I made this afghan long before I thought about writing and selling patterns. It was made specifically for my Maths classroom, to show an arrangement of pentominoes to create a rectangle.

Pentominoes are shapes made from five squares joined together, just as dominoes have two squares joined together. There are twelve different pentominoes and they fit together in many strange ways.

All twelve fit to make various shapes of rectangle. The total area of twelve shapes with five squares in each is sixty squares. They can be arranged in 3 x 20, 4 x 15, 5 x 12 and 6 x 10 rectangles. I didn’t like the proportions of any of these rectangles and tried to think of a possible solution. It should have been more obvious but it came to me eventually that when we work with pentominoes we always say that there are twelve possible shapes, not including reflections. If I did allow reflections I could have one hundred and twenty squares.

One set of pentominoes had to look like the image, the other like the reflection. The plan was to use dark colours on one side and toning lighter shades on the other. None of the ideas I experimented with would work because there was not the same amount of difference between each pair of colours and some parts stood out more than others. I worked lots of small samples and it was clear that all the shapes on the image side must be of the same brightness, or all equally dull, but that didn’t help with what was to happen on the reflection side. I think there were more samples worked for this than for any other design.

Eventually a magical solution appeared. I had some slightly fluffy, silver-grey yarn and more of the same in a darker shade of grey. These could be mixed with other yarns to give two shades from the same basic colour. The only way it would work would be if the twelve colours were dull enough to be affected by the two different greys. Everything on one side, including the borders, had the lighter grey mixed with it. On the other side everything was mixed with the darker grey.

It was worth making the effort to get it right. I hung Bunch of Fives on the wall and one pupil after another came in and said ‘It’s a mirror’ and had no difficulty in recognising reflections. It taught us a mathematical lesson. Reflection, in the mathematical sense, is extremely difficult for some pupils to grasp. Textbooks always have the image and reflection shown in the same colour, or just in outline. When they see slightly different shades pupils can readily accept that they are looking at what they might see in a mirror.

Unfortunately, the photos are very old.