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There are **21** NRICH Mathematical resources connected to **Enlargements and scale factors**, you may find related items under Transformations and constructions.

Problem
Primary curriculum
Secondary curriculum
### Poly Plug Pattern

Create a pattern on the small grid. How could you extend your pattern on the larger grid?

Age 5 to 7

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Fill Me up Too

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?

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Fit for Photocopying

Explore the relationships between different paper sizes.

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Growing Rectangles

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

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Who is the fairest of them all ?

Explore the effect of combining enlargements.

Age 11 to 14

Challenge Level

Game
Primary curriculum
Secondary curriculum
### Transformation Game

Why not challenge a friend to play this transformation game?

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Squirty

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.

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Hex

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.

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Circles Ad Infinitum

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?

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### L-triominoes

L triominoes can fit together to make larger versions of themselves. Is every size possible to make in this way?

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Scaling Clowns

These five clowns work in pairs. What is the same and what is different about each pair's faces?

Age 5 to 7

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Arrow Arithmetic 1

The first part of an investigation into how to represent numbers using geometric transformations that ultimately leads us to discover numbers not on the number line.

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### The Rescaled Map

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.

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Von Koch Curve

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.

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Squareflake

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.

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Sierpinski Triangle

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.

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Conical Bottle

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?

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Matter of Scale

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

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Golden Triangle

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.

Age 16 to 18

Challenge Level