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!
When you are ready to compare your solution with my one, please click here.
Our daughter Angelina was home schooled and from the start did not like maths. Over the years I have battled through, trying 5 different programs along the way. Angelina was surviving but not enjoying the journey but, when it came to algebra, the future looked dim. A friend recommended Graeme to me as her three sons had been tutored by him. She could not recommend him more highly. My daughter has just finished year 12 maths and did very well, thanks to Graeme (that would be an understatement). Graeme has a love for his subject and a genuine interest in his students. Graeme seems to meets his students where they are and tailors the lessons to meet their individual needs and interests. Graeme not only explains concepts clearly, but we all found him an interesting, knowledgeable and humble man. We are extremely happy that Graeme was recommended to us. Now our daughter is looking forward to uni with a grateful heart. We also could not recommend Graeme more highly.
Angela K (parent, 2013)
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