Can you draw a continuous line through 16 numbers on this grid so
that the total of the numbers you pass through is as high as
There are nasty versions of this dice game but we'll start with the nice ones...
Some Games That May Be Nice or Nasty for an adult and child. Use your knowledge of place value to beat your oponent.
Find the sum of all three-digit numbers each of whose digits is
Choose four different digits from 1-9 and put one in each box so that the resulting four two-digit numbers add to a total of 100.
This is an adding game for two players.
What is the sum of all the three digit whole numbers?
There are over sixty different ways of making 24 by adding,
subtracting, multiplying and dividing all four numbers 4, 6, 6 and
8 (using each number only once). How many can you find?
The picture shows a lighthouse and many underwater creatures. If
you know the markings on the lighthouse are 1m apart, can you work
out the distances between some of the different creatures?
How have the numbers been placed in this Carroll diagram? Which
labels would you put on each row and column?
In this 100 square, look at the green square which contains the numbers 2, 3, 12 and 13. What is the sum of the numbers that are diagonally opposite each other? What do you notice?
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
Start by putting one million (1 000 000) into the display of your
calculator. Can you reduce this to 7 using just the 7 key and add,
subtract, multiply, divide and equals as many times as you like?
Place this "worm" on the 100 square and find the total of the four
squares it covers. Keeping its head in the same place, what other
totals can you make?
Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?
Find out what a Deca Tree is and then work out how many leaves
there will be after the woodcutter has cut off a trunk, a branch, a
twig and a leaf.
This problem is based on a code using two different prime numbers
less than 10. You'll need to multiply them together and shift the
alphabet forwards by the result. Can you decipher the code?
The clockmaker's wife cut up his birthday cake to look like a clock
face. Can you work out who received each piece?
A game for 2 players. Practises subtraction or other maths
Can you substitute numbers for the letters in these sums?
The Scot, John Napier, invented these strips about 400 years ago to
help calculate multiplication and division. Can you work out how to
use Napier's bones to find the answer to these multiplications?
Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.
Place the numbers 1 to 10 in the circles so that each number is the
difference between the two numbers just below it.
Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.
What do you notice about the date 03.06.09? Or 08.01.09? This
challenge invites you to investigate some interesting dates
A game for 2 people. Use your skills of addition, subtraction, multiplication and division to blast the asteroids.
What do the digits in the number fifteen add up to? How many other
numbers have digits with the same total but no zeros?
Got It game for an adult and child. How can you play so that you know you will always win?
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.
Strike it Out game for an adult and child. Can you stop your partner from being able to go?
Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.
Here is a chance to play a version of the classic Countdown Game.
What is happening at each box in these machines?
Investigate the different distances of these car journeys and find out how long they take.
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?
Using 3 rods of integer lengths, none longer than 10 units and not
using any rod more than once, you can measure all the lengths in
whole units from 1 to 10 units. How many ways can you do this?
Vera is shopping at a market with these coins in her purse. Which
things could she give exactly the right amount for?
Lolla bought a balloon at the circus. She gave the clown six coins
to pay for it. What could Lolla have paid for the balloon?
You have 5 darts and your target score is 44. How many different
ways could you score 44?
Mrs Morgan, the class's teacher, pinned numbers onto the backs of
three children. Use the information to find out what the three
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!
This article suggests some ways of making sense of calculations involving positive and negative numbers.
Where can you draw a line on a clock face so that the numbers on
both sides have the same total?
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?
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?
This challenge focuses on finding the sum and difference of pairs of two-digit numbers.
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?
Katie had a pack of 20 cards numbered from 1 to 20. She arranged
the cards into 6 unequal piles where each pile added to the same
total. What was the total and how could this be done?
Find the sum and difference between a pair of two-digit numbers. Now find the sum and difference between the sum and difference! What happens?
A game for 2 or more players with a pack of cards. Practise your
skills of addition, subtraction, multiplication and division to hit
the target score.