Part 1: . Choose three consecutive integers e.g. 6, 7, 8 • Multiply the largest and the smallest integer 6x8 = 48 . Multiply the middle integer by itself 7x7 = 49 Do similar calculations for other sets of three consecutive integers. What patterns do you notice? Prove, using algebra, that the pattern holds for any three consecutive integers. Part 2: Investigate three other integers that "follow" each other in a different way, e.g. 6, 8, 10 or 6, 9, 12 (the difference between the numbers is constant.) • Multiply the largest and the smallest integer • Multiply the middle integer by itself Describe any patterns that you notice and prove that the pattern holds for any three numbers that "follow" each other in this way. Part 3: Investigate any three numbers that "follow" each other by going up by a constant amount n. • Multiply the largest and the smallest integer • Multiply the middle integer by itself Find and express rules for any pattern you find. You have to fully explain your thinking and prove your rule.​