Question

How can you represent −2⋅9
with a model?

Answer 1

First note the value: −2 · 9 = −18.

Ways to represent it with a model:

1. Repeated addition model
- Interpret as 9 copies of −2:
(−2) + (−2) + (−2) + (−2) + (−2) + (−2) + (−2) + (−2) + (−2) = −18.

2. Integer chips (counters)
- Use red chips for −1. Make 9 groups of 2 red chips each → 18 red chips total → −18.

3. Number line
- From 0 take 9 jumps of size −2 (each jump left by 2): you land at −18.
- (Equivalently, take 2 jumps of size −9 and you also land at −18.)

4. Area/rectangle model with sign
- Draw a 2 by 9 rectangle (area 18) and indicate the product is negative (e.g., place it below the x-axis or shade it red) to show −18.

Any of these models makes clear that −2·9 = −18.