Problem
Find the rule of changing clock times
Five clocks in a row change by a fixed rule. From the first four times, find the rule and use it to find the time on the fifth clock.
OperationsMeasurement & data
Your answer
Watch out When you add 30 minutes to 4:50 the minutes pass 60, so you must carry into the next hour rather than writing 4:80.
How to solve
Strategy Look for a Pattern — The times form a sequence, so I find how much time is added at each step (the pattern), then add that same amount to the fourth time, watching the minute-to-hour rollover (units).
1STEP 1
Find the time added each step
Every clock jumps the same amount: 3:20→3:50→4:20→4:50 each add 30 min. So the rule is add 30 minutes each step.
3{:}20 → 3{:}50 → 4{:}20 → 4{:}50
Reading each clock and comparing tells you the steady 30-minute jump.
2.MD.C.7Look For A Pattern2STEP 2
Apply the rule once more
Add 30 min to 4:50: 50 + 30 = 80 min = 1 hour 20 min, so carry the hour to reach 5:20.
4{:}50 + 30 min = 5{:}20
When the minutes pass 60 you carry one hour, just like carrying in place value.
2.MD.C.7Analyze The UnitsAdding 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
The hour goes 3, 3, 4, 4, 5 and the minutes alternate 20, 50, 20, 50, 20, which is exactly what adding 30 minutes repeatedly produces. 5:20 continues both patterns.
Takeaway
Each clock jumps 30 minutes, and when minutes pass 60 you just bump up one hour: 4:50 + 30 = 5:20!
- Find the time added each step
- Apply the rule once more
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