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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 parallelogram.
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 rhombus.
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 parallelogram.
Can you sketch triangles that fit in the cells in this grid? Which ones are impossible? How do you know?
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.
Are these statements always true, sometimes true or never true?
Take an equilateral triangle and cut it into smaller pieces. What can you do with them?
We started drawing some quadrilaterals - can you complete them?
How many questions do you need to identify my quadrilateral?
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 ...
Use the information on these cards to draw the shape that is being described.
Can you find the squares hidden on these coordinate grids?
This problem shows that the external angles of an irregular hexagon add to a circle.
This problem explores the shapes and symmetries in some national flags.
The computer has made a rectangle and will tell you the number of spots it uses in total. Can you find out where the rectangle is?
Can you recreate squares and rhombuses if you are only given a side or a diagonal?
These pictures were made by starting with a square, finding the half-way point on each side and joining those points up. You could investigate your own starting shape.
This activity focuses on similarities and differences between shapes.
A task which depends on members of the group noticing the needs of others and responding.
This task develops spatial reasoning skills. By framing and asking questions a member of the team has to find out what mathematical object they have chosen.
Can you each work out what shape you have part of on your card? What will the rest of it look like?
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.
These rectangles have been torn. How many squares did each one have inside it before it was ripped?
A game in which players take it in turns to try to draw quadrilaterals (or triangles) with particular properties. Is it possible to fill the game grid?
A game in which players take it in turns to turn up two cards. If they can draw a triangle which satisfies both properties they win the pair of cards. And a few challenging questions to follow...
A game for 2 or more people, based on the traditional card game Rummy.
Choose the size of your pegboard and the shapes you can make. Can you work out the strategies needed to block your opponent?
A tilted square is a square with no horizontal sides. Can you devise a general instruction for the construction of a square when you are given just one of its sides?
Use a single sheet of A4 paper and make a cylinder having the greatest possible volume. The cylinder must be closed off by a circle at each end.
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.
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?
Where can you put the mirror across the square so that you can still "see" the whole square? How many different positions are possible?
Use the isometric grid paper to find the different polygons.
Identical squares of side one unit contain some circles shaded blue. In which of the four examples is the shaded area greatest?
Explain how the thirteen pieces making up the regular hexagon shown in the diagram can be re-assembled to form three smaller regular hexagons congruent to each other.
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?
The challenge is to produce elegant solutions. Elegance here implies simplicity. The focus is on rhombi, in particular those formed by jointing two equilateral triangles along an edge.
Recreating the designs in this challenge requires you to break a problem down into manageable chunks and use the relationships between triangles and hexagons. An exercise in detail and elegance.
See if you can anticipate successive 'generations' of the two animals shown here.
In LOGO circles can be described in terms of polygons with an infinite (in this case large number) of sides - investigate this definition further.
This article gives an wonderful insight into students working on the Arclets problem that first appeared in the Sept 2002 edition of the NRICH website.
How many trapeziums, of various sizes, are hidden in this picture?
The image in this problem is part of a piece of equipment found in the playground of a school. How would you describe it to someone over the phone?
Bluey-green, white and transparent squares with a few odd bits of shapes around the perimeter. But, how many squares are there of each type in the complete circle? Study the picture and make an estimate.
With one cut a piece of card 16 cm by 9 cm can be made into two pieces which can be rearranged to form a square 12 cm by 12 cm. Explain how this can be done.
Follow the instructions and you can take a rectangle, cut it into 4 pieces, discard two small triangles, put together the remaining two pieces and end up with a rectangle the same size. Try it!
Two circles are enclosed by a rectangle 12 units by x units. The distance between the centres of the two circles is x/3 units. How big is x?
Which is a better fit, a square peg in a round hole or a round peg in a square hole?
Can you work out the area of the inner square and give an explanation of how you did it?
An activity making various patterns with 2 x 1 rectangular tiles.