3B · Chapter 14 · Lesson 2
Calculating Time — Part 1
Use an elapsed-time number line within a day.
Today's mathematical question
How many minutes pass from 4:00 p.m. to 4:35 p.m.?
Learning target
Use an elapsed-time number line within a day.
Before starting: Prior lesson: Units of Time. 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
Express 135 seconds in minutes and seconds.
Reveal explanation
Answer: 2 min 15 s
Group the 135 seconds into complete 60-second minutes, then count the 15 remaining seconds.
- P2
Convert 2 h 25 min into minutes.
Reveal explanation
Answer: 145 min
Each hour is 60 minutes. 2 × 60 + 25 = 145 minutes.
- P3
Convert 2 min 10 s into seconds.
Reveal explanation
Answer: 130 s
Each minute contains 60 seconds. 2 × 60 + 10 = 130 seconds.
Learn and understand
Elapsed time is the distance between two clock times. Counting forward to the next hour often helps: from 9:45 to 10:00 is 15 minutes, then continue to the finish time. Add the intervals to get total duration. From 9:45 to 10:10, count 15 minutes to 10:00 and then 10 more. The elapsed time is 25 minutes; the clock reading is not a decimal number.
Represent it three ways
- Concrete: Build equal pieces, measures, counters or shapes with real objects when useful.
- Pictorial: Draw an open timeline and label each jump in minutes. Separate the jump to an hour from the whole-hour jumps.
- Abstract: Write the matching number sentence, calculation, comparison or mathematical description. Explain each number's unit.
Important vocabulary
- elapsed time
- duration between start and finish
- timeline
- diagram of events in order
- interval
- span between two times
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 4:00 p.m. to 4:35 p.m.?
- Identify the whole, the units, and what the question asks.
- Count from 4:00 p.m. to the next whole hour, then onward to 4:35 p.m.. The intervals add to 35 minutes.
- Check that the answer uses the right units and makes sense.
Answer: 35 min
Check your understanding 1
How many minutes pass from 9:15 a.m. to 11:05 a.m.?
Reveal answer and explanation
110 min — Count from 9:15 a.m. to the next whole hour, then onward to 11:05 a.m.. The intervals add to 110 minutes.
Worked example 2
Explore, calculate, verify
How many minutes pass from 4:45 p.m. to 6:15 p.m.?
- Identify the whole, the units, and what the question asks.
- Count from 4:45 p.m. to the next whole hour, then onward to 6:15 p.m.. The intervals add to 90 minutes.
- Check that the answer uses the right units and makes sense.
Answer: 90 min
Check your understanding 2
How many minutes pass from 3:55 p.m. to 6:10 p.m.?
Reveal answer and explanation
135 min — Count from 3:55 p.m. to the next whole hour, then onward to 6:10 p.m.. The intervals add to 135 minutes.
Worked example 3
Explore, calculate, verify
How many minutes pass from 9:20 a.m. to 10:25 a.m.?
- Identify the whole, the units, and what the question asks.
- Count from 9:20 a.m. to the next whole hour, then onward to 10:25 a.m.. The intervals add to 65 minutes.
- Check that the answer uses the right units and makes sense.
Answer: 65 min
Check your understanding 3
How many minutes pass from 4:20 p.m. to 5:35 p.m.?
Reveal answer and explanation
75 min — Count from 4:20 p.m. to the next whole hour, then onward to 5:35 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 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.. - G2
How many minutes pass from 12:00 p.m. to 12:50 p.m.?
Reveal explanation
Answer: 50 min
Count from 12:00 p.m. to the next whole hour, then onward to 12:50 p.m.. The intervals add to 50 minutes.
Analog clock showing 12:00 p.m.. - G3
How many minutes pass from 9:45 a.m. to 10:50 a.m.?
Reveal explanation
Answer: 65 min
Count from 9:45 a.m. to the next whole hour, then onward to 10:50 a.m.. The intervals add to 65 minutes.
Analog clock showing 9:45 a.m.. - G4
How many minutes pass from 3:50 p.m. to 4:55 p.m.?
Reveal explanation
Answer: 65 min
Count from 3:50 p.m. to the next whole hour, then onward to 4:55 p.m.. The intervals add to 65 minutes.
Analog clock showing 3:50 p.m.. - G5
How many minutes pass from 7:30 a.m. to 8:05 a.m.?
Reveal explanation
Answer: 35 min
Count from 7:30 a.m. to the next whole hour, then onward to 8:05 a.m.. The intervals add to 35 minutes.
Analog clock showing 7:30 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 10:10 a.m. to 12:25 p.m.?
Reveal explanation
Answer: 135 min
Count from 10:10 a.m. to the next whole hour, then onward to 12:25 p.m.. The intervals add to 135 minutes.
Analog clock showing 10:10 a.m.. - I2
How many minutes pass from 7:10 a.m. to 7:35 a.m.?
Reveal explanation
Answer: 25 min
Count from 7:10 a.m. to the next whole hour, then onward to 7:35 a.m.. The intervals add to 25 minutes.
Analog clock showing 7:10 a.m.. - I3
How many minutes pass from 9:25 a.m. to 10:15 a.m.?
Reveal explanation
Answer: 50 min
Count from 9:25 a.m. to the next whole hour, then onward to 10:15 a.m.. The intervals add to 50 minutes.
Analog clock showing 9:25 a.m.. - I4
How many minutes pass from 4:40 p.m. to 5:30 p.m.?
Reveal explanation
Answer: 50 min
Count from 4:40 p.m. to the next whole hour, then onward to 5:30 p.m.. The intervals add to 50 minutes.
Analog clock showing 4:40 p.m.. - I5
How many minutes pass from 1:25 p.m. to 2:55 p.m.?
Reveal explanation
Answer: 90 min
Count from 1:25 p.m. to the next whole hour, then onward to 2:55 p.m.. The intervals add to 90 minutes.
Analog clock showing 1:25 p.m.. - I6
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.. - I7
How many minutes pass from 10:05 a.m. to 11:55 a.m.?
Reveal explanation
Answer: 110 min
Count from 10:05 a.m. to the next whole hour, then onward to 11:55 a.m.. The intervals add to 110 minutes.
Analog clock showing 10:05 a.m.. - I8
How many minutes pass from 7:10 a.m. to 8:15 a.m.?
Reveal explanation
Answer: 65 min
Count from 7:10 a.m. to the next whole hour, then onward to 8:15 a.m.. The intervals add to 65 minutes.
Analog clock showing 7:10 a.m..
Challenge · 2 questions
Challenge and error analysis
Go beyond arithmetic: justify a claim, correct reasoning, or connect two representations.
- C1
Explain how 11:45 a.m. plus 35 minutes crosses noon. At what time does it finish?
Reveal explanation
Answer: 12:20 p.m.
15 minutes reach noon; then 20 more minutes reach 12:20 p.m.
- C2
A trip begins at 11:40 p.m. and lasts 40 minutes. On which day does it finish and at what time?
Reveal explanation
Answer: Next day at 12:20 a.m.
20 minutes reach midnight; 20 minutes more reach 12:20 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 10:55 a.m. to 1:10 p.m.?
Reveal explanation
Answer: 135 min
Count from 10:55 a.m. to the next whole hour, then onward to 1:10 p.m.. The intervals add to 135 minutes.
Analog clock showing 10:55 a.m.. - E2
How many minutes pass from 4:30 p.m. to 5:05 p.m.?
Reveal explanation
Answer: 35 min
Count from 4:30 p.m. to the next whole hour, then onward to 5:05 p.m.. The intervals add to 35 minutes.
Analog clock showing 4:30 p.m.. - E3
How many minutes pass from 12:35 p.m. to 1:50 p.m.?
Reveal explanation
Answer: 75 min
Count from 12:35 p.m. to the next whole hour, then onward to 1:50 p.m.. The intervals add to 75 minutes.
Analog clock showing 12:35 p.m..