Choose a symbol to put into the number sentence.
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?
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?
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!
If you have only four weights, where could you place them in order to balance this equaliser?
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?
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?
Use the information about Sally and her brother to find out how many children there are in the Brown family.
Can you hang weights in the right place to make the equaliser balance?
Find your way through the grid starting at 2 and following these operations. What number do you end on?
Place the numbers 1 to 6 in the circles so that each number is the difference between the two numbers just below it.
Make your own double-sided magic square. But can you complete both sides once you've made the pieces?
Here is a chance to play a version of the classic Countdown Game.
Make one big triangle so the numbers that touch on the small triangles add to 10. You could use the interactivity to help you.
This task, written for the National Young Mathematicians' Award 2016, involves open-topped boxes made with interlocking cubes. Explore the number of units of paint that are needed to cover the boxes. . . .
Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.
Use the number weights to find different ways of balancing the equaliser.
Choose four of the numbers from 1 to 9 to put in the squares so that the differences between joined squares are odd.
If you hang two weights on one side of this balance, in how many different ways can you hang three weights on the other side for it to be balanced?
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.
What do you notice about the date 03.06.09? Or 08.01.09? This challenge invites you to investigate some interesting dates yourself.
The idea of this game is to add or subtract the two numbers on the dice and cover the result on the grid, trying to get a line of three. Are there some numbers that are good to aim for?
Some Games That May Be Nice or Nasty for an adult and child. Use your knowledge of place value to beat your opponent.
This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.
There are nasty versions of this dice game but we'll start with the nice ones...
Can you arrange 5 different digits (from 0 - 9) in the cross in the way described?
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.
First Connect Three game for an adult and child. Use the dice numbers and either addition or subtraction to get three numbers in a straight line.
How have the numbers been placed in this Carroll diagram? Which labels would you put on each row and column?
In a square in which the houses are evenly spaced, numbers 3 and 10 are opposite each other. What is the smallest and what is the largest possible number of houses in the square?
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?
Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.
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 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?
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?
Can you each work out the number on your card? What do you notice? How could you sort the cards?
Ahmed is making rods using different numbers of cubes. Which rod is twice the length of his first rod?
Use the interactivities to fill in these Carroll diagrams. How do you know where to place the numbers?
Can you use the numbers on the dice to reach your end of the number line before your partner beats you?
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?
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?
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.
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?
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.
Using the statements, can you work out how many of each type of rabbit there are in these pens?
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
An environment which simulates working with Cuisenaire rods.