Sensim Math · Depth 한국어

2-2 · Finding Patterns

Find the rule of changing clock times

4.OA.C.53.MD.A.1 · take · grade 4

Archetype: Repeating Cycle Patterns · step in a 6-type progression

▶ Practice — 10 problems

The clocks change according to a fixed rule. Find the rule for how the clocks change, then find the time shown on the last clock.

Five clock faces are placed in a row from left to right, joined by arrows. The first clock shows 3:203{:}20, the second shows 3:503{:}50, the third shows 4:204{:}20, and the fourth shows 4:504{:}50. Find the time shown on the fifth (last) clock.

3:20 3:50 4:20 4:50 ?
Show solution

Understand

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.

Givens
  • Clock 1 shows 3:20.
  • Clock 2 shows 3:50.
  • Clock 3 shows 4:20.
  • Clock 4 shows 4:50.
Unknowns
  • The time shown on the fifth (last) clock.
Constraints
  • The same time change is applied from each clock to the next.
  • 60 minutes make 1 hour, so 50 + 30 minutes rolls over to the next hour.

Plan

#5 Look for a Pattern · also uses: #8 Analyze the Units

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).

Execute

#5 Look for a Pattern 2.MD.C.7
From 3:20 to 3:50 is +30 minutes. From 3:50 to 4:20 is also +30 minutes (50 + 30 = 80 minutes = 1 hour 20 minutes). From 4:20 to 4:50 is +30 minutes. So the rule is: add 30 minutes each time.
3:20→+303:50→+304:20→+304:503{:}20 \xrightarrow{+30} 3{:}50 \xrightarrow{+30} 4{:}20 \xrightarrow{+30} 4{:}50
Reading each clock and comparing tells you the steady 30-minute jump.
#8 Analyze the Units 2.MD.C.7
Add 30 minutes to 4:50. Since 50 + 30 = 80 minutes, that is 1 hour past the hour with 20 minutes left, so 4:50 becomes 5:20.
4:50+30 min=5:204{:}50 + 30\text{ min} = 5{:}20
When the minutes pass 60 you carry one hour, just like carrying in place value.
Answer: 5:20

Review

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.

Notice the times come in pairs sharing an hour (:20 then :50); after 4:50 the next must restart the cycle at the following hour, giving 5:20.

Standards · min grade 2

  • 2.MD.C.7 Tell and write time from analog and digital clocks to nearest five minutes — Reading the clock times and adding 30 minutes including the hour rollover.
💡 Each clock jumps 30 minutes, and when minutes pass 60 you just bump up one hour: 4:50 + 30 = 5:20!