I like the shove it to the nearest 10 approach. It makes a lot of calculations much simpler b/c they can be transformed to a simple multiplication by 10 and a addition or subtraction or two.
1. 6⋅7 = (6⋅10) - (6⋅3) = 60 - 18 = 42
2. 7⋅7 = (7⋅10) - (7⋅3) = 70 - 21 = 49
3. 13⋅19 = (13⋅20) - (13⋅1) = 260 - 13 = 247
4. 58⋅61 = (58⋅60) + (58⋅1) = 3480 + 58 = 3538
If we go up another order of magnitude, then the system starts really grinding to a halt though tbh :)
1. 6⋅7 = (6⋅10) - (6⋅3) = 60 - 18 = 42
2. 7⋅7 = (7⋅10) - (7⋅3) = 70 - 21 = 49
3. 13⋅19 = (13⋅20) - (13⋅1) = 260 - 13 = 247
4. 58⋅61 = (58⋅60) + (58⋅1) = 3480 + 58 = 3538
If we go up another order of magnitude, then the system starts really grinding to a halt though tbh :)