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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.

Broad Topics > Transformations and constructions > Enlargements and scale factors

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Poly Plug Pattern

Age 5 to 7 Challenge Level:

Create a pattern on the left-hand grid. How could you extend your pattern on the right-hand grid?

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Fill Me up Too

Age 14 to 16 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?

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Fit for Photocopying

Age 14 to 16 Challenge Level:

Explore the relationships between different paper sizes.

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Growing Rectangles

Age 11 to 14 Challenge Level:

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

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Who Is the Fairest of Them All ?

Age 11 to 14 Challenge Level:

Explore the effect of combining enlargements.

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Transformation Game

Age 11 to 14 Challenge Level:

Why not challenge a friend to play this transformation game?

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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.

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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.

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Circles Ad Infinitum

Age 16 to 18 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?

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Similar Rectangles

Age 14 to 16 Challenge Level:

Can you find the missing length?

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L-triominoes

Age 14 to 16 Challenge Level:

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

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Scaling Clowns

Age 5 to 7 Challenge Level:

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

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Arrow Arithmetic 1

Age 14 to 16 Challenge Level:

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.

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The Rescaled Map

Age 14 to 16 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.

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Scale Draw

Age 5 to 7 Challenge Level:

Use the grids to draw pictures to different scales.

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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.

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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.

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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.

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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?

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Matter of Scale

Age 14 to 16 Challenge Level:

Prove Pythagoras' Theorem using enlargements and scale factors.

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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.