Investigate the different distances of these car journeys and find
out how long they take.
Start with four numbers at the corners of a square and put the
total of two corners in the middle of that side. Keep going... Can
you estimate what the size of the last four numbers will be?
A lady has a steel rod and a wooden pole and she knows the length
of each. How can she measure out an 8 unit piece of pole?
This article for teachers suggests ideas for activities built around 10 and 2010.
There are 78 prisoners in a square cell block of twelve cells. The
clever prison warder arranged them so there were 25 along each wall
of the prison block. How did he do it?
Twizzle, a female giraffe, needs transporting to another zoo. Which
route will give the fastest journey?
Place six toy ladybirds into the box so that there are two
ladybirds in every column and every row.
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
If you have only four weights, where could you place them in order
to balance this equaliser?
You have two egg timers. One takes 4 minutes exactly to empty and
the other takes 7 minutes. What times in whole minutes can you
measure and how?
During the third hour after midnight the hands on a clock point in
the same direction (so one hand is over the top of the other). At
what time, to the nearest second, does this happen?
Place the numbers 1 to 6 in the circles so that each number is the
difference between the two numbers just below it.
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?
These caterpillars have 16 parts. What different shapes do they make if each part lies in the small squares of a 4 by 4 square?
This problem is based on the story of the Pied Piper of Hamelin. Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!
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?
Find your way through the grid starting at 2 and following these
operations. What number do you end on?
Which times on a digital clock have a line of symmetry? Which look
the same upside-down? You might like to try this investigation and
How could you put eight beanbags in the hoops so that there are
four in the blue hoop, five in the red and six in the yellow? Can
you find all the ways of doing this?
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
You have 5 darts and your target score is 44. How many different
ways could you score 44?
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?
In Sam and Jill's garden there are two sorts of ladybirds with 7 spots or 4 spots. What numbers of total spots can you make?
On the table there is a pile of oranges and lemons that weighs
exactly one kilogram. Using the information, can you work out how
many lemons there are?
This magic square has operations written in it, to make it into a
maze. Start wherever you like, go through every cell and go out a
total of 15!
Winifred Wytsh bought a box each of jelly babies, milk jelly bears,
yellow jelly bees and jelly belly beans. In how many different ways
could she make a jolly jelly feast with 32 legs?
There are 44 people coming to a dinner party. There are 15 square
tables that seat 4 people. Find a way to seat the 44 people using
all 15 tables, with no empty places.
Arrange eight of the numbers between 1 and 9 in the Polo Square
below so that each side adds to the same total.
There are to be 6 homes built on a new development site. They could
be semi-detached, detached or terraced houses. How many different
combinations of these can you find?
In this section from a calendar, put a square box around the 1st,
2nd, 8th and 9th. Add all the pairs of numbers. What do you notice
about the answers?
Cherri, Saxon, Mel and Paul are friends. They are all different
ages. Can you find out the age of each friend using the
On Planet Plex, there are only 6 hours in the day. Can you answer
these questions about how Arog the Alien spends his day?
If the answer's 2010, what could the question be?
Can you arrange 5 different digits (from 0 - 9) in the cross in the
What happens when you add the digits of a number then multiply the
result by 2 and you keep doing this? You could try for different
numbers and different rules.
What is happening at each box in these machines?
In this game for two players, the aim is to make a row of four coins which total one dollar.
This challenge is about finding the difference between numbers which have the same tens digit.
Investigate the different distances of these car journeys and find out how long they take.
In this calculation, the box represents a missing digit. What could the digit be? What would the solution be in each case?
There were chews for 2p, mini eggs for 3p, Chocko bars for 5p and
lollypops for 7p in the sweet shop. What could each of the children
buy with their money?
Where can you draw a line on a clock face so that the numbers on
both sides have the same total?
Two children made up a game as they walked along the garden paths.
Can you find out their scores? Can you find some paths of your own?
Mrs Morgan, the class's teacher, pinned numbers onto the backs of
three children. Use the information to find out what the three
This big box adds something to any number that goes into it. If you know the numbers that come out, what addition might be going on in the box?
Can you arrange fifteen dominoes so that all the touching domino
pieces add to 6 and the ends join up? Can you make all the joins
add to 7?
In this game for two players, the idea is to take it in turns to choose 1, 3, 5 or 7. The winner is the first to make the total 37.
This challenge focuses on finding the sum and difference of pairs of two-digit numbers.
Can you follow the rule to decode the messages?
In your bank, you have three types of coins. The number of spots shows how much they are worth. Can you choose coins to exchange with the groups given to make the same total?