Pat Ashforth & Steve Plummer

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Counting Panes

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Printed Counting Panes are an adaptation of our highly acclaimed knitted Counting Pane. The original knitted version, which was made in 1996, was bought by the Mathematics Collection of the Science Museum (London). We have since made two more knitted Counting Panes which have frequently been exhibited throughout UK and featured in Educational and Craft magazines in US and UK, including Interweave Knits and Times Educational Supplement Colour Magazine.

A knitted Counting Pane takes over 100 hours to make so we now sell a booklet of instructions for anyone wanting to make their own .... and hand-printed versions.

What does Counting Pane show?

Counting Pane shows all multiplication tables up to 10
What is Counting Pane for?

It helps children see patterns in numbers and understand multiplication tables, in an informal situation. For adults, it is an original art work with a mathematical message.
Why are there 100 squares in the grid?

The squares represent the numbers 1 to 100. The squares across the top row represent 1 to 10, those on the second row 11 to 20, and so on.
How does it work?

Symbols stand for the different multiplication tables.
For example, in the yellow Counting Pane (above):

The number 2 is shown by a red crescent. Every number that divides by 2 has a red crescent in its square.

The number 3 is shown by a blue triangle. Every number that divides by 3 has a blue triangle in its square.

There is a different symbol for each number, up to 10.

There is no symbol for 1 as it would appear in every square.
How is this described mathematically?

The numbers that appear in a multiplication table are called multiples. A number that will divide exactly into another number is called a divisor or factor.
For example:

The multiples of 8 are 8, 16, 24, 32, etc.

The factors, or divisors, of 8 are 2, 4, 8 (and 1).
Why are some squares empty?

The empty squares are prime numbers. A prime number is a number that will only divide by itself and 1.
Special notes:

Some prime number squares are not empty. These are in the top row where the pattern for the tables is established.

Although the number 1 is shown as an empty square it is not now considered to be a prime number. A detailed explanation can be found here.

The Mathematics

How are the prints made?

The prints are made individually by hand. Every symbol is applied separately. This means there is scope for some customisation of your print (See below)  
What are they made from?

Fabrics vary but all are heavy weight so that they can be hung without framing.
How do I hang my print?

Each print has a channel at the top for a pole to be inserted. Poles have been left exposed in the large photos, merely to show their position. You could use:

A plain wooden pole, or broom handle, trimmed to size, with a cup hook screwed into each end.

A rigid extending curtain rod.
What size is the print?

The printed area is approximately 94cm square. The overall size is approximately 100cm square.
Can the print be framed?

Most people prefer the print unframed, because of its size but, as the edges are neatly finished before the hem is machine stitched, it would be very easy to undo the stitching and frame the print. It could also be stretched over a simple frame and stapled in place on the back.
Why are there different symbols on different prints?  

It is important that there are ten easily distinguishable symbols. Any set of symbols can be applied to any background.
What colours can I have?

Again, it is very important that the symbols are easy to identify. Backgrounds and printed colours have to work together to make this possible. Contact us if you have any particular requirements.
Can I buy the actual print I see in the photo?

We currently have only those prints that you see in the photo. You can buy any of those or we will make you another one very similar. Because they are individually hand-made there might be slight differences. Before paying, please contact us to make sure your chosen print is still available.

The Prints