Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?

Becky created a number plumber which multiplies by 5 and subtracts 4. What do you notice about the numbers that it produces? Can you explain your findings?

Look at three 'next door neighbours' amongst the counting numbers. Add them together. What do you notice?

For this challenge, you'll need to play Got It! Can you explain the strategy for winning this game with any target?

An investigation that gives you the opportunity to make and justify predictions.

Is it possible to draw a 5-pointed star without taking your pencil off the paper? Is it possible to draw a 6-pointed star in the same way without taking your pen off?

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?

This article for teachers describes how number arrays can be a useful reprentation for many number concepts.

Can you find any perfect numbers? Read this article to find out more...

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?

These red, yellow and blue spinners were each spun 45 times in total. Can you work out which numbers are on each spinner?

In this problem we are looking at sets of parallel sticks that cross each other. What is the least number of crossings you can make? And the greatest?

56 406 is the product of two consecutive numbers. What are these two numbers?

Benâ€™s class were cutting up number tracks. First they cut them into twos and added up the numbers on each piece. What patterns could they see?

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?

The sum of the first 'n' natural numbers is a 3 digit number in which all the digits are the same. How many numbers have been summed?

I throw three dice and get 5, 3 and 2. Add the scores on the three dice. What do you get? Now multiply the scores. What do you notice?

What is the lowest number which always leaves a remainder of 1 when divided by each of the numbers from 2 to 10?

Find the words hidden inside each of the circles by counting around a certain number of spaces to find each letter in turn.

The number 8888...88M9999...99 is divisible by 7 and it starts with the digit 8 repeated 50 times and ends with the digit 9 repeated 50 times. What is the value of the digit M?

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?

Work out Tom's number from the answers he gives his friend. He will only answer 'yes' or 'no'.

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.

Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?

Ben passed a third of his counters to Jack, Jack passed a quarter of his counters to Emma and Emma passed a fifth of her counters to Ben. After this they all had the same number of counters.

Can you find what the last two digits of the number $4^{1999}$ are?

Helen made the conjecture that "every multiple of six has more factors than the two numbers either side of it". Is this conjecture true?

I'm thinking of a number. When my number is divided by 5 the remainder is 4. When my number is divided by 3 the remainder is 2. Can you find my number?

Got It game for an adult and child. How can you play so that you know you will always win?

Can you work out what size grid you need to read our secret message?

Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?

Imagine we have four bags containing numbers from a sequence. What numbers can we make now?

Follow this recipe for sieving numbers and see what interesting patterns emerge.

How many integers between 1 and 1200 are NOT multiples of any of the numbers 2, 3 or 5?

Factor track is not a race but a game of skill. The idea is to go round the track in as few moves as possible, keeping to the rules.

The number 12 = 2^2 × 3 has 6 factors. What is the smallest natural number with exactly 36 factors?

Find some triples of whole numbers a, b and c such that a^2 + b^2 + c^2 is a multiple of 4. Is it necessarily the case that a, b and c must all be even? If so, can you explain why?

Play the divisibility game to create numbers in which the first two digits make a number divisible by 2, the first three digits make a number divisible by 3...

Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.

Can you work out some different ways to balance this equation?

A mathematician goes into a supermarket and buys four items. Using a calculator she multiplies the cost instead of adding them. How can her answer be the same as the total at the till?

Given the products of adjacent cells, can you complete this Sudoku?

Nine squares with side lengths 1, 4, 7, 8, 9, 10, 14, 15, and 18 cm can be fitted together to form a rectangle. What are the dimensions of the rectangle?

Can you complete this jigsaw of the multiplication square?

A three digit number abc is always divisible by 7 when 2a+3b+c is divisible by 7. Why?

Have a go at balancing this equation. Can you find different ways of doing it?

Imagine we have four bags containing a large number of 1s, 4s, 7s and 10s. What numbers can we make?

I am thinking of three sets of numbers less than 101. They are the red set, the green set and the blue set. Can you find all the numbers in the sets from these clues?

Can you see how these factor-multiple chains work? Find the chain which contains the smallest possible numbers. How about the largest possible numbers?

I am thinking of three sets of numbers less than 101. Can you find all the numbers in each set from these clues?