Build a timetable from fractional-hour task cards

model. A session starts at 9:10 a.m. and must finish at 10:00. It needs 1/4 hour of setup, 1/3 hour of practice and a 5-minute transition. How many minutes remain for reflection?

1. Identify the fixed window: from 9:10 to 10:00 there are 50 minutes. Keep that available duration separate from the times printed on the clock.
2. Convert each hour fraction using 60 minutes per hour. One quarter of an hour is 15 minutes and one third is 20 minutes; do not read them as decimal clock digits.
3. Schedule in order: setup 9:10–9:25, practice 9:25–9:45, transition 9:45–9:50. Transitions use real session time and cannot be silently omitted.
4. Use the remaining 10 minutes for reflection, ending at 10:00. Check that 15 + 20 + 5 + 10 = 50 minutes and that adjacent tasks have no unexplained overlap or gap.

Worked example: 10 minutes. Setup takes 15 minutes, practice 20 minutes and transition 5 minutes: 40 of the available 50 minutes are used.

p1. Support: how many minutes are in 1/6 of an hour? Show how you split the 60-minute whole.

Answer: 10

Teacher response: Six equal groups of ten minutes fill one hour.

p2. Core: a 45-minute session needs 1/4 hour of setup and 1/3 hour of practice. Enter the minutes left for a final check, with no transition required in this item.

Answer: 10

Teacher response: Fifteen plus twenty uses thirty-five of the forty-five minutes.

p3. Challenge: a task starts at 10:35 a.m. and lasts 1/2 hour. Enter the minute part of its finish time, and write the complete clock reading on paper.

Answer: 5

Teacher response: The finish is 11:05 a.m.; twenty-five minutes reach 11:00 and five more complete the thirty-minute task.

e1. Independent check: from 2:20 to 3:10 p.m., plan 1/3 hour of practice, 1/4 hour of discussion and a 5-minute transition. Enter the unassigned minutes and write all start/end times.

Answer: 10

Look for:

• Converts hour fractions using a 60-minute reference whole.
• Accounts for transitions and verifies the schedule against its deadline.

Teacher response: The window is 50 minutes; 20 + 15 + 5 uses 40, leaving 10. One schedule is 2:20–2:40, 2:40–2:55, 2:55–3:00, then reflection to 3:10.

transfer. If the worked practice overruns by 7 minutes but setup and transition stay unchanged, can the original 10-minute reflection still finish by 10:00? Explain the available choices.

Answer: No. With a fixed finish, reflection has only 3 minutes left. Keeping all 10 reflection minutes would move the finish to 10:07 unless another task is shortened. State which constraint changes rather than hiding the overrun.

teach-1. 3 minutes: Separate the session's clock endpoints from the task durations and identify time that is not yet assigned.

teach-2. 4 minutes: Build the worked table, including its transition, and check both elapsed minutes and the final clock reading.

teach-3. 5 minutes: Work through a support conversion and a core schedule before testing the challenge.

teach-4. 3 minutes: Complete the independent schedule and show that all tasks fit within the stated window.

misconception. One third of an hour is 30 minutes, because the fraction contains a 3.

Teacher response: Partition the 60-minute hour into three equal groups. Each is 20 minutes. Thirty minutes is one of two equal half-hour groups.

support. Write 60 minutes above a strip and partition it into equal halves, thirds or quarters before placing tasks on a clock.

extend. Reorder the three fixed tasks without changing their durations. Show why the remaining reflection duration stays 10 minutes even though intermediate times change.