Resources tagged with Visualising similar to What Shape?:
Other tags that relate to What Shape?
Solids. Team-building. Compound transformations. Mathematical reasoning & proof. Questioning. Squares. Visualising. Shape, space & measures - generally. Cubes. Regular polygons and circles.There are 261 results
Broad Topics > Using, Applying and Reasoning about Mathematics > Visualising
Coloured Edges
Stage: 3 Challenge Level: 
The whole set of tiles is used to make a square. This has a green and blue border. There are no green or blue tiles anywhere in the square except on this border. How many tiles are there in the set?
Baravelle
Stage: 2, 3 and 4 Challenge Level:
What can you see? What do you notice? What questions can you ask?
Chess
Stage: 3 Challenge Level:
What would be the smallest number of moves needed to move a Knight from a chess set from one corner to the opposite corner of a 99 by 99 square board?
Dissect
Stage: 3 Challenge Level:
It is possible to dissect any square into smaller squares. What is the minimum number of squares a 13 by 13 square can be dissected into?
All in the Mind
Stage: 3 Challenge Level:
Imagine you are suspending a cube from one vertex (corner) and allowing it to hang freely. Now imagine you are lowering it into water until it is exactly half submerged. What shape does the surface. . . .
Triangles in the Middle
Stage: 3, 4 and 5 Challenge Level:
This task depends on groups working collaboratively, discussing and reasoning to agree a final product.
Christmas Boxes
Stage: 3 Challenge Level:
Find all the ways to cut out a 'net' of six squares that can be folded into a cube.
Screwed-up
Stage: 3 Challenge Level:
A cylindrical helix is just a spiral on a cylinder, like an ordinary spring or the thread on a bolt. If I turn a left-handed helix over (top to bottom) does it become a right handed helix?
Cube Paths
Stage: 3 Challenge Level:
Given a 2 by 2 by 2 skeletal cube with one route `down' the cube. How many routes are there from A to B?
The Development of Spatial and Geometric Thinking: the Importance of Instruction.
Stage: 1 and 2
This article looks at levels of geometric thinking and the types of activities required to develop this thinking.
Bands and Bridges: Bringing Topology Back
Stage: 2 and 3
Lyndon Baker describes how the Mobius strip and Euler's law can introduce pupils to the idea of topology.
Makeover
Stage: 1 and 2 Challenge Level:
Exchange the positions of the two sets of counters in the least possible number of moves
Coordinate Patterns
Stage: 3 Challenge Level:
Charlie and Alison have been drawing patterns on coordinate grids. Can you picture where the patterns lead?
The Old Goats
Stage: 3 Challenge Level:
A rectangular field has two posts with a ring on top of each post. There are two quarrelsome goats and plenty of ropes which you can tie to their collars. How can you secure them so they can't. . . .
Ten Hidden Squares
Stage: 2 Challenge Level:
These points all mark the vertices (corners) of ten hidden squares. Can you find the 10 hidden squares?
Overlapping Again
Stage: 2 Challenge Level:
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.
Cubist Cuts
Stage: 3 Challenge Level:
A 3x3x3 cube may be reduced to unit cubes in six saw cuts. If after every cut you can rearrange the pieces before cutting straight through, can you do it in fewer?
Keep Your Distance
Stage: 3 Challenge Level:
Can you mark 4 points on a flat surface so that there are only two different distances between them?
Regular Rings 2
Stage: 2 Challenge Level:
What shape is made when you fold using this crease pattern? Can you make a ring design?
Sprouts
Stage: 2, 3, 4 and 5 Challenge Level:
A game for 2 people. Take turns joining two dots, until your opponent is unable to move.
Seeing Squares
Stage: 1 and 2 Challenge Level:
Players take it in turns to choose a dot on the grid. The winner is the first to have four dots that can be joined to form a square.
Conway's Chequerboard Army
Stage: 3 Challenge Level:
Here is a solitaire type environment for you to experiment with. Which targets can you reach?
Dicey
Stage: 2 Challenge Level:
A game has a special dice with a colour spot on each face. These three pictures show different views of the same dice. What colour is opposite blue?
Khun Phaen Escapes to Freedom
Stage: 3 Challenge Level:
Slide the pieces to move Khun Phaen past all the guards into the position on the right from which he can escape to freedom.
Dice, Routes and Pathways
Stage: 1, 2 and 3
This article for teachers discusses examples of problems in which there is no obvious method but in which children can be encouraged to think deeply about the context and extend their ability to. . . .
Tangram Paradox
Stage: 2 Challenge Level:
How can the same pieces of the tangram make this bowl before and after it was chipped? Use the interactivity to try and work out what is going on!
Rolling Around
Stage: 3 Challenge Level:
A circle rolls around the outside edge of a square so that its circumference always touches the edge of the square. Can you describe the locus of the centre of the circle?
Flight of the Flibbins
Stage: 3 Challenge Level:
Blue Flibbins are so jealous of their red partners that they will not leave them on their own with any other bue Flibbin. What is the quickest way of getting the five pairs of Flibbins safely to. . . .
Tied Up
Stage: 3 Challenge Level:
In a right angled triangular field, three animals are tethered to posts at the midpoint of each side. Each rope is just long enough to allow the animal to reach two adjacent vertices. Only one animal. . . .
Linkage
Stage: 3 Challenge Level:
Four rods, two of length a and two of length b, are linked to form a kite. The linkage is moveable so that the angles change. What is the maximum area of the kite?
Tetra Square
Stage: 3 Challenge Level:
ABCD is a regular tetrahedron and the points P, Q, R and S are the midpoints of the edges AB, BD, CD and CA. Prove that PQRS is a square.
Framed
Stage: 3 Challenge Level:
Seven small rectangular pictures have one inch wide frames. The frames are removed and the pictures are fitted together like a jigsaw to make a rectangle of length 12 inches. Find the dimensions of. . . .
Trice
Stage: 3 Challenge Level:
ABCDEFGH is a 3 by 3 by 3 cube. Point P is 1/3 along AB (that is AP : PB = 1 : 2), point Q is 1/3 along GH and point R is 1/3 along ED. What is the area of the triangle PQR?
Endless Noughts and Crosses
Stage: 2 Challenge Level:
An extension of noughts and crosses in which the grid is enlarged and the length of the winning line can to altered to 3, 4 or 5.
Pattern Power
Stage: 1, 2 and 3
Mathematics is the study of patterns. Studying pattern is an opportunity to observe, hypothesise, experiment, discover and create.
Put Yourself in a Box
Stage: 2 Challenge Level:
A game for 2 players. Given a board of dots in a grid pattern, players take turns drawing a line by connecting 2 adjacent dots. Your goal is to complete more squares than your opponent.
On the Edge
Stage: 3 Challenge Level:
If you move the tiles around, can you make squares with different coloured edges?
Square to L
Stage: 2 Challenge Level:
Find a way to cut a 4 by 4 square into only two pieces, then rejoin the two pieces to make an L shape 6 units high.
Zooming in on the Squares
Stage: 2 and 3
Start with a large square, join the midpoints of its sides, you'll see four right angled triangles. Remove these triangles, a second square is left. Repeat the operation. What happens?
Cubes Within Cubes
Stage: 2 and 3 Challenge Level:
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?
Twice as Big?
Stage: 2 Challenge Level:
Investigate how the four L-shapes fit together to make an enlarged L-shape. You could explore this idea with other shapes too.
Hexagon Transformations
Stage: 2 Challenge Level:
Can you cut a regular hexagon into two pieces to make a parallelogram? Try cutting it into three pieces to make a rhombus!
Painting Cubes
Stage: 3 Challenge Level:
Imagine you have six different colours of paint. You paint a cube using a different colour for each of the six faces. How many different cubes can be painted using the same set of six colours?
Diagonal Dodge
Stage: 2 and 3 Challenge Level:
A game for 2 players. Can be played online. One player has 1 red counter, the other has 4 blue. The red counter needs to reach the other side, and the blue needs to trap the red.
Sea Defences
Stage: 2 and 3 Challenge Level:
These are pictures of the sea defences at New Brighton. Can you work out what a basic shape might be in both images of the sea wall and work out a way they might fit together?
Three Squares
Stage: 1 and 2 Challenge Level:
What is the greatest number of squares you can make by overlapping three squares?
Eight Hidden Squares
Stage: 2 and 3 Challenge Level:
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?
Drilling Many Cubes
Stage: 2 and 3 Challenge Level:
A useful visualising exercise which offers opportunities for discussion and generalising, and which could be used for thinking about the formulae needed for generating the results on a spreadsheet.
NRICH is part of the family of activities in the Millennium Mathematics Project.