List

Being curious - geometry

Blue and White
problem

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

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".
Hexy-Metry
problem

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
problem

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
problem

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?
Where to Land
problem

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?
Curvy areas
problem

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?
Fit for photocopying
problem

Fit for photocopying

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

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?
Cola can
problem

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?

Cuboid challenge
problem

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?

Square coordinates
problem

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?

Opposite vertices
problem

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

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?

circles in quadrilaterals
problem

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

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?

Trapezium Four
problem

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?

Right angles
problem

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?

Tilted Squares
problem

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?

Which solids can we make?
problem

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?

On the Edge
problem

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?

Perimeter Possibilities
problem

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?

Can they be equal?
problem

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?

Marbles in a box
problem

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?

Sending a Parcel
problem

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?