Reference / Curriculum / 3B / Chapter 14

3B · Chapter 14 · Lesson 1

Units of Time

Convert days/hours/minutes/seconds and distinguish clock time from duration.

MATH-3B-C14-L01Independent and tutor-supported

Today's mathematical question

Convert 4 h 5 min into minutes.

Learning target

Convert days/hours/minutes/seconds and distinguish clock time from duration.

Before starting: Grade 3A: multiplication and addition in tens and sixties. 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.

  1. P1

    Find 6 × 10.

    Reveal explanation

    Answer: 60

    Six equal groups of ten contain 60 objects. You can represent this with six bundles of ten or six rows of ten counters.

  2. P2

    Calculate 45 + 20.

    Reveal explanation

    Answer: 65

    Add two tens to 45 while keeping the five ones unchanged: 45 + 10 = 55 and 55 + 10 = 65.

  3. P3

    How many days are in two weeks?

    Reveal explanation

    Answer: 14

    One week contains seven days, so two complete weeks contain 7 + 7 = 14 days. The units change from weeks to days.

Learn and understand

Clock time describes when an event happens; duration describes how long it lasts. An hour has 60 minutes and a minute has 60 seconds, so minutes do not behave like decimal hundredths. Two hours 35 minutes equals 155 minutes, not 235 minutes. A clock groups minutes into sets of sixty, while weeks group days into sets of seven. Choose the correct exchange rule for the two units you are converting.

Represent it three ways

  1. Concrete: Build equal pieces, measures, counters or shapes with real objects when useful.
  2. Pictorial: Show 60 one-minute segments forming one hour and regroup whole hours before adding leftover minutes.
  3. Abstract: Write the matching number sentence, calculation, comparison or mathematical description. Explain each number's unit.

Important vocabulary

duration
length of time
clock time
when something occurs
hour
60 minutes

Fully worked examples and checks

Try each new understanding check before revealing the explanation.

Worked example 1

Explore, calculate, verify

Convert 4 h 5 min into minutes.

  1. Identify the whole, the units, and what the question asks.
  2. Each hour is 60 minutes. 4 × 60 + 5 = 245 minutes.
  3. Check that the answer uses the right units and makes sense.

Answer: 245 min

Check your understanding 1

Convert 2 h 5 min into minutes.

Reveal answer and explanation

125 min — Each hour is 60 minutes. 2 × 60 + 5 = 125 minutes.

Worked example 2

Explore, calculate, verify

Convert 4 min 10 s into seconds.

  1. Identify the whole, the units, and what the question asks.
  2. Each minute contains 60 seconds. 4 × 60 + 10 = 250 seconds.
  3. Check that the answer uses the right units and makes sense.

Answer: 250 s

Check your understanding 2

Convert 3 min 5 s into seconds.

Reveal answer and explanation

185 s — Each minute contains 60 seconds. 3 × 60 + 5 = 185 seconds.

Worked example 3

Explore, calculate, verify

Express 31 days in weeks and days.

  1. Identify the whole, the units, and what the question asks.
  2. One week is seven days. 31 = 7 × 4 + 3.
  3. Check that the answer uses the right units and makes sense.

Answer: 4 weeks 3 days

Check your understanding 3

Express 10 days in weeks and days.

Reveal answer and explanation

1 weeks 3 days — One week is seven days. 10 = 7 × 1 + 3.

Guided · 5 questions

Guided practice

Keep the model and earlier examples visible while practising.

  1. G1

    Convert 3 min 35 s into seconds.

    Reveal explanation

    Answer: 215 s

    Each minute contains 60 seconds. 3 × 60 + 35 = 215 seconds.

  2. G2

    Express 245 minutes in hours and minutes.

    Reveal explanation

    Answer: 4 h 5 min

    There are 4 full groups of 60 minutes and 5 more minutes.

  3. G3

    Express 250 seconds in minutes and seconds.

    Reveal explanation

    Answer: 4 min 10 s

    Group the 250 seconds into complete 60-second minutes, then count the 10 remaining seconds.

  4. G4

    Convert 3 h 35 min into minutes.

    Reveal explanation

    Answer: 215 min

    Each hour is 60 minutes. 3 × 60 + 35 = 215 minutes.

  5. G5

    Convert 3 min 15 s into seconds.

    Reveal explanation

    Answer: 195 s

    Each minute contains 60 seconds. 3 × 60 + 15 = 195 seconds.

Independent · 8 questions

Independent practice

Work these without hints and explain the method used. Write answers on paper.

  1. I1

    Convert 1 h 5 min into minutes.

    Reveal explanation

    Answer: 65 min

    Each hour is 60 minutes. 1 × 60 + 5 = 65 minutes.

  2. I2

    Convert 3 min 25 s into seconds.

    Reveal explanation

    Answer: 205 s

    Each minute contains 60 seconds. 3 × 60 + 25 = 205 seconds.

  3. I3

    Express 105 minutes in hours and minutes.

    Reveal explanation

    Answer: 1 h 45 min

    There are 1 full groups of 60 minutes and 45 more minutes.

  4. I4

    Express 205 seconds in minutes and seconds.

    Reveal explanation

    Answer: 3 min 25 s

    Group the 205 seconds into complete 60-second minutes, then count the 25 remaining seconds.

  5. I5

    Convert 4 h 45 min into minutes.

    Reveal explanation

    Answer: 285 min

    Each hour is 60 minutes. 4 × 60 + 45 = 285 minutes.

  6. I6

    Express 32 days in weeks and days.

    Reveal explanation

    Answer: 4 weeks 4 days

    One week is seven days. 32 = 7 × 4 + 4.

  7. I7

    Express 75 minutes in hours and minutes.

    Reveal explanation

    Answer: 1 h 15 min

    There are 1 full groups of 60 minutes and 15 more minutes.

  8. I8

    Express 70 seconds in minutes and seconds.

    Reveal explanation

    Answer: 1 min 10 s

    Group the 70 seconds into complete 60-second minutes, then count the 10 remaining seconds.

Challenge · 2 questions

Challenge and error analysis

Go beyond arithmetic: justify a claim, correct reasoning, or connect two representations.

  1. C1

    Why is 5 hours 15 minutes not 515 minutes?

    Reveal explanation

    Answer: 315 minutes

    Each hour has 60 minutes, so 5 hours 15 minutes is 300+15=315 minutes.

  2. C2

    A student says 5 h 50 min + 20 min = 5 h 70 min. Explain and correct.

    Reveal explanation

    Answer: 6 h 10 min

    Trade 60 minutes for an extra hour, leaving 10 minutes.

Exit · 3 questions

Exit check

Solve independently, then return on another day to check retention.

  1. E1

    Convert 4 h 15 min into minutes.

    Reveal explanation

    Answer: 255 min

    Each hour is 60 minutes. 4 × 60 + 15 = 255 minutes.

  2. E2

    Convert 1 min 35 s into seconds.

    Reveal explanation

    Answer: 95 s

    Each minute contains 60 seconds. 1 × 60 + 35 = 95 seconds.

  3. E3

    Express 165 minutes in hours and minutes.

    Reveal explanation

    Answer: 2 h 45 min

    There are 2 full groups of 60 minutes and 45 more minutes.

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