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BUNCH OF FIVES
Pentominoes are shapes made from five squares (just as dominoes are made from two squares). There are 12 of them and they can be fitted together in many interesting ways.
The afghan shows the twelve pentominoes and their reflections.
Each shape has the same area.
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Bunch of Fives
The afghan needs 12 different shades plus a border colour. The yarns in one half are mixed with a pale grey yarn; those in the other half are mixed with medium grey, to create the shadow effect.
This is good stashbuster if you happen to have lots of yarn in the same weight. The yarns used for the afghan in the photo were very pale and uninteresting individually but combine to give a subtle overall effect.
‘EQUAL AREA’ AFGHANS
‘EQUAL AREA’ CUSHION
Worked in twelve strips which are stitched together.
The twelve pentominoes can be fitted together to make various rectangles. The proportions of the possible rectangles are 3 x 20, 4 x 15, 5 x 12, and 6 x 10. Although we were anxious to show just the twelve pentominoes we were not happy with the overall shape of any of the rectangles we would get by using the shapes just once. We needed two rectangles together.
When studying shapes such as pentominoes one of the first questions is always ‘Are these the same?’ when one is a reflection of the other. Some judgement has to be made. (To arrive at twelve different pentominoes reflections cannot be allowed though in other circumstances they might be acceptable) We decided that we would show the shapes and their reflections.
To make the two rectangles ‘the same but different’ the same twelve yarns were used in both but mixed with light grey yarn in one rectangle and with dark grey yarn in the other rectangle.
We were very surprised by the reaction of pupils to Bunch of Fives. The first comment was always ‘It’s like a mirror!’ Pupils who had struggled to understand the mathematics of reflection now understood instantly with no further explanation. Maths text books tend to explain reflection by using a blue square reflecting a blue square or a red triangle reflecting a red triangle. Our afghan made one side more shadowy than the other and this somehow seemed much more acceptable as being like a mirror. This was an unexpected bonus from our revised plan.
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