multiplying directed numbers

using a grid can establish some rationale for the multiplication of two negative numbers being a positive number

this approach was suggested to me by Gill Hatch, when she was at Manchester Metropolitan University

a powerpoint goes through the solution steps
but it's probably better developed with student suggestions

firstly, using some examples of numbers that sum to 5 (down) times two numbers adding up to 6 (across)
establish that the result of adding the four boxes must be 30

eventually there may be a suggestion that involves two negatives (as in the 4th one)

knowing that the overall total must be 30 identifies the bottom right hand product needed to make this total