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?

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

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...

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!

Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.

This package contains a collection of problems from the NRICH website that could be suitable for students who have a good understanding of Factors and Multiples and who feel ready to take on some. . . .

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?

A game for 2 or more people. Starting with 100, subratct a number from 1 to 9 from the total. You score for making an odd number, a number ending in 0 or a multiple of 6.

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.

A game that tests your understanding of remainders.

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.

If you have only four weights, where could you place them in order to balance this equaliser?

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?

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

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?

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?"

Can you complete this jigsaw of the multiplication square?

A game in which players take it in turns to choose a number. Can you block your opponent?

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

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

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?

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?

Can you order the digits from 1-6 to make a number which is divisible by 6 so when the last digit is removed it becomes a 5-figure number divisible by 5, and so on?

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

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?

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

Each light in this interactivity turns on according to a rule. What happens when you enter different numbers? Can you find the smallest number that lights up all four lights?

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.

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

Imagine a wheel with different markings painted on it at regular intervals. Can you predict the colour of the 18th mark? The 100th mark?

Using the digits 1, 2, 3, 4, 5, 6, 7 and 8, mulitply a two two digit numbers are multiplied to give a four digit number, so that the expression is correct. How many different solutions can you find?

Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.

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

A game for 2 people using a pack of cards Turn over 2 cards and try to make an odd number or a multiple of 3.

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

The planet of Vuvv has seven moons. Can you work out how long it is between each super-eclipse?

Suppose we allow ourselves to use three numbers less than 10 and multiply them together. How many different products can you find? How do you know you've got them all?

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?

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

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

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?

An environment which simulates working with Cuisenaire rods.

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?

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?

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

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?

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

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?