Enlargements and scale factors

problem
Scale draw

Age

5 to 7

Challenge level

Use the grids to draw pictures to different scales.
problem
Von Koch curve

Age

16 to 18

Challenge level

Make a poster using equilateral triangles with sides 27, 9, 3 and 1 units assembled as stage 3 of the Von Koch fractal. Investigate areas & lengths when you repeat a process infinitely often.
problem
Squareflake

Age

16 to 18

Challenge level

A finite area inside and infinite skin! You can paint the interior of this fractal with a small tin of paint but you could never get enough paint to paint the edge.
problem
Sierpinski triangle

Age

16 to 18

Challenge level

What is the total area of the triangles remaining in the nth stage of constructing a Sierpinski Triangle? Work out the dimension of this fractal.
problem
Flower show

Age

14 to 16

Challenge level

How long will it take six gardeners to dig six circular flower beds?
problem
Squirty

Age

14 to 16

Challenge level

Using a ruler, pencil and compasses only, it is possible to construct a square inside any triangle so that all four vertices touch the sides of the triangle.
problem
Conical bottle

Age

14 to 16

Challenge level

A right circular cone is filled with liquid to a depth of half its vertical height. The cone is inverted. How high up the vertical height of the cone will the liquid rise?
problem
Matter of scale

Age

14 to 16

Challenge level

Can you prove Pythagoras' Theorem using enlargements and scale factors?
problem
Hex

Age

11 to 14

Challenge level

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.
problem
Golden triangle

Age

16 to 18

Challenge level

Three triangles ABC, CBD and ABD (where D is a point on AC) are all isosceles. Find all the angles. Prove that the ratio of AB to BC is equal to the golden ratio.