Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.
Can you make a train the same length as Laura's but using three differently coloured rods? Is there only one way of doing 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.
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 put the numbers 1 to 8 into the circles so that the four calculations are correct?
Exactly 195 digits have been used to number the pages in a book. How many pages does the book have?
Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.
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?
This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.
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!
Number problems at primary level that require careful consideration.
You have 5 darts and your target score is 44. How many different ways could you score 44?
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.
This challenge extends the Plants investigation so now four or more children are involved.
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?
Look carefully at the numbers. What do you notice? Can you make another square using the numbers 1 to 16, that displays the same properties?
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 each work out the number on your card? What do you notice? How could you sort the cards?
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 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!
At the beginning of May Tom put his tomato plant outside. On the same day he sowed a bean in another pot. When will the two be the same height?
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?
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?
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 see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?
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?
This task, written for the National Young Mathematicians' Award 2016, focuses on 'open squares'. What would the next five open squares look like?
How many starfish could there be on the beach, and how many children, if I can see 28 arms?
Make your own double-sided magic square. But can you complete both sides once you've made the pieces?
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 jugs.
Choose a symbol to put into the number sentence.
What do the digits in the number fifteen add up to? How many other numbers have digits with the same total but no zeros?
In how many ways could Mrs Beeswax put ten coins into her three puddings so that each pudding ended up with at least two coins?
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?
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
What do you notice about the date 03.06.09? Or 08.01.09? This challenge invites you to investigate some interesting dates yourself.
Got It game for an adult and child. How can you play so that you know you will always win?
A group of children are using measuring cylinders but they lose the labels. Can you help relabel them?
This task follows on from Build it Up and takes the ideas into three dimensions!
This task, written for the National Young Mathematicians' Award 2016, invites you to explore the different combinations of scores that you might get on these dart boards.
Using the statements, can you work out how many of each type of rabbit there are in these pens?
We can arrange dots in a similar way to the 5 on a dice and they usually sit quite well into a rectangular shape. How many altogether in this 3 by 5? What happens for other sizes?
Suppose there is a train with 24 carriages which are going to be put together to make up some new trains. Can you find all the ways that this can be done?
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?
Use these head, body and leg pieces to make Robot Monsters which are different heights.
Can you arrange 5 different digits (from 0 - 9) in the cross in the way described?
Cherri, Saxon, Mel and Paul are friends. They are all different ages. Can you find out the age of each friend using the information?
Can you use the numbers on the dice to reach your end of the number line before your partner beats you?