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

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How many ways can you find to put in operation signs (+, −, ×, ÷) to make 100?

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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?

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

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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?

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I'm thinking of a number. My number is both a multiple of 5 and a multiple of 6. What could my number be?

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

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

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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?

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

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Play this game and see if you can figure out the computer's chosen number.

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

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

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

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

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

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

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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.

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

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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?

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Take a look at the video and try to find a sequence of moves that will untangle the ropes.

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

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

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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?

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

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

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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.

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

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

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

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

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Aisha's division and subtraction calculations both gave the same answer! Can you find some more examples?

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

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Can you use the clues to complete these 5 by 5 Mathematical Sudokus?