A class starts at 1:15 and ends at 3:00. A student subtracts: 3:00 − 1:15 = 1:85. Why is this answer wrong?
AThe student should have subtracted minutes before hours
BTime is not base-10 — hours have 60 minutes, not 100 — so '85 minutes' is not a valid result
CThe student forgot to convert hours to seconds first
D3:00 − 1:15 cannot be calculated and must be estimated from a clock
Regular subtraction treats numbers as base-10 (10 units = 1 of the next unit). But time uses base-60 for minutes: 60 minutes = 1 hour, not 100. Subtracting 1:15 from 3:00 as if they were decimals produces a nonsense answer because '85 minutes' is not a unit in the time system. The reliable approach is a number-line strategy: jump to the next clean hour, then count remaining minutes.
Question 2 Multiple Choice
What is the best strategy for finding elapsed time from 9:40 to 10:25?
ASubtract: 10:25 − 9:40 = 0:85, so 85 minutes
BJump from 9:40 to 10:00 (20 minutes), then from 10:00 to 10:25 (25 minutes) — total: 45 minutes
CConvert both times to minutes since midnight, then subtract
DCount forward from 9:40 by individual minutes until reaching 10:25
The jump-to-the-hour strategy breaks elapsed time into manageable chunks that respect the 60-minute structure of hours. From 9:40 to 10:00 is 20 minutes (60 − 40 = 20). From 10:00 to 10:25 is 25 minutes. Total: 20 + 25 = 45 minutes. This approach avoids the base-10 error and is far less error-prone than counting by individual minutes. Option A is the classic mistake: treating time notation like base-10 decimal numbers.
Question 3 True / False
Drawing a number line is a useful strategy for elapsed time problems because it makes the passage of time visible and helps avoid base-10 errors.
TTrue
FFalse
Answer: True
A number line makes elapsed time spatial: mark the start, mark the end, and the distance between them is the elapsed time. More importantly, a number line naturally leads you to the jump-to-the-hour strategy — you can see the nearest clean hour between start and end, and the problem becomes two simple additions. This visual approach prevents the mistake of treating time like base-10 subtraction, where students produce answers like '1:85' or '0:85.'
Question 4 True / False
To find elapsed time from 2:30 to 4:00, you can subtract: 4:00 − 2:30 = 1:70, so 1 hour and 70 minutes.
TTrue
FFalse
Answer: False
This is the base-10 subtraction error. '1:70' would mean 1 hour and 70 minutes — but hours only contain 60 minutes, so this is not valid. The correct calculation using the jump strategy: from 2:30 to 3:00 is 30 minutes; from 3:00 to 4:00 is 60 minutes; total = 90 minutes, or 1 hour and 30 minutes. Regular subtraction on time notation always risks this error because minutes are base-60, not base-10.
Question 5 Short Answer
Why doesn't regular subtraction work for elapsed time, and what should you do instead?
Think about your answer, then reveal below.
Model answer: Regular subtraction assumes a base-10 system where borrowing works in groups of 10. But time uses base-60 for minutes — there are 60 minutes in an hour, not 100. Subtracting 1:15 from 3:00 as if it were 300 − 115 gives 185, which is meaningless as a time. Instead, use a number line and jump to the next clean hour: from 1:15 to 2:00 is 45 minutes, from 2:00 to 3:00 is 60 minutes, total 105 minutes = 1 hour 45 minutes.
The foundational issue is that time is not a decimal system. Hours have 60 minutes; you cannot treat '3:00 − 1:15' the way you'd treat 300 − 115. The jump strategy works because it decomposes the problem into segments that each respect the 60-minute hour: getting to the next clean hour is always a subtraction within 60 (easy); then whole hours are added; then remaining minutes are added. Each step is simple; the combination handles any elapsed time problem correctly.