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Three Consecutive Integers
Any three consecutive integers have an interesting property.
Write down any three consecutive integers, such as 5, 6, 7.
Square the second number.
Multiply the first number by the third.
Note how the numbers that you got in steps b and c are related.
Try this with at least three different sets of starting numbers.
Show the integers you used each time and the calculations that you did, then compare the resulting two numbers.
By using algebraic expressions with a variable, show that your conclusion will always be true.
Extra: If the resulting two numbers differ by four, describe how the three starting numbers are related.