I wanted the students to “discover” finding the least common multiple before going through examples. We started with a “Jumping Jack” experiment. I asked for two volunteers to come up. I warned them they would be doing some a lot of physical activity …may even break a sweat! …(some sensed my sarcasm:) ) The scenario is this:
One student would jump every 4 seconds. The other student would jump every 10 seconds. The class would watch the timer and the jumpers to see at what point they would jump at the exact same time.
We continued watching and finally saw that after 20 seconds they both jumped at the exact same time.
The next scenario involved an example of 2 people going to the gym. One goes every 5 days, one goes every 3 days. My students marked these days into a calendar on the Smart Board and realized after 15 days they would go to the gym on the exact same day.
Most were catching on to the idea of the least common multiple, so for the last scenario I asked them to anticipate the solution without actually using the calendar. In this example, we had a student cleaning his room every 6 days, and sweeping the kitchen every 9 days. I asked, “How many days will it take for him to sweep and clean on the exact same day?” I heard multiple answers, but most said 18 would come first. Several students said 36 days, which brought up a good teachable moment! The class was able to explain that the boy would clean and sweep on the 36th day, and really any multiple of “18”. He would clean and sweep on the 36th day, 72nd day, 108th day, and so on. But the FIRST time he would clean and sweep on the same day would be the 18th. This led us right to the lesson of Least Common Multiple. I love when they can discover it themselves!