List

Being Curious - Geometry

Blue and White
problem
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Blue and White

Age
11 to 14
Challenge level
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Identical squares of side one unit contain some circles shaded blue. In which of the four examples is the shaded area greatest?
Arclets
problem
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Arclets

Age
14 to 16
Challenge level
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Each of the following shapes is made from arcs of a circle of radius r. What is the perimeter of a shape with 3, 4, 5 and n "nodes".
Marbles in a box
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Marbles in a box

Age
11 to 16
Challenge level
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How many winning lines can you make in a three-dimensional version of noughts and crosses?
Hexy-Metry
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Hexy-Metry

Age
14 to 16
Challenge level
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A hexagon, with sides alternately a and b units in length, is inscribed in a circle. How big is the radius of the circle?
Three by One
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Three by One

Age
16 to 18
Challenge level
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There are many different methods to solve this geometrical problem - how many can you find?
Triangles and petals
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Triangles and petals

Age
14 to 16
Challenge level
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An equilateral triangle rotates around regular polygons and produces an outline like a flower. What are the perimeters of the different flowers?
Tilted Squares
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Tilted Squares

Age
11 to 14
Challenge level
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It's easy to work out the areas of most squares that we meet, but what if they were tilted?
On the Edge
problem
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On the Edge

Age
11 to 14
Challenge level
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If you move the tiles around, can you make squares with different coloured edges?
Sending a Parcel
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Sending a Parcel

Age
11 to 14
Challenge level
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What is the greatest volume you can get for a rectangular (cuboid) parcel if the maximum combined length and girth are 2 metres?
Where to Land
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Where to Land

Age
14 to 16
Challenge level
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Chris is enjoying a swim but needs to get back for lunch. How far along the bank should she land?
Right angles
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Right angles

Age
11 to 14
Challenge level
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Can you make a right-angled triangle on this peg-board by joining up three points round the edge?
Trapezium Four
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Trapezium Four

Age
14 to 16
Challenge level
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The diagonals of a trapezium divide it into four parts. Can you create a trapezium where three of those parts are equal in area?
Cola Can
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Cola Can

Age
11 to 14
Challenge level
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An aluminium can contains 330 ml of cola. If the can's diameter is 6 cm what is the can's height?
Can they be equal?
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Can they be equal?

Age
11 to 14
Challenge level
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Can you find rectangles where the value of the area is the same as the value of the perimeter?
Curvy areas
problem
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Curvy areas

Age
14 to 16
Challenge level
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Have a go at creating these images based on circles. What do you notice about the areas of the different sections?
Which solids can we make?
problem
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Which solids can we make?

Age
11 to 14
Challenge level
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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?
Fit for photocopying
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Fit for photocopying

Age
14 to 16
Challenge level
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Explore the relationships between different paper sizes.
Vector journeys
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Vector journeys

Age
14 to 18
Challenge level
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Charlie likes to go for walks around a square park, while Alison likes to cut across diagonally. Can you find relationships between the vectors they walk along?
Perimeter Possibilities
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Perimeter Possibilities

Age
11 to 14
Challenge level
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I'm thinking of a rectangle with an area of 24. What could its perimeter be?
Square coordinates
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Square coordinates

Age
11 to 14
Challenge level
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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?

circles in quadrilaterals
problem
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Circles in quadrilaterals

Age
14 to 16
Challenge level
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Explore when it is possible to construct a circle which just touches all four sides of a quadrilateral.

Triangle midpoints
problem
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Triangle midpoints

Age
14 to 16
Challenge level
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You are only given the three midpoints of the sides of a triangle. How can you construct the original triangle?

Opposite vertices
problem
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Opposite vertices

Age
11 to 14
Challenge level
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Can you recreate squares and rhombuses if you are only given a side or a diagonal?

Semi-regular Tessellations
problem
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Semi-regular Tessellations

Age
11 to 16
Challenge level
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Semi-regular tessellations combine two or more different regular polygons to fill the plane. Can you find all the semi-regular tessellations?

Cuboid challenge
problem
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Cuboid Challenge

Age
11 to 16
Challenge level
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What's the largest volume of box you can make from a square of paper?