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There are 78 NRICH Mathematical resources connected to DMC, you may find related items under Developing mathematical creativity.
Broad Topics > Developing mathematical creativity > DMCHave a go at making a few of these shapes from paper in different sizes. What patterns can you create?
Can you work out what shape is made when this piece of paper is folded up using the crease pattern shown?
Play around with sets of five numbers and see what you can discover about different types of average...
For this task, you'll need an A4 sheet and two A5 transparent sheets. Decide on a way of arranging the A5 sheets on top of the A4 sheet and explore ...
Can you do a little mathematical detective work to figure out which number has been wiped out?
A cinema has 100 seats. Is it possible to fill every seat and take exactly £100?
Here are some arrangements of circles. How many circles would I need to make the next size up for each? Can you create your own arrangement and investigate the number of circles it needs?
If you'd like to explore the game freely, without any nudges from us, choose this version.
Use the applet to explore the area of a parallelogram and how it relates to vectors.
Use the applet to make some squares. What patterns do you notice in the coordinates?
Can you find all the ways to get 15 at the top of this triangle of numbers? Many opportunities to work in different ways.
Charlie has made a Magic V. Can you use his example to make some more? And how about Magic Ls, Ns and Ws?
Alison, Bernard and Charlie have been exploring sequences of odd and even numbers, which raise some intriguing questions...
Sets of integers like 3, 4, 5 are called Pythagorean Triples, because they could be the lengths of the sides of a right-angled triangle. Can you find any more?
Use the animation to help you work out how many lines are needed to draw mystic roses of different sizes.
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.
Can all unit fractions be written as the sum of two unit fractions?
If you have a large supply of 3kg and 8kg weights, how many of each would you need for the average (mean) of the weights to be 6kg?
If you are given the mean, median and mode of five positive whole numbers, can you find the numbers?
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
Think of a number, square it and subtract your starting number. Is the number you're left with odd or even? How do the images help to explain this?
Choose four consecutive whole numbers. Multiply the first and last numbers together. Multiply the middle pair together. What do you notice?
Nine squares with side lengths 1, 4, 7, 8, 9, 10, 14, 15, and 18 cm can be fitted together to form a rectangle. What are the dimensions of the rectangle?
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.
Can you work out how to win this game of Nim? Does it matter if you go first or second?
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.
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?
Many numbers can be expressed as the difference of two perfect squares. What do you notice about the numbers you CANNOT make?
Can you guarantee that, for any three numbers you choose, the product of their differences will always be an even number?
Three people chose this as a favourite problem. It is the sort of problem that needs thinking time - but once the connection is made it gives access to many similar ideas.
15 = 7 + 8 and 10 = 1 + 2 + 3 + 4. Can you say which numbers can be expressed as the sum of two or more consecutive integers?
Want a serious challenge? Have a look at these ideas for changing the Approaching Midnight game.
Want some suggestions about where to go next with the game?
What is special about the relationships between vectors that define a square?
Like a bit of help getting into the game? Then have a look at this.
Take a look at the video showing areas of different shapes on dotty grids...
Take a look at the video showing rhombuses and their diagonals...
Move the corner of the rectangle. Can you work out what the purple number represents?
Can you find a strategy that ensures you get to take the last biscuit in this game?
A game for two people, who take turns to move the counters. The player to remove the last counter from the board wins.
Five numbers added together in pairs produce: 0, 2, 4, 4, 6, 8, 9, 11, 13, 15 What are the five numbers?