Problem
Time regroups in base sixty
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.
Measurement & data
Your answer
Watch out It's tempting to add four 50-minute blocks, but there are only three gaps between the 1st and 4th period starts.
How to solve
Strategy Look for a Pattern — 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.
1STEP 1
Find the gap between consecutive period starts
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 min
The same 'class then break' chunk repeats, so each start is one fixed step after the last.
3.MD.A.1Look For A Pattern2STEP 2
Count how many gaps to the 4th period
From the 1st period to the 4th period there are 3 gaps (1st → 2nd, 2nd → 3rd, 3rd → 4th). Each gap is 50 minutes.
3 × 50 = 150 min
Three equal 50-minute jumps gets you from the 1st start to the 4th start.
3.OA.A.3Identify Subproblems3STEP 3
Convert 150 minutes to hours and minutes
Regroup 150 minutes using 60 minutes = 1 hour: 150 = 120 + 30, so 150 minutes is 2 hours 30 minutes.
150 min = 2 h 30 min
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.
Why?
150 minutes splits into 120 minutes plus 30 leftover minutes, and those 120 minutes are exactly 2 whole hours.
Why?
Cutting 150 into 120 and 30 and then pushing the two pieces back together gives 150 again, so no time is lost or added.
🧱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?
120 minutes is 2 hours because an hour is a bundle of 60 minutes and 120 is two of those bundles.
Why?
One hour is by definition a fixed 60 minutes, the same way every larger time unit is a set number of smaller ones.
🧱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?
Two bundles of 60 minutes is 60 counted twice, which comes to 120 minutes.
🧱Multiplication as equal groupsa times b means a equal groups of b — it is just repeated adding of the same amount.
4STEP 4
Add the elapsed time to the start time
Add 2 hours 30 minutes to 8:50: first to 10:50, then +30 min carries past the hour to 11:20.
8:50 + 2:30 = 11:20
When the minutes pass 60 you carry an hour, just like reading the clock forward.
3.MD.A.1Identify SubproblemsAnswer
11:20
8:50 + 2:30 = 11:20
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.
Takeaway
Spot the repeating 50-minute 'class + break' chunk, multiply by 3, and add - that's all Grade 3 time sense!
- Find the gap between consecutive period starts
- Count how many gaps to the 4th period
- Convert 150 minutes to hours and minutes
- Add the elapsed time to the start time
Where next?
Another one like thissuggested
Step back and solidifysuggested