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

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

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

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.

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

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?

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?

How many ways can you find to put in operation signs (+ - x ÷) to make 100?

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

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?

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

Can all unit fractions be written as the sum of two unit fractions?

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

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?

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?

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?

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?

The Egyptians expressed all fractions as the sum of different unit fractions. Here is a chance to explore how they could have written different fractions.

The Egyptians expressed all fractions as the sum of different unit fractions. The Greedy Algorithm might provide us with an efficient way of doing this.

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?

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.

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?

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

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

Use 2 straight lines to split the clock face into 3 parts so that the sums of the numbers in each of the parts are equal.

Jane accidentally multiplied by 54 instead of 45, and her answer was 198 too big. What number did she multiply 54 by?

What is the last digit in this calculation involving powers?