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There are 206 NRICH Mathematical resources connected to Visualising and representing, you may find related items under Thinking mathematically.
Broad Topics > Thinking mathematically > Visualising and representingCan you work out what shape is made when this piece of paper is folded up using the crease pattern shown?
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 ...
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?
How could you arrange at least two dice in a stack so that the total of the visible spots is 18?
Look at different ways of dividing things. What do they mean? How might you show them in a picture, with things, with numbers and symbols?
Here are some short problems for you to try. Talk to your friends about how you work them out.
This task looks at the different turns involved in different Olympic sports as a way of exploring the mathematics of turns and angles.
Exploring the structure of a number square: how quickly can you put the number tiles in the right place on the grid?
An activity centred around observations of dots and how we visualise number arrangement patterns.
Looking at the 2012 Olympic Medal table, can you see how the data is organised? Could the results be presented differently to give another nation the top place?
Create a pattern on the small grid. How could you extend your pattern on the larger grid?
This challenge involves eight three-cube models made from interlocking cubes. Investigate different ways of putting the models together then compare your constructions.
This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
I've made some cubes and some cubes with holes in. This challenge invites you to explore the difference in the number of small cubes I've used. Can you see any patterns?
What can you see? What do you notice? What questions can you ask?
Can you find a reliable strategy for choosing coordinates that will locate the treasure in the minimum number of guesses?
On the graph there are 28 marked points. These points all mark the vertices (corners) of eight hidden squares. Can you find the eight hidden squares?
What shape is the overlap when you slide one of these shapes half way across another? Can you picture it in your head? Use the interactivity to check your visualisation.
What does the overlap of these two shapes look like? Try picturing it in your head and then use some cut-out shapes to test your prediction.
Imagine a pyramid which is built in square layers of small cubes. If we number the cubes from the top, starting with 1, can you picture which cubes are directly below this first cube?
Investigate how the four L-shapes fit together to make an enlarged L-shape. You could explore this idea with other shapes too.
Can you predict when you'll be clapping and when you'll be clicking if you start this rhythm? How about when a friend begins a new rhythm at the same time?
How can you arrange the 5 cubes so that you need the smallest number of Brush Loads of paint to cover them? Try with other numbers of cubes as well.
This practical problem challenges you to make quadrilaterals with a loop of string. You'll need some friends to help!
How many different triangles can you make on a circular pegboard that has nine pegs?
These points all mark the vertices (corners) of ten hidden squares. Can you find the 10 hidden squares?
If you split the square into these two pieces, it is possible to fit the pieces together again to make a new shape. How many new shapes can you make?
A hundred square has been printed on both sides of a piece of paper. What is on the back of 100? 58? 23? 19?
Here are shadows of some 3D shapes. What shapes could have made them?
Each of the nets of nine solid shapes has been cut into two pieces. Can you see which pieces go together?
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?
You have been given three shapes made out of sponge: a sphere, a cylinder and a cone. Your challenge is to find out how to cut them to make different shapes for printing.
Use the lines on this figure to show how the square can be divided into 2 halves, 3 thirds, 6 sixths and 9 ninths.
Where can you put the mirror across the square so that you can still "see" the whole square? How many different positions are possible?
A magician took a suit of thirteen cards and held them in his hand face down. Every card he revealed had the same value as the one he had just finished spelling. How did this work?
How many balls of modelling clay and how many straws does it take to make these skeleton shapes?
We start with one yellow cube and build around it to make a 3x3x3 cube with red cubes. Then we build around that red cube with blue cubes and so on. How many cubes of each colour have we used?
What is the greatest number of counters you can place on the grid below without four of them lying at the corners of a square?
Here are the six faces of a cube - in no particular order. Here are three views of the cube. Can you deduce where the faces are in relation to each other and record them on the net of this cube?
How many DIFFERENT quadrilaterals can be made by joining the dots on the 8-point circle?
In a square in which the houses are evenly spaced, numbers 3 and 10 are opposite each other. What is the smallest and what is the largest possible number of houses in the square?
Eight children each had a cube made from modelling clay. They cut them into four pieces which were all exactly the same shape and size. Whose pieces are the same? Can you decide who made each set?
Can you split each of the shapes below in half so that the two parts are exactly the same?
How would you find out how many football cards Catrina has collected?
Make one big triangle so the numbers that touch on the small triangles add to 10.
In this town, houses are built with one room for each person. There are some families of seven people living in the town. In how many different ways can they build their houses?
What is the greatest number of squares you can make by overlapping three squares?
Cut four triangles from a square as shown in the picture. How many different shapes can you make by fitting the four triangles back together?