Question

How can you represent −3⋅8
with a model?

Answer 1

−3⋅8 = −24.

You can model it several ways. Two simple ones:

1) Number line (3 jumps of size 8 to the left because the factor −3 tells you to go left):
0 → −8 → −16 → −24
(three jumps of 8 left gives −24)

2) Chip/array model (three groups of eight negative counters):
Row1: − − − − − − − −
Row2: − − − − − − − −
Row3: − − − − − − − −
Each "−" is a negative unit, total = 3×8 negative units = −24.

(Also you can view it as repeated addition: (−3) added 8 times = −3 + −3 + … + −3 (8 times) = −24.)