Sullivan multiplication solution
The Sullivan multiplication solution is a visual method for teaching Basic Multiplication developed by Paul Sullivan of Cambridge, Ontario, Canada. Sullivan describes it as a Universal Solution for Basic Multiplication, used Universally and applicable universally in classrooms and homes. The method uses a coded multiplication grid to make the steps of multi-digit multiplication visible to the Student. It is designed so that the largest single calculation a Student must perform is 9 x 9.
Sullivan presents the method as one written standard for Basic Multiplication. In his account, the Student begins with instructional codes in the grid, then works with the codes removed, then drops the grid and the times table, and finally performs the standard algorithm without support.
Background
Sullivan argues that children leaving Grade 4 are too often unable to do Basic Multiplication because elementary instruction exposes Students to several written procedures for the same calculation without giving them one reliable method. In his published comparison, the five written methods are the standard algorithm, partial products, the area model or box method, the lattice method, and the grid method. He argues that four of the five are not used in later algebra, the trades, or digital work, while the standard algorithm is difficult for many Students because it is commonly taught through spoken steps that the Student cannot see or check.
He developed this argument in two essays, The Virus Within and One Equation, Six Methods. The latter compares the methods on the equation 34 x 27 = 918 and includes The Sullivan Multiplication Solution as a visual alternative.
Method
The Sullivan Multiplication Solution uses a worksheet range for the multiplication forms Students are expected to master: 1 x 1 (one digit by one digit), 2 x 1 (two digits by one digit), 2 x 2 (two digits by two digits), and 3 x 2 (three digits by two digits). The grid contains instructional codes that show where each partial result belongs. The Teacher introduces the worksheet with a times table available, and the Student calculates in their head where possible or uses the times table where needed.
The intended progression has three stages. First, the Student practises with the codes visible. Second, the codes are removed while the grid remains. Third, the grid and the times table are dropped, and the Student performs the standard algorithm alone. Sullivan describes accuracy, rather than speed, as the measure of success.
Assistive technology
The online service includes an Assistive Technology section. Sullivan has described that section as usable in the manner of a basic app, so a Student can practise with a Parent away from a desk or classroom.
Evidence status
As of October 2026, The Sullivan Multiplication Solution has not been independently evaluated in a completed formal trial. Sullivan has proposed school pilot studies in which baseline scores from the first part of the school year would be compared with results at the end of the pilot, with Friday test worksheets recorded by worksheet type and by whether the times table was used. Data handling in the proposed pilot removes Student names at the school level before results are returned.
References
Sullivan, Paul. One Equation, Six Methods. Substack, 14 October 2026. https://rackrunner1963.substack.com/p/one-equation-six-methods
Sullivan, Paul. The Virus Within. Substack, 16 September 2026. https://rackrunner1963.substack.com/p/the-virus-within
Statistics Canada. Elementary-Secondary Education Survey, Table 37-10-0007, regular programs for youth, public schools, Canada, 2023/24.
OECD. PISA mathematics results for Canada, score 485.
External links
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