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Get startedPhase 1: Work out the calculations and colour in the patches to complete the brightly coloured symmetrically patterned buttery shown below. A colour code is provided - but you could choose your own colours if you wish, just make sure they match on both sides.

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Colour code: 12 – Blue 10 – Purple 9 – Yellow 8 – Red 7 – Pink 5 – Black

From red admiral to painted lady and from chalk hill blue to marsh fritillary, British butteries are among the most colourful bugs in the world. Not only that, they are wonderfully symmetrical; the patterns on one set of wings match those on the other.

Your task is to solve some mathematical problems that will help you successfully colour in a large symmetrical buttery diagram!

You will need– Assorted selection of

coloured pencils or felt pens

– Thick paper/thin card

– Scissors, tracing paper

(optional)

Your mission

O 1-2 hoursIndependent learningDifficulty: VVVVV

Learning objectives– Learn about the colourful symmetrical nature of butteries

– Solve assorted number problems

– Understand the meaning of the equals sign

COLOURFUL NUMBERSButterfly Maths!

AQUiLA Bugs! activity

Things to think about

r r Your buttery designs don't have to use mathematics. The possibilities are almost endless. Why not make some matching buttery designs by using synonyms (words that have the same meaning), like ‘disappear’ on one side and ‘vanish’ on the other, or ‘agile’ and ‘nimbl‘nimble’? Then there are homonyms (words that sound the same but have different meanings) such as ‘brake’ and ‘break’, ‘road’ and ‘rode’, or antonyms (opposites) like ‘black’ and ‘white’ and ‘short’ and ‘tall’. There is plenty of scope in geography as well. Go for countries anand their capital cities for starters. For example, France would match up with Paris, and Beijing with China.

Phase 2: NNow make some colourful buttery designs of your own. Take a sheet of thick plain paper or thin card (A4 size or bigger) and fold it in half, short side to short side. Draw half of a buttery shape up against the fold line with a pencil. Cut round the line carefully and open it out to make a fully symmetrical buttery. Decide on your design and draw it on. If you want to make sure they are really accurate you could use the imprint off some tracing paper on the second side.

Phase 3: Phase 3: IIf you want to make things trickier, you could bring mathematical equivalence into play. You might use the butteries to help learn or revise your tables. For example, 10 x 2 on one side and 4 x 5 on the other would give you the same answer. Or why not match equivalent simple fractions like 5/10 and ½ and 2/3 and 8/12. Move on to matching simple fractions and decimal equivalents e.g. 7/10 and 0.7 and 0.03 and 3/100, or decimals and percentages e.g. 0.8 and 80% and 34% and 0.34. You could even be reallreally clever and pair up denary and binary equivalents e.g. 6 and 110 and 1101 and 13.

We want to see your butteries! Don’t forget to send photos of your clever and colourful creatures to the address on the readers’ page of the AQUILA website, and we’ll share as many as we can.

© AQUILA magazine. Written by John Davis

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