Traditional long multiplication taught in many older text-books exclusively use the "scacchero" or "chessboard" method. The grid layout uses left cascading displacement and the need for placeholder 0's, 00s, 000's etc. This also demands fully memorising large areas of single-number products and recording and remembering to "carry over" the higher power number to the left each time. The important column headings are often omitted from books by lazy editors and lack of squared layout paper can lead to chaos for some children.

The Gelosia or "grating" method is well illustrated below by two examples in the "Treviso Arithmetic" found near Venice in 1478. The diagonals separate the tens and units and render unnecessary the carrying process except in adding the partial products. These diagonals sometimes slant one way and sometimes another, but in general the layout on the left was the favourite. The method is very old having appeared in the "Lilavati" about 1150) and in other Hindu books.

"I recommend adding the decimal power headings (e.g. units, tens, hundreds across the top and down the right hand side. This method is less strenuous and very secure for many children- teachers and trainees are invited to try it themselves. Like mediaeval traders I have found that initially many children like a small (usefully laminated) product table ready reckoner (12 x 12) to assist their growing memories of significant number patterns"-

John Dodridge ex teacher, senior lecturer and Maths Inspector