Most of us love manipulating things. Yet, the word manipulate is a rather new one. The first recorded instance of its use was less than 200 years ago, in 1834. It derives ultimately from the Latin manipulus which meant a “full hand” or “handful” … and we certainly like to keep our hands full (or occupied).
This is a wonderful form of play and discovery … not simply arranging shapes, but changing them or arranging/combining them in three dimensions.
The match sticks depicted here have been cleverly manipulated and hint at a relationship. Mathematical relationships are different from the one hinted at here, of course, but I thought the image would present a clever visual pun … that we manipulate objects to discover or show relationships between things!
Balancing a Coin
How can you balance a twenty cent piece on the (vertical) edge of a ten dollar note?
This is not a particularly difficult challenge, but it will give you a 'taste' for manipulation questions.
Carefully examine what you HAVE been asked to do and then examine your assumptions and whether you have been asked explicity NOT to do certain things. Sometimes, we assume that there are more restrictions than there really are!
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Graeme Henderson tutored me throughout my entire high school mathematics education, and through his expert tutelage and exceptional ability to explain the concepts that would otherwise be very hard to understand, I was able to grasp and excel at topics that I would have otherwise been unable to. He was an excellent tutor, and I would not hesitate to recommend him to anyone looking for help with mathematics problems!
Matthew T (student, c2005-2013)
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