Bottleneck - Free Classroom Simulation

Math (Algebra) Grades 8-10 8 roles 56 min 1 class period

Port Kestrel Container Terminal, peak season. Four rounds of berth allocation between August and October, as pre-holiday import volume climbs and dock capacity does not.

Rival freight companies compete for scarce priority berths at a single import terminal during peak season. Each round a team must solve its own one-variable inequality to find how many pallets it can actually afford to move - then decide how much of its budget to gamble on a sealed bid for the fast lane.

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Class Time

56 minutes

Designed For

1 class period

Roles

8 roles

Class Sizes

Core (4 groups), Standard (6 groups), Full (8 groups)

Learning Objectives

4 objectives

Standards

6 standards aligned

Where This Fits in Your Curriculum

This is an Algebra 1 game for the first six weeks of the year - Unit 1 and Unit 2 in most pacing guides, where students are working with linear expressions, one-variable equations, and one-variable inequalities. Every team carries a different fee formula of the form ax + b, and the only way to learn your real shipping capacity is to solve ax + b <= R for the largest whole number x. That is the whole mathematical spine: no systems, no two-variable graphing, no slope-intercept work - those belong to Breaking Even and Kudzu later in the year. Students need to be able to substitute, isolate a variable, and interpret a solution in context, including why the answer must be rounded DOWN to a whole pallet rather than up. They do not need any prior exposure to inequalities as a graphing topic, and they do not need to have seen compound inequalities at all. Underneath the freight theme, the real lesson is that an inequality describes a ceiling you have to respect, and that changing one number on the left side - a fuel surcharge added to the coefficient - moves that ceiling for everyone at once, but not by the same amount. It serves Algebra 1 teachers looking for a first-month application day, Integrated Math 1 teachers on the same content, and CTE logistics or business-math courses that want the algebra attached to a real industry decision.

What Students Will Learn

Solve a one-variable linear inequality of the form ax + b <= R for the largest whole-number solution, and explain why the context forces rounding down.
Interpret the coefficient and the constant of a linear expression as distinct real quantities - a per-unit rate and a fixed overhead - and predict how changing each one moves the solution.
Evaluate the same inequality repeatedly as its right-hand side changes, and use those results to price a decision made under uncertainty.
Identify when a resource is worth more to someone else than to you, and negotiate a price for it that leaves both sides better off.

Cases Included

CCSS.MATH.HSA.CED.A.1 - Create equations and inequalities in one variable and use them to solve problems (the fee formula ax + b <= R is built from the team's own cost structure each round).
CCSS.MATH.HSA.REI.B.3 - Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.
CCSS.MATH.HSA.SSE.A.1 - Interpret expressions that represent a quantity in terms of its context; interpret parts of an expression such as terms, factors, and coefficients (a as the per-pallet rate, b as the fixed dock fee).
CCSS.MATH.8.EE.C.7 - Solve linear equations in one variable (grade 8 entry point for the same solve).
CCSS.MATH.MP.2 - Reason abstractly and quantitatively (moving between the dollar budget and the pallet count it buys).
CCSS.MATH.MP.4 - Model with mathematics (the inequality models a real allocation constraint, and its solution is acted on immediately).

Social & Emotional Learning (CASEL)

Aligned to the CASEL framework's core competencies. These are the SEL skills students actively practice while playing.

Responsible Decision-Making The bid is committed BEFORE the solve resolves, and every dollar bid is a pallet not shipped. Teams weigh an uncertain upside - a priority berth worth 33 percent more per pallet - against a certain cost, round after round, with no way to see what rivals are doing.
Self-Management Four timed rounds against a hard budget. The pull toward a bigger number is constant and usually wrong: overbidding costs real capacity and, past a computable point, scores worse than not bidding at all.
Relationship Skills The Trade Window is face-to-face negotiation with no app-mediated chat. Teams propose, price, and confirm cargo deals with rivals they will meet again next round, so reputation and follow-through carry across the whole game.

Flexible Class Sizes

Core (4 groups)

Four freight companies, 2 priority berths in Rounds 1-3 and 1 in the finale. Keeps a clean two-seller / two-buyer market in every trading round. Best for a class of 8-20.

Standard (6 groups)

Six companies across the full spread of fee formulas, from the cheapest per-pallet rate with the highest overhead to the steepest rate with almost none. 2 priority berths in Rounds 1-3, 1 in the finale. Best for a class of 12-30.

Full (8 groups)

Eight companies, 3 priority berths in Rounds 1-3 and 2 in the finale. The trade floor gets genuinely crowded - budget an extra minute for each Trade Window. Best for a class of 24-40.

How the Game Plays Out

Turn 1: Open Water

Tutorial round - learn the solve

"How many pallets can you actually afford to move - and how much of that capacity is a berth worth?"

Turn 2: Building Season

The Trade Window opens

"What is a pallet worth to somebody who cannot move it - and to somebody who can?"

Turn 3: Fuel Surcharge

Every rate goes up - permanently

"When one number in your formula changes, what else changes with it?"

Turn 4: Peak Season Crunch

The smallest berth allotment, higher stakes, less time

"With the smallest berth allotment of the season and no time, is the bid worth what it costs you?"

Roles Your Students Will Play

Click any role to see their background and what they are trying to accomplish.

Anchor Freight

A mid-sized regional carrier with a mid-range per-pallet rate and low fixed overhead. Anchor has no structural edge and no structural handicap, which is why the terminal's own analysts use it as the baseline when they compare everyone else.

Your base fee formula is 8x + 30, where x is pallets shipped. Before any surcharge, every pallet costs you $8 to move. You owe a $30 dock fee every round whether you ship anything or not. Your rate is average and your overhead is low, so you can ship a respectable amount without spending much before the first pallet moves.

Goals

Finish with the highest score in the terminal at the end of the game.
Solve your inequality correctly every round so you never leave affordable pallets sitting on the dock.
Bid only when the priority premium is worth more than the pallets the bid costs you.

Northline Shipping

Northline runs a lean, high-volume operation with a genuinely cheap per-pallet rate, paid for by an expensive long-term lease on its dock space. Once the overhead is covered it moves cargo cheaper than almost anyone - but that overhead has to be covered first, every single round.

Your base fee formula is 6x + 55, where x is pallets shipped. Before any surcharge, every pallet costs you only $6 to move - one of the cheapest rates at the terminal. You owe a $55 dock fee every round whether you ship anything or not. Your high fixed cost eats a large share of a small budget before you move anything, so an aggressive bid is more dangerous for you than for most.

Goals

Finish with the highest score in the terminal at the end of the game.
Use your cheap per-pallet rate to move real volume once the dock fee is covered.
Protect the $55 you owe before you gamble anything on a berth.

Ridgeway Logistics

Ridgeway is a boutique carrier with almost no fixed overhead - it leases dock time by the hour rather than by the season - but it pays a premium per pallet for the privilege. It is the cheapest company at the terminal to simply show up, and the most expensive to move volume with.

Your base fee formula is 10x + 15, where x is pallets shipped. Before any surcharge, every pallet costs you $10 to move - the highest rate at the terminal. You owe only a $15 dock fee each round, the lowest fixed cost here. Almost all of your budget is available for pallets or for a bid, but each pallet is expensive, so your ceiling is low.

Goals

Finish with the highest score in the terminal at the end of the game.
Use your very low overhead to keep more of your budget in play than anyone else.
Recognize that a low ceiling makes each pallet you do ship worth protecting.

Coastal Freightways

Coastal sits deliberately in the middle of the market on both rate and overhead - the result of a merger between a cheap-rate carrier and a low-overhead one, which left it with neither edge and neither weakness. Its managers call this resilience. Its rivals call it forgettable.

Your base fee formula is 7x + 40, where x is pallets shipped. Before any surcharge, every pallet costs you $7 to move, slightly below the terminal average. You owe a $40 dock fee every round whether you ship anything or not. You have no structural advantage and no structural handicap, so your results come almost entirely from your decisions.

Goals

Finish with the highest score in the terminal at the end of the game.
Turn a balanced cost structure into a flexible one - you can afford either strategy in a given round.
Read the room in the Trade Window; you are rarely the most desperate party there.

Vantage Cargo

Vantage runs rented, short-term equipment that costs more per pallet to operate but requires very little standing dock commitment. It is the closest thing the terminal has to a challenger brand: expensive to run, cheap to keep waiting.

Your base fee formula is 9x + 20, where x is pallets shipped. Before any surcharge, every pallet costs you $9 to move, on the expensive end. You owe only a $20 dock fee each round, near the lowest here. Like Ridgeway, most of your budget stays live - but your pallets are costly, so your ceiling sits low.

Goals

Finish with the highest score in the terminal at the end of the game.
Keep your low overhead working for you by having real money available when a berth is worth chasing.
Buy cargo when your budget can move more than you are holding.

Ironclad Shipping

Ironclad is the terminal's volume king: the cheapest per-pallet rate on the waterfront, funded by the largest standing dock commitment anyone here carries. In a good round it can ship as much cargo as anyone at the terminal. In a bad round it cannot get out of its own overhead.

Your base fee formula is 5x + 65, where x is pallets shipped. Before any surcharge, every pallet costs you only $5 to move - the cheapest rate at the terminal by a clear margin. You owe a $65 dock fee every round, the highest fixed cost here. Your ceiling is the highest at the terminal, or tied for it, but a large bid can wipe it out faster than you expect.

Goals

Finish with the highest score in the terminal at the end of the game.
Convert the cheapest rate at the terminal into the most pallets moved.
Notice that the company with the most shipping power has the least room to bid, and decide what to do about that.

Crossroads Freight

Crossroads is an inland trucking firm that added ocean freight late, and it still pays for terminal access it did not grow up with. It bought its way to a cheap per-pallet rate by committing to expensive dock space - and it has a management team that is unusually willing to make a deal.

Your base fee formula is 6x + 45, where x is pallets shipped. Before any surcharge, every pallet costs you only $6 to move, among the cheapest here. You owe a $45 dock fee every round whether you ship anything or not, which is on the high side. Cover the fee and you can move real volume; fail to and the round is wasted.

Goals

Finish with the highest score in the terminal at the end of the game.
Cover an above-average dock fee before committing anything to a bid.
Trade actively - re-solve your ceiling every round before you deal.

Summit Cargo

Summit is the terminal's quiet efficiency story - a slightly-below-average per-pallet rate paired with modest overhead, the result of two decades of unglamorous investment in its own equipment. Nothing about its numbers is remarkable, and that is the point.

Your base fee formula is 7x + 35, where x is pallets shipped. Before any surcharge, every pallet costs you $7 to move, a little below the terminal average. You owe a $35 dock fee each round, on the low side. Neither number is extreme, so nothing about your position is decided for you.

Goals

Finish with the highest score in the terminal at the end of the game.
Use a steady, unremarkable cost structure to buy and move other companies' stranded cargo when the round allows it.
Avoid the trap of assuming a tidy formula wins the game by itself.

Hand Each Student Their Own Sheet

One click on the teacher dashboard prints a dossier for every role - background, goals, key facts, and their confidential briefing - plus the primary-source packet and a vocabulary sheet. Print them, or save as PDF, so each student reads their role on paper instead of huddling around one screen. The app still runs the votes and the action; the paper just carries the reading.

Primary Sources

Every role includes real historical documents. Students read them because they need the information to make their case.

Port Tariff - Dockage and Wharfage Rates (excerpt, paraphrased from published US port schedules)

Peak season import pattern (summary of NRF Global Port Tracker data and industry reporting)

Key Terms Students Will Learn

palletberthpriority berthstandard lanesealed biddock feepeak seasonsurchargecarrierfreightbackhaulbrokergains from tradecoefficientconstantlinear inequalitysolve for xceilingterminal capacitydemurrage

After the Game: Debrief Questions

Did you ever bid enough to lose pallets you could have shipped? If you did, what did that buy you?
A company with the cheapest rate in this game also had the biggest dock fee, so the least money left over to bid with. Why do those two things go together, and would you rather have that formula or the one with the steepest rate?
Was there a round where solving the inequality correctly still was not enough to win? What else mattered?
The fuel surcharge added $2 to every company's rate. Whose ceiling did it cut the most - and why was it not the company with the highest rate?
If you traded, who was it with, and why them? Did you ever turn down a deal that would have helped you this round because of where it would leave you next round?
The Trade tab showed an even-split price: the pallets valued at the Standard lane rate, then halved. Did anyone negotiate better than that? Did anyone accept worse - and why?
Real ports charge every ship from a published fee schedule, and in peak season berth time is scarce. Why would a shipping company invest in getting this arithmetic right, beyond one round's score?

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