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

The clues for this Sudoku are the product of the numbers in adjacent squares.

Given the products of diagonally opposite cells - can you complete this Sudoku?

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

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?

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?

The items in the shopping basket add and multiply to give the same amount. What could their prices be?

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

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

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

A game for two people, or play online. Given a target number, say 23, and a range of numbers to choose from, say 1-4, players take it in turns to add to the running total to hit their target.

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?

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

The puzzle can be solved by finding the values of the unknown digits (all indicated by asterisks) in the squares of the $9\times9$ grid.

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?

Does this 'trick' for calculating multiples of 11 always work? Why or why not?

Can you order the digits from 1-3 to make a number which is divisible by 3 so when the last digit is removed it becomes a 2-figure number divisible by 2, and so on?

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

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

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

Are these statements always true, sometimes true or never true?

A collection of resources to support work on Factors and Multiples at Secondary level.

I added together some of my neighbours' house numbers. Can you explain the patterns I noticed?

A student in a maths class was trying to get some information from her teacher. She was given some clues and then the teacher ended by saying, "Well, how old are they?"

List any 3 numbers. It is always possible to find a subset of adjacent numbers that add up to a multiple of 3. Can you explain why and prove it?

Choose any 3 digits and make a 6 digit number by repeating the 3 digits in the same order (e.g. 594594). Explain why whatever digits you choose the number will always be divisible by 7, 11 and 13.

Can you explain the strategy for winning this game with any target?

Three people chose this as a favourite problem. It is the sort of problem that needs thinking time - but once the connection is made it gives access to many similar ideas.

Find some examples of pairs of numbers such that their sum is a factor of their product. eg. 4 + 12 = 16 and 4 × 12 = 48 and 16 is a factor of 48.

Can you find different ways of creating paths using these paving slabs?

Do you know a quick way to check if a number is a multiple of two? How about three, four or six?

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

Number problems at primary level to work on with others.

Number problems at primary level that may require resilience.

A number N is divisible by 10, 90, 98 and 882 but it is NOT divisible by 50 or 270 or 686 or 1764. It is also known that N is a factor of 9261000. What is N?

Ben, Jack and Emma passed counters to each other and ended with the same number of counters. How many did they start with?

Can you find a relationship between the number of dots on the circle and the number of steps that will ensure that all points are hit?

Can you find a way to identify times tables after they have been shifted up or down?

Can you find a cuboid that has a surface area of exactly 100 square units. Is there more than one? Can you find them all?

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

Find the highest power of 11 that will divide into 1000! exactly.

How can you use just one weighing to find out which box contains the lighter ten coins out of the ten boxes?

Explain why the arithmetic sequence 1, 14, 27, 40, ... contains many terms of the form 222...2 where only the digit 2 appears.

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

How many numbers less than 1000 are NOT divisible by either: a) 2 or 5; or b) 2, 5 or 7?

Play this game and see if you can figure out the computer's chosen number.

In this activity, the computer chooses a times table and shifts it. Can you work out the table and the shift each time?

Find the number which has 8 divisors, such that the product of the divisors is 331776.