An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.

Take any four digit number. Move the first digit to the 'back of the queue' and move the rest along. Now add your two numbers. What properties do your answers always have?

Charlie and Abi put a counter on 42. They wondered if they could visit all the other numbers on their 1-100 board, moving the counter using just these two operations: x2 and -5. What do you think?

How many solutions can you find to this sum? Each of the different letters stands for a different number.

Can you find six numbers to go in the Daisy from which you can make all the numbers from 1 to a number bigger than 25?

Find at least one way to put in some operation signs (+ - x ÷) to make these digits come to 100.

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.

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?

Which set of numbers that add to 10 have the largest product?

A cinema has 100 seats. Show how it is possible to sell exactly 100 tickets and take exactly £100 if the prices are £10 for adults, 50p for pensioners and 10p for children.

A car's milometer reads 4631 miles and the trip meter has 173.3 on it. How many more miles must the car travel before the two numbers contain the same digits in the same order?

Can you arrange these numbers into 7 subsets, each of three numbers, so that when the numbers in each are added together, they make seven consecutive numbers?

Watch our videos of multiplication methods that you may not have met before. Can you make sense of them?

If a sum invested gains 10% each year how long before it has doubled its value?

Your school has been left a million pounds in the will of an ex- pupil. What model of investment and spending would you use in order to ensure the best return on the money?

A game that tests your understanding of remainders.

Here is a chance to play a version of the classic Countdown Game.

Who said that adding, subtracting, multiplying and dividing couldn't be fun?

Mathematicians are always looking for efficient methods for solving problems. How efficient can you be?

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

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

Can you rank these sets of quantities in order, from smallest to largest? Can you provide convincing evidence for your rankings?

Just because a problem is impossible doesn't mean it's difficult...

Can you find ways to put numbers in the overlaps so the rings have equal totals?

A collection of short Stage 3 and 4 problems on number operations and calculation methods.