Making MoneyThe 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 MoneyIf 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 Money5p 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 MoneyIf coins were arranged on very large sheets (partially shown) how much wastage would there be?

Making Money: HintDetermine what type of triangle this is and then find its area.

Making Money: HintHow 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 MoneyThis 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 MoneySlide 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 MoneySlides 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 = x 100 = 21.5%

This is replicated along the strip of metal.

324 – 254.5

324

Teacher notes: Making MoneySlides 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 = √243h = 15.59mm

Area of triangle = ½ x 18 x 15.59 = 140.31mm2

Teacher notes: Making MoneySlides 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 MoneySlides 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 =

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.

100 x 26.16

26.16 + 254.5

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-and-what-they-are-made-of.html accessed 31/3/14