How have the numbers been placed in this Carroll diagram? Which
labels would you put on each row and column?
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?
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.
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.
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 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?
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?
Can you each work out the number on your card? What do you notice?
How could you sort the cards?
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?
Choose a symbol to put into the number sentence.
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
If you have only four weights, where could you place them in order
to balance this equaliser?
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!
Some Games That May Be Nice or Nasty for an adult and child. Use your knowledge of place value to beat your opponent.
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?
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
What do the digits in the number fifteen add up to? How many other
numbers have digits with the same total but no zeros?
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
Here is a chance to play a version of the classic Countdown Game.
A group of children are using measuring cylinders but they lose the
labels. Can you help relabel them?
Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.
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.
Have a go at this game which involves throwing two dice and adding
their totals. Where should you place your counters to be more
likely to win?
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
Tim had nine cards each with a different number from 1 to 9 on it.
How could he have put them into three piles so that the total in
each pile was 15?
Write the numbers up to 64 in an interesting way so that the shape they make at the end is interesting, different, more exciting ... than just a square.
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!
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?
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?
Three children are going to buy some plants for their birthdays. They will plant them within circular paths. How could they do this?
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?
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?
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.
These two group activities use mathematical reasoning - one is
numerical, one geometric.
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.
Who said that adding couldn't be fun?
Exactly 195 digits have been used to number the pages in a book.
How many pages does the book have?
Number problems at primary level that require careful consideration.
What do you notice about the date 03.06.09? Or 08.01.09? This
challenge invites you to investigate some interesting dates
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?
A game for 2 players. Practises subtraction or other maths
Ben has five coins in his pocket. How much money might he have?
In this game, you can add, subtract, multiply or divide the numbers
on the dice. Which will you do so that you get to the end of the
number line first?
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?
Can you arrange 5 different digits (from 0 - 9) in the cross in the
This challenge focuses on finding the sum and difference of pairs of two-digit numbers.
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?
Cherri, Saxon, Mel and Paul are friends. They are all different
ages. Can you find out the age of each friend using the
Imagine a pyramid which is built in square layers of small cubes. If we number the cubes from the top, starting with 1, can you picture which cubes are directly below this first cube?