Duration and Elapsed Time
Warm-up
The tide was high at 6:35 am. The next high tide is 12 hours 25 minutes later. When is the next high tide? 6:35 + 12:25. Hours: 6+12=18:35. Minutes: 35+25=60 = 1 extra hour. 18:35 + 1:00 = 19:35 = 7:35 pm. This is elapsed time in a real ecological context.
Explore
Natural cycle elapsed time challenge: each group investigates one natural cycle (tidal, lunar, seasonal, migration). They research the cycle length and solve 3 elapsed time problems using that cycle. Share: if low tide was at 3:18 pm, when is the next low tide? What day is the next full moon after today?
Formalize
School day elapsed time: school starts at 8:30 am. Morning block ends at 10:45 am (elapsed: 2 h 15 min). Lunch is 45 minutes. Afternoon block 1:30 to 3:15 pm (elapsed: 1 h 45 min). Total instructional time: 2h15min + 1h45min = 4 hours. How does this connect to the school year? 200 days x 4 hours = 800 hours of instruction per year.
Duration and Elapsed Time
First Peoples seasonal calendar: map a traditional seasonal calendar onto a timeline. At what point in the year does the salmon arrive? (varies: late summer to early fall for most Pacific salmon). How long is the harvest season? (weeks to months). How does this elapsed time define the rhythm of the year?
Practice
Students calculate elapsed time for 6 problems (including 2 crossing noon), solve 2 natural cycle problems, and map a school-day schedule on a timeline. Exit ticket: a movie starts at 7:25 pm and lasts 2 hours 15 minutes. When does it end?
Exit ticket
Students calculate elapsed time for 6 problems (including 2 crossing noon), solve 2 natural cycle problems, and map a school-day schedule on a timeline. Exit ticket: a movie starts at 7:25 pm and lasts 2 hours 15 minutes. When does it end?
The plan: three films back-to-back — 1 h 48 min, 2 h 25 min, 1 h 52 min. Total sitting time?
Step 1: Add hours and minutes SEPARATELY (mixed units resist column addition): hours 1 + 2 + 1 = 4; minutes 48 + 25 + 52 = 125.
Step 2: Convert the minute overflow: 125 min = 120 + 5 = 2 h 5 min.
Step 3: Combine: 4 h + 2 h 5 min = 6 h 5 min.
Step 4: The error this method prevents: column-adding 148 + 225 + 152 as if base-10 = 525 → read as "5 h 25 min" — WRONG (it treated 100 min as an hour). Time is base-60; the separate-then-convert method respects that. Show the wrong way once, name the disease (base-10 thinking in a base-60 world), bury it.
Step 5: Practical wrap: doors open 10:00 a.m. — when does the marathon end (with two 15-min breaks)? 6 h 5 min + 30 min = 6 h 35 min after 10:00 → 4:35 p.m. Hop the number line to confirm.
The schedule (24-hour): Bus A departs 08:12, arrives 09:47. Bus B departs 08:35, arrives 09:58. Which ride is shorter, and does "leaving later" mean "arriving later"?
Step 1: Duration of A: 08:12 → 09:47. Hop: +48 min → 09:00, +47 → 09:47: total 1 h 35 min.
Step 2: Duration of B: 08:35 → 09:58. Hop: +25 → 09:00, +58 → 09:58: total 1 h 23 min.
Step 3: Compare: B is 12 minutes faster (an express, presumably) — AND it leaves later while arriving only 11 minutes after A. If you're at the stop at 8:30, B dominates: more platform time AND less bus time.
Step 4: The general reading skill: schedules answer three different questions — when do I leave (departure), when am I there (arrival), how long am I travelling (elapsed). Confusing them books wrong buses. Circle which question each word problem is actually asking before computing.
Exit: with a 10:15 appointment near B's terminal (5-min walk), which bus, and how much buffer? (B: arrive 9:58 + 5 walk = 10:03 → 12 min buffer.)
The setup: it's 4:00 p.m. Saturday for you (Vancouver). Grandma in Halifax is 4 hours AHEAD. The call is set for HER 7:30 p.m. — what time is that for you, and is it before dinner?
Step 1: Establish the offset direction with a sun story: Halifax meets the morning first; her clock runs 4 hours ahead of yours. Ahead = add going there, subtract coming back.
Step 2: Convert her 7:30 p.m. to your time: subtract 4 → 3:30 p.m. your time.
Step 3: Sanity-check the direction (the step everyone skips): her evening call happens in your AFTERNOON — earlier on your clock ✓. If you'd added instead, you'd get 11:30 p.m. — a bedtime call that should smell wrong.
Step 4: The return question: you want to call her right after your 6:00 p.m. dinner — what's her clock say? 6:00 + 4 = 10:00 p.m. Late-ish for grandma. Negotiate: your 4:45 = her 8:45 ✓.
The transferable core: a time zone is a fixed offset; converting is one addition or subtraction PLUS a direction check told by the sun.