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Broad Topics > Transformations and their Properties > Scale factors

Growing Rectangles

Stage: 3 Challenge Level:

What happens to the area and volume of 2D and 3D shapes when you enlarge them?

Who Is the Fairest of Them All ?

Stage: 3 Challenge Level:

Explore the effect of combining enlargements.

Stage: 5 Challenge Level:

A circle is inscribed in an equilateral triangle. Smaller circles touch it and the sides of the triangle, the process continuing indefinitely. What is the sum of the areas of all the circles?

Similar Rectangles

Stage: 4 Challenge Level:

Can you find the missing length?

Fill Me up Too

Stage: 4 Challenge Level:

In Fill Me Up we invited you to sketch graphs as vessels are filled with water. Can you work out the equations of the graphs?

Fit for Photocopying

Stage: 4 Challenge Level:

Explore the relationships between different paper sizes.

Where Am I?

Stage: 3 and 4 Challenge Level:

From the information you are asked to work out where the picture was taken. Is there too much information? How accurate can your answer be?

The Rescaled Map

Stage: 4 Challenge Level:

We use statistics to give ourselves an informed view on a subject of interest. This problem explores how to scale countries on a map to represent characteristics other than land area.

Von Koch Curve

Stage: 5 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.

Squareflake

Stage: 5 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.

Sierpinski Triangle

Stage: 5 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.

Arrh!

Stage: 4 Challenge Level:

Triangle ABC is equilateral. D, the midpoint of BC, is the centre of the semi-circle whose radius is R which touches AB and AC, as well as a smaller circle with radius r which also touches AB and AC. . . .

Conical Bottle

Stage: 4 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?

Matter of Scale

Stage: 4 Challenge Level:

Prove Pythagoras' Theorem using enlargements and scale factors.

Golden Triangle

Stage: 5 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.