A game that tests your understanding of remainders.

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?"

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

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 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.

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

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

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?

Here is a machine with four coloured lights. Can you develop a strategy to work out the rules controlling each light?

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?

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.

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

What is the smallest number of answers you need to reveal in order to work out the missing headers?

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?

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 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. . . .

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

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

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

Use the interactivity to create some steady rhythms. How could you create a rhythm which sounds the same forwards as it does backwards?

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

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...

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?

Can you complete this jigsaw of the multiplication square?

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?

What is the remainder when 2^2002 is divided by 7? What happens with different powers of 2?

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

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!

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

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

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.

Factors and Multiples game for an adult and child. How can you make sure you win this game?

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

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?

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?

Find a cuboid (with edges of integer values) that has a surface area of exactly 100 square units. Is there more than one? Can you find them all?

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

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

Using your knowledge of the properties of numbers, can you fill all the squares on the board?

There is a clock-face where the numbers have become all mixed up. Can you find out where all the numbers have got to from these ten statements?

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

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.

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

The five digit number A679B, in base ten, is divisible by 72. What are the values of A and B?

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

Use the interactivities to complete these Venn diagrams.

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?

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?