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

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

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?

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.

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?

A game that tests your understanding of remainders.

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

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?

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?

Can you explain the strategy for winning this game with any target?

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.

A jigsaw where pieces only go together if the fractions are equivalent.

Where will the point stop after it has turned through 30 000 degrees? I took out my calculator and typed 30 000 ÷ 360. How did this help?

Take a look at the video and try to find a sequence of moves that will take you back to zero.

It would be nice to have a strategy for disentangling any tangled ropes...

In this game the winner is the first to complete a row of three. Are some squares easier to land on than others?

Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?

How can we help students make sense of addition and subtraction of negative numbers?

Different combinations of the weights available allow you to make different totals. Which totals can you make?

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

Charlie has made a Magic V. Can you use his example to make some more? And how about Magic Ls, Ns and Ws?

Imagine a very strange bank account where you are only allowed to do two things...

Play this game to learn about adding and subtracting positive and negative numbers

Can you work out the solution to this tricky summation problem?

Can you work out how long it will take for John to walk to and from school?

The sum of 10 distinct positive integers is 100. What is the largest possible value of one of the numbers?

Can you work out how many quizzes have to be played before we have a winner?

How many positive two-digit numbers are there whose square and cube both end in the same digit?

What is the last digit in this calculation involving powers?

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

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.

At the beginning and end of Alan's journey, his milometer showed a palindromic number. Can you find his maximum possible average speed?

How many hot dogs did this hot dog lover eat on the first day of her binge?

77 is multiplied by another two-digit number with identical digits. What is the product?

How many questions did Sarah answer correctly in this multiple choice exam?

What is the difference between the sum of the first 2014 odd numbers and the sum of the first 2014 even numbers?

Choose some fractions and add them together. Can you get close to 1?