Depth · one concept from first principles · step 2 of 4
The class schedule at Mia's school is shown below. Find the time that the 4th period starts.
| Period | Start time | Class length | Break |
|---|---|---|---|
| 1st period | 8:50 | 40 min | 10 min |
| 2nd period | 40 min | 10 min | |
| 3rd period | 40 min | 10 min | |
| 4th period |
The 1st period starts at 8:50. Each period lasts 40 minutes and is followed by a 10-minute break.
A period is 40 minutes and the following break is 10 minutes, so the next period starts 40 + 10 = 50 minutes after the previous one started.
The same 'class then break' chunk repeats, so each start is one fixed step after the last.
3.MD.A.1Look For A PatternFrom the 1st period to the 4th period there are 3 gaps (1st → 2nd, 2nd → 3rd, 3rd → 4th). Each gap is 50 minutes.
Three equal 50-minute jumps gets you from the 1st start to the 4th start.
3.OA.A.3Identify SubproblemsRegroup 150 minutes using 60 minutes = 1 hour: 150 = 120 + 30, so 150 minutes is 2 hours 30 minutes.
Trading every 60 minutes for an hour is the base-sixty regrouping kids use for clocks.
3.MD.A.1Identify Subproblems150 minutes of elapsed time is the same as 2 hours and 30 minutes.
150 minutes splits into 120 minutes plus 30 leftover minutes, and those 120 minutes are exactly 2 whole hours.
Cutting 150 into 120 and 30 and then pushing the two pieces back together gives 150 again, so no time is lost or added.
120 minutes is 2 hours because an hour is a bundle of 60 minutes and 120 is two of those bundles.
One hour is by definition a fixed 60 minutes, the same way every larger time unit is a set number of smaller ones.
Two bundles of 60 minutes is 60 counted twice, which comes to 120 minutes.
Add 2 hours 30 minutes to 8:50: first to 10:50, then +30 min carries past the hour to 11:20.
When the minutes pass 60 you carry an hour, just like reading the clock forward.
3.MD.A.1Identify SubproblemsSpot the repeating 50-minute 'class + break' chunk, multiply by 3, and add - that's all Grade 3 time sense!
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The same shape shows up later on the AMC, as Arithmetic Expression Decomposition. Why the shapes repeat →