3B · Chapter 14 · Lesson 4
Calculating Time — Part 3
Solve elapsed-time problems crossing noon or midnight.
Today's mathematical question
How many minutes pass from 11:45 p.m. to 12:15 a.m. the next day?
Learning target
Solve elapsed-time problems crossing noon or midnight.
Before starting: Prior lesson: Calculating Time — Part 2. Try the warm-up independently.
Prerequisite · 3 questions
Check earlier skills first
These are earlier ideas you need for today; revisit them if they are difficult.
- P1
A lesson begins at 11:50 a.m. and lasts 35 minutes. When does it finish?
Reveal explanation
Answer: 12:25 p.m.
Add 35 minutes to the start time, crossing each next hour carefully. 11:50 a.m. plus 35 minutes is 12:25 p.m..
Analog clock showing 11:50 a.m.. - P2
A lesson begins at 9:25 a.m. and lasts 90 minutes. When does it finish?
Reveal explanation
Answer: 10:55 a.m.
Add 90 minutes to the start time, crossing each next hour carefully. 9:25 a.m. plus 90 minutes is 10:55 a.m..
Analog clock showing 9:25 a.m.. - P3
A lesson begins at 7:30 a.m. and lasts 50 minutes. When does it finish?
Reveal explanation
Answer: 8:20 a.m.
Add 50 minutes to the start time, crossing each next hour carefully. 7:30 a.m. plus 50 minutes is 8:20 a.m..
Analog clock showing 7:30 a.m..
Learn and understand
A schedule can cross noon or midnight. Noon marks the change from a.m. to p.m.; midnight begins a new day. For example, 11:45 p.m. plus 30 minutes is 12:15 a.m. the next day. Make the day change explicit when interpreting an answer. To cross midnight, first count to 12:00 a.m. and then continue into the next day. To cross noon, switch from a.m. to p.m. without adding a day.
Represent it three ways
- Concrete: Build equal pieces, measures, counters or shapes with real objects when useful.
- Pictorial: Draw a timeline with labeled noon or midnight. Use separate jumps before and after the change, then add durations.
- Abstract: Write the matching number sentence, calculation, comparison or mathematical description. Explain each number's unit.
Important vocabulary
- noon
- 12 p.m.
- midnight
- 12 a.m.
- duration
- time between events
Fully worked examples and checks
Try each new understanding check before revealing the explanation.
Worked example 1
Explore, calculate, verify
How many minutes pass from 11:45 p.m. to 12:15 a.m. the next day?
- Identify the whole, the units, and what the question asks.
- Count 15 minutes to midnight, then 15 minutes to 12:15 a.m. The total duration is 30 minutes.
- Check that the answer uses the right units and makes sense.
Answer: 30 min
Check your understanding 1
How many minutes pass from 11:35 a.m. to 1:50 p.m.?
Reveal answer and explanation
135 min — Count from 11:35 a.m. to the next whole hour, then onward to 1:50 p.m.. The intervals add to 135 minutes.
Worked example 2
Explore, calculate, verify
How many minutes pass from 11:40 a.m. to 12:15 p.m.?
- Identify the whole, the units, and what the question asks.
- Twenty minutes lead to noon, then fifteen more minutes reach 12:15 p.m.: 35 minutes.
- Check that the answer uses the right units and makes sense.
Answer: 35 min
Check your understanding 2
How many minutes pass from 11:15 p.m. to 12:45 a.m.?
Reveal answer and explanation
90 min — Count from 11:15 p.m. to the next whole hour, then onward to 12:45 a.m.. The intervals add to 90 minutes.
Worked example 3
Explore, calculate, verify
How many minutes pass from 10:50 a.m. to 11:15 a.m.?
- Identify the whole, the units, and what the question asks.
- Count from 10:50 a.m. to the next whole hour, then onward to 11:15 a.m.. The intervals add to 25 minutes.
- Check that the answer uses the right units and makes sense.
Answer: 25 min
Check your understanding 3
How many minutes pass from 11:35 a.m. to 12:50 p.m.?
Reveal answer and explanation
75 min — Count from 11:35 a.m. to the next whole hour, then onward to 12:50 p.m.. The intervals add to 75 minutes.
Guided · 5 questions
Guided practice
Keep the model and earlier examples visible while practising.
- G1
How many minutes pass from 11:35 a.m. to 1:25 p.m.?
Reveal explanation
Answer: 110 min
Count from 11:35 a.m. to the next whole hour, then onward to 1:25 p.m.. The intervals add to 110 minutes.
Analog clock showing 11:35 a.m.. - G2
How many minutes pass from 11:15 p.m. to 11:50 p.m.?
Reveal explanation
Answer: 35 min
Count from 11:15 p.m. to the next whole hour, then onward to 11:50 p.m.. The intervals add to 35 minutes.
Analog clock showing 11:15 p.m.. - G3
How many minutes pass from 11:40 p.m. to 1:30 a.m.?
Reveal explanation
Answer: 110 min
Count from 11:40 p.m. to the next whole hour, then onward to 1:30 a.m.. The intervals add to 110 minutes.
Analog clock showing 11:40 p.m.. - G4
How many minutes pass from 10:50 a.m. to 12:40 p.m.?
Reveal explanation
Answer: 110 min
Count from 10:50 a.m. to the next whole hour, then onward to 12:40 p.m.. The intervals add to 110 minutes.
Analog clock showing 10:50 a.m.. - G5
How many minutes pass from 11:35 a.m. to 1:05 p.m.?
Reveal explanation
Answer: 90 min
Count from 11:35 a.m. to the next whole hour, then onward to 1:05 p.m.. The intervals add to 90 minutes.
Analog clock showing 11:35 a.m..
Independent · 8 questions
Independent practice
Work these without hints and explain the method used. Write answers on paper.
- I1
How many minutes pass from 11:35 a.m. to 12:10 p.m.?
Reveal explanation
Answer: 35 min
Count from 11:35 a.m. to the next whole hour, then onward to 12:10 p.m.. The intervals add to 35 minutes.
Analog clock showing 11:35 a.m.. - I2
How many minutes pass from 10:50 a.m. to 1:05 p.m.?
Reveal explanation
Answer: 135 min
Count from 10:50 a.m. to the next whole hour, then onward to 1:05 p.m.. The intervals add to 135 minutes.
Analog clock showing 10:50 a.m.. - I3
How many minutes pass from 11:40 p.m. to 12:30 a.m.?
Reveal explanation
Answer: 50 min
Count from 11:40 p.m. to the next whole hour, then onward to 12:30 a.m.. The intervals add to 50 minutes.
Analog clock showing 11:40 p.m.. - I4
How many minutes pass from 11:35 a.m. to 12:25 p.m.?
Reveal explanation
Answer: 50 min
Count from 11:35 a.m. to the next whole hour, then onward to 12:25 p.m.. The intervals add to 50 minutes.
Analog clock showing 11:35 a.m.. - I5
How many minutes pass from 11:40 p.m. to 12:15 a.m.?
Reveal explanation
Answer: 35 min
Count from 11:40 p.m. to the next whole hour, then onward to 12:15 a.m.. The intervals add to 35 minutes.
Analog clock showing 11:40 p.m.. - I6
How many minutes pass from 11:35 a.m. to 12:00 p.m.?
Reveal explanation
Answer: 25 min
Count from 11:35 a.m. to the next whole hour, then onward to 12:00 p.m.. The intervals add to 25 minutes.
Analog clock showing 11:35 a.m.. - I7
How many minutes pass from 11:40 p.m. to 12:55 a.m.?
Reveal explanation
Answer: 75 min
Count from 11:40 p.m. to the next whole hour, then onward to 12:55 a.m.. The intervals add to 75 minutes.
Analog clock showing 11:40 p.m.. - I8
How many minutes pass from 11:15 p.m. to 11:40 p.m.?
Reveal explanation
Answer: 25 min
Count from 11:15 p.m. to the next whole hour, then onward to 11:40 p.m.. The intervals add to 25 minutes.
Analog clock showing 11:15 p.m..
Challenge · 2 questions
Challenge and error analysis
Go beyond arithmetic: justify a claim, correct reasoning, or connect two representations.
- C1
Explain how 11:55 a.m. plus 45 minutes crosses noon. At what time does it finish?
Reveal explanation
Answer: 12:40 p.m.
5 minutes reach noon; then 40 more minutes reach 12:40 p.m.
- C2
A trip begins at 11:50 p.m. and lasts 50 minutes. On which day does it finish and at what time?
Reveal explanation
Answer: Next day at 12:40 a.m.
10 minutes reach midnight; 40 minutes more reach 12:40 a.m. on the next day.
Exit · 3 questions
Exit check
Solve independently, then return on another day to check retention.
- E1
How many minutes pass from 11:40 p.m. to 1:55 a.m.?
Reveal explanation
Answer: 135 min
Count from 11:40 p.m. to the next whole hour, then onward to 1:55 a.m.. The intervals add to 135 minutes.
Analog clock showing 11:40 p.m.. - E2
How many minutes pass from 11:15 p.m. to 1:05 a.m.?
Reveal explanation
Answer: 110 min
Count from 11:15 p.m. to the next whole hour, then onward to 1:05 a.m.. The intervals add to 110 minutes.
Analog clock showing 11:15 p.m.. - E3
How many minutes pass from 11:15 p.m. to 12:05 a.m.?
Reveal explanation
Answer: 50 min
Count from 11:15 p.m. to the next whole hour, then onward to 12:05 a.m.. The intervals add to 50 minutes.
Analog clock showing 11:15 p.m..