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Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?
Four of these clues are needed to find the chosen number on this grid and four are true but do nothing to help in finding the number. Can you sort out the clues and find the number?
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?
These eleven shapes each stand for a different number. Can you use the number sentences to work out what they are?
This challenge is a game for two players. Choose two of the numbers to multiply or divide, then mark your answer on the number line. Can you get four in a row?
Ben and his mum are planting garlic. Can you find out how many cloves of garlic they might have had?
Can you see how these factor-multiple chains work? Find the chain which contains the smallest possible numbers. How about the largest possible numbers?
This big box multiplies anything that goes inside it by the same number. If you know the numbers that come out, what multiplication might be going on in the box?
Can you complete this jigsaw of the multiplication square?
Can you predict when you'll be clapping and when you'll be clicking if you start this rhythm? How about when a friend begins a new rhythm at the same time?
If you count from 1 to 20 and clap more loudly on the numbers in the two times table, as well as saying those numbers loudly, which numbers will be loud?
A game in which players take it in turns to choose a number. Can you block your opponent?
What do the numbers shaded in blue on this hundred square have in common? What do you notice about the pink numbers? How about the shaded numbers in the other squares?
Can you work out how to make each side of this balance equally balanced? You can put more than one weight on a hook.
If there are 3 squares in the ring, can you place three different numbers in them so that their differences are odd? Try with different numbers of squares around the ring. What do you notice?
Choose four of the numbers from 1 to 9 to put in the squares so that the differences between joined squares are odd.
Do you agree with Badger's statements? Is Badger's reasoning 'watertight'? Why or why not?
These sixteen children are standing in four lines of four, one behind the other. They are each holding a card with a number on it. Can you work out the missing numbers?
Frances and Rishi were given a bag of lollies. They shared them out evenly and had one left over. How many lollies could there have been in the bag?
Yasmin and Zach have some bears to share. Which numbers of bears can they share so that there are none left over?
One block is needed to make an up-and-down staircase, with one step up and one step down. How many blocks would be needed to build an up-and-down staircase with 5 steps up and 5 steps down?
Think of a number, square it and subtract your starting number. Is the number you're left with odd or even? How do the images help to explain this?
Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?
Can you replace the letters with numbers? Is there only one solution in each case?
Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?
I'm thinking of a number. My number is both a multiple of 5 and a multiple of 6. What could my number be?
We start with one yellow cube and build around it to make a 3x3x3 cube with red cubes. Then we build around that red cube with blue cubes and so on. How many cubes of each colour have we used?
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 make square numbers by adding two prime numbers together?
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
Can you work out the arrangement of the digits in the square so that the given products are correct? The numbers 1 - 9 may be used once and once only.
This multiplication uses each of the digits 0 - 9 once and once only. Using the information given, can you replace the stars in the calculation with figures?
Mrs Morgan, the class's teacher, pinned numbers onto the backs of three children. Use the information to find out what the three numbers were.
Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?
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 fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
The planet of Vuvv has seven moons. Can you work out how long it is between each super-eclipse?
Norrie sees two lights flash at the same time, then one of them flashes every 4th second, and the other flashes every 5th second. How many times do they flash together during a whole minute?
Find at least one way to put in some operation signs to make these digits come to 100.
48 is called an abundant number because it is less than the sum of its factors (without itself). Can you find some more abundant numbers?
On the planet Vuv there are two sorts of creatures. The Zios have 3 legs and the Zepts have 7 legs. The great planetary explorer Nico counted 52 legs. How many Zios and how many Zepts were there?
Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.
How would you find out how many football cards Catrina has collected?
Can you work out how many flowers there will be on the Amazing Splitting Plant after it has been growing for six weeks?
On Friday the magic plant was only 2 centimetres tall. Every day it doubled its height. How tall was it on Monday?
What happens if you join every second point on this circle? How about every third point? Try with different steps and see if you can predict what will happen.
How many different shaped boxes can you design for 36 sweets in one layer? Can you arrange the sweets so that no sweets of the same colour are next to each other in any direction?
Place four pebbles on the sand in the form of a square. Keep adding as few pebbles as necessary to double the area. How many extra pebbles are added each time?