Units of Time
Semester 4B · Chapter 10 · Lesson 5 · MATH-4B-C10-L05
Before you begin: prerequisite check
Recall: 3B elapsed-time work. Attempt these questions independently first.
Convert 7 gallons to quarts.
Show answer and reasoning
Each gallon has 4 quarts; multiply by 7.
Convert 5 pints to cups.
Show answer and reasoning
Each pint has 2 cups; multiply by 5.
Convert 7 quarts to pints.
Show answer and reasoning
Each quart has 2 pints; multiply by 7.
Key vocabulary
- metric unit
- meter, gram or liter family with decimal relationships
- customary unit
- inch, foot, pound or gallon family with its own conversion factor
- mixed units
- one measurement written using two units
- reference whole
- the full quantity of which a fraction is taken
Understand the concept
Clock time tells when an event occurs; elapsed time describes the duration between two times. Time is not based on hundreds: one minute contains 60 seconds and one hour contains 60 minutes. There are 24 hours in a day and seven days in a week. For an interval that crosses noon or midnight, draw a timeline through a convenient benchmark. For example, from 11:40 a.m. to 12:10 p.m. is 20 minutes to noon plus 10 minutes afterward, or 30 minutes. State both the number and the unit in your answer.
Fully worked examples and immediate checks
Read each example, predict how to begin, then follow its numerical explanation. The check below it is a fresh problem.
Worked example 1
Convert 4 h 34 min to minutes.
4×60+34=274 minutes.
Check 1: try it yourself
Convert 6 h 24 min to minutes.
Show answer and reasoning
6×60+24=384 minutes.
Worked example 2
Convert 3162 seconds to minutes and seconds.
Each 60 seconds is one minute; 3162=60×52+42.
Check 2: try it yourself
Convert 3146 seconds to minutes and seconds.
Show answer and reasoning
Each 60 seconds is one minute; 3146=60×52+26.
Worked example 3
How many days are in 2 weeks and 4 days?
2×7+4=18.
Check 3: try it yourself
How many days are in 7 weeks and 4 days?
Show answer and reasoning
7×7+4=53.
Guided practice
Convert 4 h 46 min to minutes.
Show answer and reasoning
4×60+46=286 minutes.
Convert 2847 seconds to minutes and seconds.
Show answer and reasoning
Each 60 seconds is one minute; 2847=60×47+27.
How many days are in 4 weeks and 4 days?
Show answer and reasoning
4×7+4=32.
An activity begins at 11:39 a.m. and lasts 6 hours 25 minutes. When does it end?
Show answer and reasoning
Add duration on a timeline, passing noon: 6 hours and 25 minutes after 11:39 a.m. is 6:04 p.m..
Is 4 hours equal to 400 minutes? Explain.
Show answer and reasoning
An hour is 60 minutes, so 4 hours is 240 minutes, not 400.
Independent practice
Convert 2 h 14 min to minutes.
Show answer and reasoning
2×60+14=134 minutes.
Convert 1283 seconds to minutes and seconds.
Show answer and reasoning
Each 60 seconds is one minute; 1283=60×21+23.
How many days are in 5 weeks and 4 days?
Show answer and reasoning
5×7+4=39.
An activity begins at 11:55 a.m. and lasts 4 hours 25 minutes. When does it end?
Show answer and reasoning
Add duration on a timeline, passing noon: 4 hours and 25 minutes after 11:55 a.m. is 4:20 p.m..
Is 2 hours equal to 200 minutes? Explain.
Show answer and reasoning
An hour is 60 minutes, so 2 hours is 120 minutes, not 200.
Convert 5 h 46 min to minutes.
Show answer and reasoning
5×60+46=346 minutes.
Convert 2915 seconds to minutes and seconds.
Show answer and reasoning
Each 60 seconds is one minute; 2915=60×48+35.
How many days are in 6 weeks and 4 days?
Show answer and reasoning
6×7+4=46.
Challenge and transfer
Use a diagram or verbal justification where appropriate. The goal is transfer rather than speed.
Convert 7 h 55 min to minutes. Explain or sketch the mathematical relationship.
Show answer and reasoning
7×60+55=475 minutes. State which quantities or geometric properties justify the method.
A learner claims: “2 hours is 200 minutes.” Identify what is wrong or incomplete and give a mathematically correct explanation.
Show answer and reasoning
False: an hour is 60 minutes, so 2 hours is 120 minutes. Explain the relevant quantities or properties, not merely the final answer.
Exit check
Convert 1 h 42 min to minutes.
Show answer and reasoning
1×60+42=102 minutes.
Convert 1181 seconds to minutes and seconds.
Show answer and reasoning
Each 60 seconds is one minute; 1181=60×19+41.
How many days are in 3 weeks and 4 days?
Show answer and reasoning
3×7+4=25.
Mastery check: Solve a new instance without hints, explain why the method works, and return later to confirm retention.