problem
Tilted Squares
Age
11 to 14
Challenge level
It's easy to work out the areas of most squares that we meet, but what if they were tilted?
problem
Square It
Age
11 to 16
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.
problem
Triangles in circles
Age
11 to 14
Challenge level
Can you find triangles on a 9-point circle? Can you work out their angles?
problem
Semi-regular Tessellations
Age
11 to 16
Challenge level
Semi-regular tessellations combine two or more different regular polygons to fill the plane. Can you find all the semi-regular tessellations?
problem
Cyclic Quadrilaterals
Age
11 to 16
Challenge level
Draw some quadrilaterals on a 9-point circle and work out the angles. Is there a theorem?
problem
Hidden Squares
Age
11 to 14
Challenge level
Can you find the squares hidden on these coordinate grids?
problem
Guess \my Quad
Age
11 to 14
Challenge level
How many questions do you need to identify my quadrilateral?
problem
Polygon Rings
Age
11 to 14
Challenge level
Join pentagons together edge to edge. Will they form a ring?
problem
Completing Quadrilaterals
Age
11 to 14
Challenge level
We started drawing some quadrilaterals - can you complete them?
problem
Polygon Pictures
Age
11 to 14
Challenge level
Can you work out how these polygon pictures were drawn, and use that to figure out their angles?
problem
An Equilateral Triangular Problem
Age
11 to 14
Challenge level
Take an equilateral triangle and cut it into smaller pieces. What can you do with them?
problem
Angles inside
Age
11 to 14
Challenge level
Draw some angles inside a rectangle. What do you notice? Can you prove it?
problem
Parallelogram It
Age
11 to 16
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 parallelogram.
problem
Rhombus It
Age
11 to 16
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 rhombus.
problem
Square coordinates
Age
11 to 14
Challenge level
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?
problem
Subtended angles
Age
11 to 14
Challenge level
What is the relationship between the angle at the centre and the
angles at the circumference, for angles which stand on the same
arc? Can you prove it?
problem
Right angles
Age
11 to 14
Challenge level
Can you make a right-angled triangle on this peg-board by joining up three points round the edge?
problem
Shapely pairs
Age
11 to 14
Challenge level
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...
problem
Property chart
Age
11 to 14
Challenge level
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?
problem
Opposite vertices
Age
11 to 14
Challenge level
Can you recreate squares and rhombuses if you are only given a side or a diagonal?
problem
Quadrilaterals in a Square
Age
11 to 14
Challenge level
What's special about the area of quadrilaterals drawn in a square?
problem
Star Polygons
Age
11 to 14
Challenge level
Draw some stars and measure the angles at their points. Can you find and prove a result about their sum?
problem
Which solids can we make?
Age
11 to 14
Challenge level
Interior angles can help us to work out which polygons will tessellate. Can we use similar ideas to predict which polygons combine to create semi-regular solids?
problem
Of all the areas
Age
14 to 16
Challenge level
Can you find a general rule for finding the areas of equilateral triangles drawn on an isometric grid?
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You may also be interested in this collection of activities from the STEM Learning website, that complement the NRICH activities above.