Plan the Fireworks Show

Overview

A summer fireworks finale becomes a schedule. Students lay cue cards on a timeline, mark which shells must follow others (the finale can’t fire before the build-up) and which can launch at the same time (red-left and red-right don’t wait on each other), and discover the punchline: the show’s length is set by the longest chain of must-follow cues — the critical path — not by how many fireworks there are. They’ve met sequencing, parallelism, and scheduling, the ideas behind every project plan and every multi-core computer. Point the show at whatever you teach.

Then they run it. The live sequencer at the top of this page turns their paper timeline into an actual show: press Run the show and the night sky launches each cue in order, fires the parallel ones together, and bursts them in color with a whistle and a boom. Add a launch crew and the show gets shorter; add another and — surprise — it doesn’t, because you’ve hit the longest must-follow chain. The punchline stops being something you tell students and becomes something they see and hear.

A base integrated lesson — scheduling and parallelism any single-subject teacher can run as-is, with a callout for your subject. Unplugged core, a live in-browser show, and an optional plugged twin.

Pre / Post assessment

• Pre: “If a show has 20 fireworks, does adding more helpers always make it finish sooner? Why or why not?”
• Post: “You shortened one cue and the show didn’t get shorter. What does that tell you about which cue mattered?”

Objectives

Students will (1) represent a process as cues with must-follow dependencies, (2) identify which cues can run in parallel, and (3) find and verify the critical path that sets the total time.

CONTEXTUALIZE — why it matters

Building a bridge, launching a rocket, getting a meal out of a busy kitchen, and running the apps on a phone all come down to the same question: what must happen in order, what can happen at once, and what’s the bottleneck? Schedule it well and you save time, money, and risk; schedule it badly and the whole thing slips. The people who design those schedules decide what runs in parallel and where the critical path lies. The students who can find a critical path — and ask who pays when it slips — are the ones equipped to coordinate the big, important things their communities depend on.

REFRAME — surface the wrong model, install the right one

Students think “more stuff = longer,” and “doing things at the same time always makes it faster.” Reframe: the total time is the longest chain of dependent steps. Cues that overlap cost no extra time; speeding up a cue that isn’t on the critical path doesn’t shorten the show at all. Length comes from dependencies, not from the count.

ASSEMBLE — I do / we do / you do

• I do: On the projector, lay three cues in the sequencer, draw a “must-follow” arrow (Build waits on Open, Finale waits on Build), and read off the time so far. Press Run the show so the room sees the three cues fire in order.
• We do: Add cues that can overlap — Red-L and Red-R only wait on Open, so they fire together and cost no extra time. Point out the two bursts going up side by side. Find the longest must-follow chain (Open → Build → Finale).
• You do: Teams choreograph a full finale on the cue cards and timeline strip, mark all dependencies, and compute the show length from the critical path — then rebuild it in the sequencer and run it to check. Set crews to 1, then 2, then 3, and watch the crews-vs-show-length chart: the bar stops dropping at the dashed floor line.

FORTIFY — Check the Machine

The verification is the lesson. (1) Replay the timeline cue by cue — watch the sequencer’s playhead sweep across, or read its play-by-play log: does anything fire before a cue it depends on? Any violation is a scheduling bug. (2) Test the parallels: for every pair marked “at the same time,” confirm neither depends on the other — in the tool they sit in the same seconds on different crew rows. (3) Confirm the length equals the longest must-follow chain, not the sum of all cues. Then the “errors are features” twist: in the sequencer, shorten a cue that is not on the critical path (the Lull, or a Red) and run it again — the show length doesn’t change, proof you optimized the wrong step. Then shorten a cue that is on the chain and watch the whole finale pull in. Knowing which step actually controls the outcome is the whole game.

TRANSFER — forward + plugged twin

• Forward: “Where else does a longest chain set the time?” (building a house, a relay race, loading a video game). Name the bigger arc: the students finding critical paths now are the future engineers who schedule how a community builds, launches, and coordinates the things it depends on.
• Design your own show: in the sequencer, let teams change the cue lengths and which cues wait on which to compose a finale they like — a slow build, twin bursts, a big close — then predict the show length before they press play. It’s choreography and critical-path reasoning in the same move.
• Plugged twin (+15 min): build the cue list in a spreadsheet with start/finish times and use a formula to find the latest finish (the critical path), or block out the schedule in a simple planning tool and watch the end time move only when a critical cue changes.

What to listen for

Use the Post prompt — “You shortened one cue and the show didn’t get shorter. What does that tell you about which cue mattered?” — as your read on mastery.

• Proficient: sees the shortened cue wasn’t on the critical path. “It had slack — only the longest must-follow chain sets the length.”
• Getting there: notices no change but can’t explain it. Nudge: “Was that cue on the longest chain of must-follows?”
• Not yet: thinks shortening any cue shortens the show. Reframe: only critical-path cues set the length.

Proficient when a team replays the timeline to confirm no cue fires before its prerequisite and explains the show length as the longest must-follow chain.

Differentiation

• K-2 adaptation: 4–5 picture cues, “what comes first?” arrows only; the show is “follow the arrows in order.”
• 3-5: whole-second durations, one or two parallel pairs, find the longest chain.
• 6-8 extension: more cues and crossing dependencies; introduce “slack” (how much a non-critical cue could slip before it matters).
• 9-12 bridge: name the critical-path method and connect to the subject-tier Fireworks Finale Sequencer drop.

3-2-1 Review

3 cues on your critical path · 2 cues that ran in parallel · 1 cue you could shorten with no effect on the show.

Family / community connection

“Plan a real event with your family — a cookout, getting everyone out the door. Find what must happen in order and what can happen at the same time. What’s the one step that decides how long it all takes?”