Choose four consecutive odd counting numbers. Take the product of the middle two numbers and subtract the product of the first number and the last number. Try a few samples and formulate a rule. Explain why the rule works.
What would happen if you used four consecutive even counting numbers in the above problem? Would your rule change? If so, find a new rule, and explain why this new rule works and why it is different from the original rule. If the rule does not change, does your explanation change?