Teacher Guide

Nothing changed about the ratio and everything changed about the totals. A student who says the ratio measures them against the other stall while the total measures the day has it.

Under 45 cents each, so under $1.80 for a pack of 4. $1.79 works. A student who answers $2.70 has compared packs, not items.

Not $4.20. A 40 percent margin means cost is 60 percent of the price, so price is $3.00 divided by 0.6, which is $5.00. Students who add 40 percent to the cost have computed a markup.

At 25 percent markup, $8.00 becomes $10.00. At 25 percent margin, $8.00 becomes $10.67. The right answer is to ask which they mean, and a student who says so has understood the week.

Running totals are -6, +5, +3, +7. The whole four days are up by $7, and the first day back above zero for the week is day 2.

Anything not for sale: making one at home, borrowing, doing without. You compete with those on convenience and on time, never on price.

Better product, better position on the floor, a reputation, or a different customer entirely. Three plausible answers is the bar.

Five days at a mean of 10 is 50 altogether. The four known days are 14, so the fifth is 36, and the median of 2, 3, 4, 5, 36 is 4. The median describes this week much better than the mean does.

Ask them what the sessions actually were. A range of 15 says at least one session was far from 8, not how many: one wild day among four near 8 is a different team from five scattered days.

Profit = p x q - c x q - f. On row a that is 42.00 - 16.80 - 12.00 = $13.20. Students who write p x q - c - f have taken the cost off once instead of once per item.

With a cost of $1.50 the profits are -$12.00, $9.00, $19.50, $22.50 and $21.00, so the best profit is at $4.00 and the best revenue is at $3.00. They are different rows, and that surprises plenty of adults too.

Anything that raises cups per sale without cutting the price per cup: a bigger pack, a bundle, a second cup at a small discount. The number that would tell you is revenue per customer.

The useful answer is a rule agreed in advance, not a renegotiation afterwards. Anything of the form if X happens we do Y counts.

The strongest case for the corner they rejected, made honestly, is the test that they understood the trade rather than just preferring one.

If both teams write the same sentence, one of them will have to move, and finding that out in week 15 is much cheaper than in week 29.

3 in 10 of 120 people is 36 customers. That number, not a feeling, is what decides how many to make.

Halving the build time doubles how many you can make in an hour, which changes week 23's target. A team that times itself here has a real number to plan with instead of a guess.

Signals that survive fifteen answers are worth acting on. Ones that appeared once in ten and never again were noise.

Dropping to $3.00 leaves them $1.00 of margin, which is 33 percent. They can hold it for a while and not forever, and a team that says so has read the number correctly.

You go to $3.60, they go to $3.24, you go to $2.92, they go to $2.63. Margins end at $0.92 for you and $0.63 for them, from $2.00 each at the start. Nobody wins; the customer does. That is a price war and it is the right name for it.

At 50 percent off there is no margin at all, so no number of extra sales helps. That row is the one worth spending time on.

Add something that costs almost nothing: a card, a wrap, a choice of color. The bundle price rises and the cost barely does.

Aiming at 18 and selling 11 could be a wrong target or a wrong plan. The question that separates them is how many people looked and did not buy.

Writing the other team's page forces a team to state what it thinks the rival's position is, which is exactly what week 33 will need.

A pitch that survives being copied is one built on something the other team cannot honestly claim: who made it, how, or for whom.

Showing both prices honestly and letting the reason sign carry the difference is a real strategy and takes nerve.

State both numbers and put the reason beside them. A customer who can check you and still chooses you is worth two who cannot.

$12 of float covers one $6.50 change and leaves $5.50, so the second customer cannot get change, and nor can the third or fourth. Only one of the four is served. A team that works this out brings more coins.

Revenue divided by sold is the average price actually achieved. Below the sign price means undocumented discounts.

Half the units at twice the price is the same revenue and a different margin. Revenue, units and margin can disagree, and which one matters depends on the position.

Share up and revenue down happens when the whole market shrinks. Real numbers are the bar here, not a description.

Six sales to break even and fourteen to finish $10 up. Both are achievable numbers, which is the point of writing the loss down.

Writing the rival's decision first can change a team's own. That is not cheating, it is what strategy is.

A busier market lifts everybody. Whether a particular move worked is a question about share, not about totals, and week 35 is where that lands.

Anything that gets closer to a clean answer: changing price for half the session, or comparing against a team that did not move. Neither is perfect and saying so is part of the answer.

Writing the other team's page about you, then comparing, is the closest thing to feedback this book can arrange.