Time regroups in base sixty

3.MD.A.1 · take · grade 3

Archetype: Elapsed Time and Base-Sixty Regrouping · step in a 10-type progression

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.

Show solution

Understand

Periods at Mia's school each last 40 minutes and are followed by a 10-minute break. The 1st period starts at 8:50. I need to find what time the 4th period begins.

Givens

1st period starts at 8:50.
Each period is 40 minutes long.
After each period there is a 10-minute break.

Unknowns

The start time of the 4th period.

Constraints

60 minutes = 1 hour (regroup when minutes reach 60).
Between the start of one period and the start of the next is 40 + 10 = 50 minutes.

Plan

#5 Look for a Pattern · also uses: #7 Identify Subproblems

Each period-then-break repeats the same 50-minute block, so the gap from one start to the next is constant. Finding that pattern lets me add three 50-minute blocks to reach the 4th period, regrouping minutes into hours as needed.

Execute

#5 Look for a Pattern 3.MD.A.1

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.

40 + 10 = 50 \text{ min}

The same 'class then break' chunk repeats, so each start is one fixed step after the last.

#7 Identify Subproblems 3.OA.A.3

From the 1st period to the 4th period there are 3 gaps (1st->2nd, 2nd->3rd, 3rd->4th). Each gap is 50 minutes.

3 \times 50 = 150 \text{ min}

Three equal 50-minute jumps gets you from the 1st start to the 4th start.

#7 Identify Subproblems 3.MD.A.1

Regroup 150 minutes using 60 minutes = 1 hour: 150 = 120 + 30, so 150 minutes is 2 hours 30 minutes.

150 \text{ min} = 2 \text{ h } 30 \text{ min}

Trading every 60 minutes for an hour is the base-sixty regrouping kids use for clocks.

#7 Identify Subproblems 3.MD.A.1

Add 2 hours 30 minutes to 8:50. First add 2 hours to get 10:50, then add 30 minutes: 50 + 30 = 80 minutes = 1 hour 20 minutes, so 10:50 + 30 min = 11:20.

8{:}50 + 2{:}30 = 11{:}20

When the minutes pass 60 you carry an hour, just like reading the clock forward.

Answer: 11:20

Review

Each period plus break is 50 minutes, so four periods of school start across about 2.5 hours; starting at 8:50, ending near 11:20 in the late morning is a sensible school schedule.

Make a systematic list (tool 2): 1st 8:50, 2nd 9:40, 3rd 10:30, 4th 11:20 - adding 50 minutes each line gives the same 11:20.

Standards · min grade 3

3.MD.A.1 Tell and write time to the nearest minute and solve elapsed time problems — Adding elapsed minutes to a start time and regrouping minutes into hours.
3.OA.A.3 Solve multiplication and division word problems within 100 — Multiplying 3 gaps x 50 minutes to find the total elapsed time.

💡 Spot the repeating 50-minute 'class + break' chunk, multiply by 3, and add - that's all Grade 3 time sense!