A game that tests your understanding of remainders.

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

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.

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?

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

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

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

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

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

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.

Andrew decorated 20 biscuits to take to a party. He lined them up and put icing on every second biscuit and different decorations on other biscuits. How many biscuits weren't decorated?

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

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. . . .

Can you complete this jigsaw of the multiplication square?

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!

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

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

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...

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

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

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?

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

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?"

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

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

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?

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

Find the frequency distribution for ordinary English, and use it to help you crack the code.

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

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

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?

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

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

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

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

Use the interactivities to complete these Venn diagrams.

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

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.

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?

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

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?

Rectangles are considered different if they vary in size or have different locations. How many different rectangles can be drawn on a chessboard?

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

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?

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

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

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?