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
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?
How many triangles can you make using sticks that are 3cm, 4cm and 5cm long?
Here are some rods that are different colours. How could I make a dark green rod using yellow and white rods?
Jack has nine tiles. He put them together to make a square so that
two tiles of the same colour were not beside each other. Can you
find another way to do it?
Can you cover the camel with these pieces?
Cut four triangles from a square as shown in the picture. How many
different shapes can you make by fitting the four triangles back
How many different rhythms can you make by putting two drums on the
Place six toy ladybirds into the box so that there are two
ladybirds in every column and every row.
Arrange 3 red, 3 blue and 3 yellow counters into a three-by-three
square grid, so that there is only one of each colour in every row
and every column
An activity making various patterns with 2 x 1 rectangular tiles.
A merchant brings four bars of gold to a jeweller. How can the
jeweller use the scales just twice to identify the lighter, fake
Use the clues to find out who's who in the family, to fill in the family tree and to find out which of the family members are mathematicians and which are not.
George and Jim want to buy a chocolate bar. George needs 2p more
and Jim need 50p more to buy it. How much is the chocolate bar?
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?
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?
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?
How many triangles can you make on the 3 by 3 pegboard?
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.
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?
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?
Zumf makes spectacles for the residents of the planet Zargon, who
have either 3 eyes or 4 eyes. How many lenses will Zumf need to
make all the different orders for 9 families?
In this maze of hexagons, you start in the centre at 0. The next
hexagon must be a multiple of 2 and the next a multiple of 5. What
are the possible paths you could take?
A package contains a set of resources designed to develop
students’ mathematical thinking. This package places a
particular emphasis on “being systematic” and is
designed to meet. . . .