A 30-minute break-even lesson that needs no preparation

Break-even is in the Class 8 syllabus as linear equations, and it is one of the few topics where the textbook version and the real version are genuinely the same thing. The difficulty is not the algebra. It is that 5n − 20 = 0 does not feel like it is about anything.

This activity fixes that in one period.

Before the lesson

Nothing to install. Book a computer period, and have the class code ready on the board. Students type the code, their first name and their roll number — that is the entire sign-in.

Minutes 0–5 — set the problem, do not solve it

Put this on the board and leave it there:

Your stall costs ₹20 a day to rent. You keep ₹5 profit on every glass. How many glasses before you have earned anything at all?

Take answers. Do not confirm. Some students will say 4 immediately, some will say 20, several will not be sure whether the rent comes off the start or the end. All of that is useful and none of it needs correcting yet.

Minutes 5–25 — they trade

Students run three days of a lemonade business. They buy stock with limited money, set a price, and see the result. Rent is charged every day whether they sell one glass or fifty.

Walk the room. The sentence you are listening for is "wait, I sold loads and still lost money." That student has just met fixed costs, and they will remember the meeting.

Minutes 25–30 — the discussion that matters

Come back to the board. Now ask:

1. Who covered their rent on day one? How many glasses did it take you?
2. If the rent went up to ₹60, how many glasses would you need? (12 — and watch them get there by dividing, then formalise it.)
3. Would you move to a busier street for ₹60 rent? (Only if it brings at least 8 more customers. This is the question the arithmetic exists to answer.)
4. Write it properly: 5n − 20 = 0, so n = 4. Now the equation is a summary of something they did, not a ritual.

The extension, if you have time

Ask them to work out their break-even before they open on day three, and write the number down. Then check it against what happened. Predicting and then verifying is the single most useful habit this activity can build.

What you get afterwards

A class report showing participation, average profit, and which concepts came out strong and weak across the group — so you know whether to move on or spend another period on it.

Free for teachers and schools, permanently. If you want class codes, register your class — it takes a minute.