Making Money
The Royal Mint has announced the introduction of a
new £1 coin for 2017. It will be based on an old
‘threepenny bit’ – a 12-sided coin in circulation from
1937 to 1971.
Making Money
Many coins are made by cutting out blank shapes
from a long strip of metal and then stamping the
appropriate design on them.
In the UK we currently have circular coins, coins
which are heptagonal (50p and 20p) and in 2017 we
will be getting a coin which is a dodecagon.
Which of these shapes do you think are most cost
effective to make?
Making Money
If circular coins are cut from a strip of metal:
• How much is wasted?
• How can wastage be minimised?
What information do you need to know?
Making Money
5p coins have a diameter of 18.0mm
If there are no gaps between coins or between coins
and the edge of the strip, how much metal is wasted
producing the coins?
Making Money: Hint
Work out the wastage for 1 circle enclosed by a
square.
Making Money
If coins were arranged on very large sheets (partially
shown) how much wastage would there be?
Making Money: Hint
Determine what type of triangle this is and then find
its area.
Making Money: Hint
How many of the ‘white’ pieces are there for each
circle?
Making Money: Exploring Further
If heptagons or dodecagons are cut from a strip of
metal, how should they be arranged to minimise
wastage?
Teacher notes: Making Money
This activity involves problem solving, finding areas of plane shapes
and using Pythagoras’ theorem or trigonometry.
The activity could also be approached in practical ways which do not
require the use of trigonometry or Pythagoras theorem.
Teacher notes: Making Money
Slide 4
Information that might be needed:
• How long the strip of metal is
• How big the coin is
• How close the coins can be to each other as they are cut out of the
strip
• If the coins can be cut out right to the edges of the strip
Teacher notes: Making Money
Slides 5 & 6
Area of a circle within a square
Area of square = 18 x 18 = 324 mm2
Area of circle = π x 92 = 254.5mm2
Wastage =
324 – 254.5
324
x 100 = 21.5%
This is replicated along the strip of metal.
Teacher notes: Making Money
Slides 7, 8 & 9
Each side of the triangle is formed from 2 radii,
therefore it is equilateral.
Height of the triangle (using Pythagoras’ theorem)
h = √(182 - 92)
h = √243
h = 15.59mm
Area of triangle = ½ x 18 x 15.59 = 140.31mm2
Teacher notes: Making Money
Slides 7, 8 & 9
Each side of the triangle is formed from 2 radii,
therefore it is equilateral.
Each of the segments is 1/6 of a circle
White piece = area of triangle – area of half a circle
Area of white piece = 140.31 – 127.23 = 13.08mm2
Teacher notes: Making Money
Slides 7,8 & 9
Area of two white pieces = 13.08 x 2 =
26.16mm2
Wastage = 100 x (area of two white
pieces ) ÷ (area of two white pieces +
area of a circle)
Wastage =
100 x 26.16
26.16 + 254.5
Wastage = 9.31%
However this is for an ‘infinite sheet’, in
reality there would be additional wastage
at the edges. The bigger the sheet, the
less the relative wastage.
Teacher notes: Making Money
Slide 10
Pupils could explore fitting coins on strips of paper, deciding whether
rotating coins or having them all the same orientation will fit onto a
shorter strip. They could do this with real coins (or cut-outs!) or by
using a dynamic geometry package.
Acknowledgements
http://www.bbc.co.uk/news/uk-politics-26632863 accessed 31/3/14
http://www.royalmint.com/aboutus/policies-and-guidelines/advertising-guidelines
accessed 31/3/14
http://www.fleur-de-coin.com/articles/unusual-coins accessed 31/3/14
http://www.telegraph.co.uk/finance/currency/8655340/How-the-UKs-coins-are-made-andwhat-they-are-made-of.html accessed 31/3/14