Problem
Find the rule of changing clock times
Five clocks are joined by arrows, and the time changes by a fixed rule: 3:20 → 3:50 → 4:20 → 4:50 → ?. What time does the fifth (last) clock show?
OperationsMeasurement & data
Your answer
Watch out When you add 30 minutes to 4:50, don't write it as 4:80 — 60 minutes make 1 hour, so carry that hour up and leave only the remaining 20 minutes as minutes.
How to solve
Strategy Look for a Pattern — The times form a sequence, so first find how much is added at each step (the pattern), then apply that rule to the last time while watching minutes roll over into hours (the units).
1STEP 1
Find the time added each step
3:20 → 3:50 → 4:20 → 4:50 — each step adds 30 minutes.
3:20 +30 → 3:50 +30 → 4:20 +30 → 4:50
Each clock links to the next by the same fixed change. Comparing neighboring times shows every gap is the same 30 minutes.
Look For A PatternFinding Patterns4.OA.C.52STEP 2
Apply the rule once more
Adding 30 minutes to 4:50 rolls the hour forward to 5:20.
4:50 + 30 min = 5:20
50 plus 30 minutes is 80 minutes, which splits into 60 minutes (one full hour) and 20 minutes left over. That 60-minute block renames as one hour on the clock, so the hour rises by one and only the leftover 20 minutes remain.
Analyze The UnitsFinding Patterns2.MD.C.7Adding the 30-minute step to 4:50 carries the minutes past a full hour, so the clock rolls up into the next hour instead of reading 4:80.
Why?
Fifty minutes and thirty more minutes come to eighty minutes, which is more than one full hour.
Why?
Eighty minutes is one whole hour of sixty minutes with twenty minutes left over.
Why?
Eighty minutes splits with no gap or overlap into sixty minutes and twenty minutes.
🧱Whole is the sum of its partsBreak a thing into pieces with no gaps or overlaps and the pieces add back to the whole.
Why?
A full sixty minutes is exactly one hour, so that block of sixty renames as one hour on the clock.
🧱A bigger unit is a fixed count of smaller unitsA bigger unit always equals the same fixed number of smaller units (1 hour = 60 minutes, 1 km = 1000 m), so a measure can be renamed between them.
Why?
The one whole hour is carried up so the hour count rises by one, while the leftover minutes stay behind as the new minute reading.
Why?
Joining one more hour to the hours already on the clock makes a total that is exactly one hour greater.
🧱Whole is the sum of its partsBreak a thing into pieces with no gaps or overlaps and the pieces add back to the whole.
Answer
5:20
4:50 + 30 min = 5:20
Check — the hours go 3, 3, 4, 4, 5 and the minutes alternate 20, 50, 20, 50, 20, exactly what repeatedly adding 30 minutes produces, so 5:20 is correct.
Takeaway
When times change by a fixed rule, find the gap between neighbors to spot the rule, and remember to carry one hour whenever the minutes pass 60.
- Compare neighboring times → increases by 30 minutes each time
- Add 30 minutes to 4:50 → 80 minutes = 60 + 20
- 60 minutes make 1 hour, so the hour rises to 5:20
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