Problem
Starting from 8:40, the Boston train leaves every 8 minutes. So the minutes after 8:40 when it departs are the multiples of 8.
Skip-counting by 8 just lists when the same train comes back; a 4th grader can count 8, 16, 24.
4.OA.B.4Make A Systematic ListFrom the same start, the Chicago train leaves every 6 minutes, so its departure minutes after 8:40 are the multiples of 6.
Skip-counting by 6 lists the Chicago train's returns; comparing two lists is something kids can do by eye.
4.OA.B.4Make A Systematic ListThe first number on both lists is the least common multiple of 8 and 6, which is 24.
The first matching multiple is the soonest moment both repeating events can happen together.
6.NS.B.4Look For A PatternThe two trains next leave together 24 minutes after 8:40.
Each train's departures come around on its own fixed cycle, so the Boston train leaves at whole 8-minute gaps from the start and the Chicago train at whole 6-minute gaps.
They can only leave together at a minute count that both cycles land on, and 24 is the first such count.
A count both trains land on has to be built out of whole 8-minute gaps and also out of whole 6-minute gaps, so it is a multiple of each.
Adding those 24 minutes to 8:40 brings the next shared departure to 9:04.
Once we know the gap is 24 minutes, finding the clock time is just adding minutes.
4.OA.A.3Look For A PatternTwo events that repeat on their own beats line up again at the least common multiple of their gaps.