Chapter 12 — Instructor Material

Teaching Notes

What this chapter is really for

Chapter 12 is where the book's central claim — you bank dollars, not percentages — stops being a slogan and becomes an operating procedure. Students arrive believing food cost percentage is the scoreboard, because that is what every kitchen they have worked in talks about. The chapter's job is to break that belief with arithmetic they cannot argue with, hand them a better tool, and then spend §12.7 taking the better tool apart so they do not simply transfer their credulity from one number to another.

If students leave able to compute the matrix but not to say what it cannot see, the chapter has failed. §12.7 is the assessment target, not §12.3.

Timing

Plan two 75-minute sessions, or one 3-hour block with a break.

If you are short on time, cut §12.6's three-way ranking table and the compliance callout. Never cut §12.7.

Common misconceptions, in the order they surface

1. "Lower food cost percentage means a better dish." The one everybody arrives with. Kill it in the first ten minutes with the trout and the burger, before students have had a chance to defend it.
2. "Contribution margin is the same as profit." It is not. CM covers labor, occupancy, and everything else before anything is profit. A menu of $20 contribution margins can still lose money. Say this out loud at least twice.
3. "The matrix tells you what to cut." The single most damaging misreading, and the one Case Study 2 exists to inoculate against. The matrix ranks items against each other. It does not know about substitution, cross-utilization, or why a guest came.
4. "The average is the same as the simple average." Students will compute $\$18.99$ (unweighted) rather than $\$19.06$ (weighted) roughly half the time on a first attempt. Make them do both and show which one reconciles to $6,291.02 ÷ 330.
5. "70% is a rule." It is a convention. Have them run the analysis at 100% of expected share and watch two of five items change quadrant.
6. "More data will settle it." §12.8's finding — that a full season still cannot place an item sitting a point off the line — genuinely surprises good students, and it is the most professionally useful thing in the chapter.
7. "A vegetarian dish is a low-margin dish." Bellwether's squash and grains, at a $3.95 plate cost, is the menu's second-largest generator of contribution-margin dollars. Worth naming explicitly.

The hardest point to teach

That both axes are relative to the menu you already have.

Students nod at this and then immediately reason as though "Dog" were a property of a dish. The fix is Figure 12.7 worked live on the board, not read. Do it in three rounds, and after each round ask the room: "which item changed, and what did we do to it?" The answer in Round 3 — nothing; the average moved — has to come from a student, not from you, or it does not land.

The moment that lands hardest: in Round 3 the Hearth Chicken, the book's own anchor dish and the menu's largest earner, clears the margin line by 1.6 cents. Let the room sit with that for five seconds before you say anything.

A demonstration that works

The two-plate opener. Before anyone opens the book, put two lines on the board and nothing else:

   TROUT     costs $10.40   sells for $28.00
   BURGER    costs $ 5.10   sells for $21.00

Ask: "Which one do you want more of?" Take a show of hands. In most rooms a clear majority picks the burger, and several students will say "24% versus 37%" without being prompted — which is exactly the reflex you want on the record.

Then write $28.00 - 10.40 = 17.60$ and $21.00 - 5.10 = 15.90$ underneath, and say nothing.

Follow with: "Now — 45 trout a week, 73 burgers. Which one do you want more of?" The room usually splits, which is correct, and you now have both halves of the chapter's argument in the room from students rather than from you: dollars per plate, and plates per week. Everything after this is elaboration.

The substitution reversal. For §12.5, give half the room the 60/25/15 assumption and half the room the 80/20/0 assumption, ten minutes, and have them compute the annual effect of cutting the trout. One half gets −$10,273**; the other gets **+$4,596. They will assume one group made an error. Letting them discover that the assumption did it — not the arithmetic — is worth more than any lecture on model limitations.

Board work that is worth the time

• The eight steps of §12.3 against Bellwether's data, computed by the room. Insist on the reconciliation check ($\sum \text{units} \times \text{CM}$ against sales minus ideal cost). Students who never learn to cross-check will produce beautiful wrong matrices for their entire careers.
• The gap-closing rule: $d = \text{gap} \div (1 - \text{mix})$. Work Exercise 12.21 on the board. The squash flipping from Star to Plowhorse on $1.22 of ingredient cost is the most memorable single number in the chapter after the $1.70.

Assessment guidance

• Exercise 12.26 is the natural exam problem: five items, clean data, one item of each type, and two items deliberately within a whisker of a line (fish tacos, seven cents below the margin average; grain bowl, 2.7 points above the popularity line). Award real weight for flagging those two as unplaced. A student who confidently labels all five has not read §12.3's step 8.
• Exercise 12.13 distinguishes students who understand the relative-axes problem from those who have memorized quadrant names.
• Exercise 12.37 is the ethics item and should be graded on part (c), not part (a). The arithmetic is trivial; the honest treatment of a portion change against a stated menu claim is not.
• For a practicum, have students bring a real menu from a restaurant they have worked in and estimate the matrix. They will not have plate costs. That is the lesson — send them to Chapter 11.

Sensitivities

• Students who cook will hear §12.5 as a threat to dishes they care about. Get ahead of it: the chapter's own position is that the matrix generates questions and that the person who cooks the food gets the first answer to every question about it. Say so early.
• Case Study 2 is a labeled composite, and the file says so at the top. Point students at the label and make the methodological question explicit — prompt 6 below does this directly. Do not let anyone leave thinking it is a real named restaurant.
• Case Study 1 involves real companies. Keep the discussion on the structural argument (royalty on gross sales vs. profit on one building) and off speculation about any particular brand's finances.