When the Daily Step Leader Still Loses the Week

Introduce the driving question with a concrete story hook: two coworkers in a 7-day step challenge, one of whom tops the leaderboard almost every day.

• Frame the scenario: a 7-day step challenge between two people.
• State the driving question plainly on screen.
• Invite the learner to notice the tension between daily wins and the weekly total.

Let the learner commit to an initial answer before any totals are revealed.

• Forces a single explicit prediction about whether the daily leader wins the week.
• Commits the learner to a hypothesis they will later check against evidence.

A small interactive table where the learner enters or adjusts each walker's seven daily step totals and immediately sees both the daily winner column and the running weekly total.

• Enter seven daily step totals for Walker A and Walker B.
• See, per day, who led and by how much.
• Watch the running weekly total so the gap or lead is visible at all times.

Show one concrete 7-day dataset where Walker A leads the day on every single day but still finishes the week behind Walker B.

• Display Walker A and Walker B's daily steps for all seven days.
• Highlight that Walker A wins the daily column every single day.
• Reveal the weekly totals so the leader clearly loses the week.

Explain the arithmetic: the weekly gap is the sum of daily gaps, so a huge loss on the leader's worst day can erase the small daily leads.

• Weekly total = sum of daily steps.
• Each day's lead contributes only that day's difference to the weekly gap.
• A single very low day for the leader costs the leader the full size of the deficit on that day; small daily leads cannot recover it.

Show the boundary case: if Walker A's smallest day is still at least as large as Walker B's largest day, then leading every day does guarantee winning the week.

• State the condition: leader's minimum day is greater than or equal to rival's maximum day.
• Sketch a tiny example confirming the intuition survives in that edge case.
• Clarify that this is a strict boundary, not a typical real-world outcome.

Let the learner try to construct a scenario where the daily leader loses the week by manipulating one sliding scale: how small the leader's worst day should be.

• Adjust the leader's worst-day slider.
• See in real time whether the rival can overtake the weekly total despite trailing every day.
• Notice which value of the worst day is the tipping point.

State the final answer directly and tie it back to the opening scenario.

• Restate the driving question and give the concise rule.
• Show that weekly outcome = sum of daily gaps, so the leader's worst days decide everything.
• Close the loop with the original story of the two coworkers.