Proportion, Scale And The Improbable Barbie

beach barbie1 Our eldest Little Spark, aged 10 (nearly 11 she keeps reminding us!) has outgrown Barbie dolls, but has Barbie outgrown her own feet?  Here is a really fun mathematical investigation we carried out before consigning Barbie to history. (She will be handed down to some Littler Sparks.)  It is a maths activity that can involve all the family and will get children measuring and thinking about proportion and scale.  For this math activity you will need:

  • Assorted humans of various sizes!
  • Improvised measuring tools, which might include lengths of string
  • You could use rulers and tape measures.
  • A Barbie Doll

First of all you need to test the following propositions on a variety of different humans by measuring various parts of their bodies!  You can be creative about the way in which you choose to measure, this is a good way to get children problem solving and often they will invent their own non-standard units of measurements. This can give rise to further problem-solving and all sorts of interesting mathematical concepts.  Sometimes you might find it easier to employ lengths of string.  We just used our slippers to check the wrist to elbow measurement!  Consider the following:

  • Your height is roughly six times the length of your foot.
  • The measurement from your wrist to your elbow is roughly the same length as your foot.
  • If you stand with your arms outstretched, their length from finger tip to finger tip will be roughly the same length as your height.
  • The broadness of your shoulders is roughly a quarter of your height.

Now get measuring! Measure yourselves, measure Dad, measure Grandma.  Give or take a few centimetres (or however you chose to measure) you will probably find the above to be true of all the people you measure.    Now it is time to measure Barbie!  You might come to the conclusion she either has very small feet or is unusually tall!  What are the new rules?  Approximately, what do you have to multiply the length of her foot by to reach her height?  Starting with foot length measurements how tall would everyone in the family be if they had the same proportions as Barbie?

Little Sparks Wisdom:

When I first wrote this post I was going to call it The Impossible Barbie but my daughter insisted it wasn’t necessarily impossible and that there were probably people who didn’t conform to the ‘rules’ of proportion.  I accordingly bowed down to her wisdom and used the revised title of The Improbable Barbie.  Probability was a whole new field that then had to be explored!


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