How have the numbers been placed in this Carroll diagram? Which labels would you put on each row and column?
How could you arrange at least two dice in a stack so that the total of the visible spots is 18?
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.
Place the numbers 1 to 10 in the circles so that each number is the
difference between the two numbers just below it.
If you have only four weights, where could you place them in order
to balance this equaliser?
Here is a chance to play a version of the classic Countdown Game.
Can you each work out the number on your card? What do you notice?
How could you sort the cards?
Choose a symbol to put into the number sentence.
If you take a three by three square on a 1-10 addition square and
multiply the diagonally opposite numbers together, what is the
difference between these products. Why?
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?
Number problems at primary level that require careful consideration.
Can you be the first to complete a row of three?
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
Place the numbers from 1 to 9 in the squares below so that the difference between joined squares is odd. How many different ways can you do this?
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?
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
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?
Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.
Three children are going to buy some plants for their birthdays. They will plant them within circular paths. How could they do this?
Starting with the number 180, take away 9 again and again, joining up the dots as you go. Watch out - don't join all the dots!
Five numbers added together in pairs produce: 0, 2, 4, 4, 6, 8, 9, 11, 13, 15 What are the five numbers?
This challenge extends the Plants investigation so now four or more children are involved.
This challenging activity involves finding different ways to distribute fifteen items among four sets, when the sets must include three, four, five and six items.
Can you make a cycle of pairs that add to make a square number
using all the numbers in the box below, once and once only?
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?
A game for 2 players. Practises subtraction or other maths
Some Games That May Be Nice or Nasty for an adult and child. Use your knowledge of place value to beat your opponent.
These two group activities use mathematical reasoning - one is
numerical, one geometric.
Add the sum of the squares of four numbers between 10 and 20 to the
sum of the squares of three numbers less than 6 to make the square
of another, larger, number.
Can you make square numbers by adding two prime numbers together?
Ben has five coins in his pocket. How much money might he have?
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
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
A game for 2 people using a pack of cards Turn over 2 cards and try
to make an odd number or a multiple of 3.
Look carefully at the numbers. What do you notice? Can you make
another square using the numbers 1 to 16, that displays the same
This is an adding game for two players.
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
Ram divided 15 pennies among four small bags. He could then pay any sum of money from 1p to 15p without opening any bag. How many pennies did Ram put in each bag?
Ten cards are put into five envelopes so that there are two cards in each envelope. The sum of the numbers inside it is written on each envelope. What numbers could be inside the envelopes?
Investigate what happens when you add house numbers along a street
in different ways.
A game for 2 people. Use your skills of addition, subtraction, multiplication and division to blast the asteroids.
Do you notice anything about the solutions when you add and/or
subtract consecutive negative numbers?
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?
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?
There is a clock-face where the numbers have become all mixed up. Can you find out where all the numbers have got to from these ten statements?
Can you substitute numbers for the letters in these sums?
You have 5 darts and your target score is 44. How many different
ways could you score 44?
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?
An environment which simulates working with Cuisenaire rods.
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