This original classroom packet uses cost cards, a blank quantity ledger and an independent check. Its simplified arithmetic is a teaching model, not a forecast, actual sale or complete business-profit calculation.
Declare one exercise period and its assumptions
The fictional paper-badge model supplies:
| Input | Original amount | Meaning within this exercise |
|---|---|---|
| F: fixed setup cost | $12 | Incurred for the stated exercise period, regardless of quantity |
| V: variable cost | $1 per badge | Added for each produced unit |
| P: selling price | $3 per badge | Revenue per sold unit |
| q: quantity | Nonnegative whole badges | All produced units are assumed sold at the stated price |
The US-dollar amounts are illustration data, not market rates. The same q is produced and sold only because the model explicitly assumes that. Real unsold inventory, demand, taxes, wages, financing and other costs are not supplied or silently treated as measured zeros.
Keep that scope on the printable cost cards. A model can answer its own cost comparison without establishing that customers will buy the break-even quantity.
EconEdLink's break-even lesson distinguishes fixed/variable costs, total revenue and total cost, then compares price less variable cost with fixed cost. This packet uses original badge quantities and teaching materials. It does not adopt the source's equipment-purchase decision, worksheets, competition or business-outcome claims.
Build the ledger with the same quantity
Under the declared assumptions:
Total revenue = P × q = 3q.
Total modeled cost = F + V × q = 12 + q.
Modeled difference = revenue − modeled cost = 2q − 12.
Keep the teacher reference separate from the clean learner ledger:
| Produced and sold badges q | Revenue | Total modeled cost | Modeled difference |
|---|---|---|---|
| 0 | $0 | $12 | −$12 |
| 4 | $12 | $16 | −$4 |
| 5 | $15 | $17 | −$2 |
| 6 | $18 | $18 | $0 |
| 7 | $21 | $19 | $2 |
At q = 0, the fixed setup cost remains. At q = 4, the $12 revenue covers only the numerical setup amount; total modeled cost also includes $4 for the units. The model is still $4 below break-even.
At q = 6, revenue and cost both equal $18. The $18 is revenue, not $18 net profit. The modeled difference is zero.
Explain the contribution without changing the unit
Each sold badge contributes P − V = $3 − $1 = $2 per unit toward the fixed setup cost under this model. Dividing $12 by $2 per unit gives six units.
Check that result in the ledger rather than memorize a formula without its inputs. The $2 contribution is not total revenue and is not the final per-unit profit after allocating every real business cost. The model deliberately does not supply that broader calculation.
With a positive fixed cost, if P = V, each unit contributes zero toward setup; there is no finite break-even quantity in this constant model. If P < V, additional units do not cover setup either. Do not divide by zero or present a negative computed quantity as viable sales.
A proposed 35-minute teaching sequence
- Cost cards, 5 minutes: Identify the period, fixed setup, per-unit cost, price and all-sold assumption.
- Model ledger, 8 minutes: Compute q = 0 and q = 4 with both revenue and total cost.
- Partner quantity checks, 10 minutes: Work through q = 5, 6 and 7, keeping units and differences visible.
- Counterclaim review, 7 minutes: Explain why revenue is not profit and why q = 4 has not broken even.
- Independent exit, 5 minutes: Use the different cost cards below.
The phases total 5 + 8 + 10 + 7 + 5 = 35 minutes. Confirm actual class fit, materials, access and standards requirements with the teacher. The timing and model are original proposals, not observed teaching results.
Transfer to different cost cards
The original exit model has F = $15, V = $1 per unit and P = $4 per unit, retaining the same nonnegative whole-unit/all-sold assumptions. Ask learners to find the break-even quantity and verify it with revenue and cost. Leave their ledger and explanation blank.
The separate teacher key is $15 ÷ ($4 − $1) = 5 units. At five, revenue is $20 and cost $15 + $5 = $20, giving zero modeled difference. At four, revenue is $16 and cost $19, giving −$3.
Add an explanation question: What does the calculation establish, and what does it not tell us about buyers? It establishes equality within the stated model; it supplies no demand evidence. Teacher review is needed for the actual explanation, not automatic grading from a selected quantity.
Copy a cost-and-revenue lesson brief
Create one complete, self-contained US-English HTML companion for “Business studies • badge cost lab”. Return the full HTML document, with inline CSS and any JavaScript needed for the local interactions. Use the original scenario, named records, numbers and expected cases below.
Design the page for this task: use clearly labeled input or source records, a readable result or worked example, and an adjacent explanation of the evidence. Use a restrained visual hierarchy, left-aligned text, readable tables or stacked records, and a responsive layout at 720px and 360px. Provide meaningful labeled controls for Compare q = 4; Compare q = 6; Restore original cost cards; Check original-model ledger; Restore original timing; Select text. Use keyboard-accessible native controls and visible focus. Keep the complete content readable without an external dependency.
The following brief supplies the substantive content and constraints. Native-format requests describe the material to represent or copy manually; this HTML must not pretend to create DOCX, XLSX, PDF, PPTX, H5P or another native file, run Python/Flask/Django/Snowflake/Power BI, connect a live service, send messages, or perform an authorized real-world action. Where the task requires a native source, actual observation or separate approval, retain that requirement and leave unsupplied evidence blank.
Draft a business-studies lesson plan in US English.
Class/access context, duration and required printable/school format: [enter]
Exercise period, fixed cost, variable cost/unit and price/unit: [paste]
Quantity unit and produced/sold assumptions: [paste]
Model quantities, independent exit inputs and teacher criteria: [enter]
Classify fixed versus per-unit costs within the declared period/model. Compute
revenue = P * q, cost = F + V * q, difference = revenue - cost at the same quantity. Keep contribution P - V separate from revenue and modeled difference. For positive
F, P <= V gives no finite break-even quantity in this constant model; do not divide
by zero or claim negative quantities viable. Preserve omitted real business
factors as unsupplied, not measured zeros. Cost equality does not establish demand. Make phases sum to the lesson duration. Keep teacher keys separate from blank
learner ledgers and explanations. Do not invent sales, profit, buyers or achievement.
Original model F = 12, V = 1, P = 3: q = 0 difference -12; q = 4 difference -4;
q = 5 difference -2; q = 6 difference 0; q = 7 difference +2. Independent F = 15, V = 1, P = 4: q = 5 revenue 20, cost 20, difference 0;
q = 4 difference -3. All monetary inputs and outputs are illustrative USD. Return the proposed plan, cost cards, clean ledger, separate keys and model-limit
question. If requested, specify an HTML teacher-review copy. No transactions,
market forecasting, automatic grading, student collection or saved edits.
COMPLETE AUTHORED SCENARIO AND EXPECTED CASES
The following is the supplied reading/teaching/calculation record to represent in the companion. Preserve its particular content, examples, source references and unknowns. Wording about a future native implementation refers to that native task, not permission to omit this HTML companion.
# Business Studies Lesson Plan Template: Show Why Revenue Is Not the Break-Even Answer
A learner says selling four badges covers a $12 setup cost because revenue is $12. The statement leaves out the cost of making those four units. Put revenue and total modeled cost at the same quantity before deciding whether the model breaks even.
This original classroom packet uses cost cards, a blank quantity ledger and an independent check. Its simplified arithmetic is a teaching model, not a forecast, actual sale or complete business-profit calculation.
## Declare one exercise period and its assumptions
The fictional paper-badge model supplies:
| Input | Original amount | Meaning within this exercise |
| --- | --- | --- |
| F: fixed setup cost | $12 | Incurred for the stated exercise period, regardless of quantity |
| V: variable cost | $1 per badge | Added for each produced unit |
| P: selling price | $3 per badge | Revenue per sold unit |
| q: quantity | Nonnegative whole badges | All produced units are assumed sold at the stated price |
The US-dollar amounts are illustration data, not market rates. The same q is produced and sold only because the model explicitly assumes that. Real unsold inventory, demand, taxes, wages, financing and other costs are not supplied or silently treated as measured zeros.
Keep that scope on the printable cost cards. A model can answer its own cost comparison without establishing that customers will buy the break-even quantity.
[EconEdLink's break-even lesson](https://econedlink.org/resources/break-even-analysis/) distinguishes fixed/variable costs, total revenue and total cost, then compares price less variable cost with fixed cost. This packet uses original badge quantities and teaching materials. It does not adopt the source's equipment-purchase decision, worksheets, competition or business-outcome claims.
## Build the ledger with the same quantity
Under the declared assumptions:
**Total revenue = P × q = 3q**.
**Total modeled cost = F + V × q = 12 + q**.
**Modeled difference = revenue − modeled cost = 2q − 12**.
Keep the teacher reference separate from the clean learner ledger:
| Produced and sold badges q | Revenue | Total modeled cost | Modeled difference |
| --- | --- | --- | --- |
| 0 | $0 | $12 | −$12 |
| 4 | $12 | $16 | −$4 |
| 5 | $15 | $17 | −$2 |
| 6 | $18 | $18 | $0 |
| 7 | $21 | $19 | $2 |
At q = 0, the fixed setup cost remains. At q = 4, the $12 revenue covers only the numerical setup amount; total modeled cost also includes $4 for the units. The model is still $4 below break-even.
At q = 6, revenue and cost both equal $18. The $18 is revenue, not $18 net profit. The modeled difference is zero.
## Explain the contribution without changing the unit
Each sold badge contributes **P − V = $3 − $1 = $2 per unit** toward the fixed setup cost under this model. Dividing **$12 by $2 per unit** gives **six units**.
Check that result in the ledger rather than memorize a formula without its inputs. The $2 contribution is not total revenue and is not the final per-unit profit after allocating every real business cost. The model deliberately does not supply that broader calculation.
With a positive fixed cost, if **P = V**, each unit contributes zero toward setup; there is no finite break-even quantity in this constant model. If **P < V**, additional units do not cover setup either. Do not divide by zero or present a negative computed quantity as viable sales.
## A proposed 35-minute teaching sequence
1. **Cost cards, 5 minutes:** Identify the period, fixed setup, per-unit cost, price and all-sold assumption.
2. **Model ledger, 8 minutes:** Compute q = 0 and q = 4 with both revenue and total cost.
3. **Partner quantity checks, 10 minutes:** Work through q = 5, 6 and 7, keeping units and differences visible.
4. **Counterclaim review, 7 minutes:** Explain why revenue is not profit and why q = 4 has not broken even.
5. **Independent exit, 5 minutes:** Use the different cost cards below.
The phases total **5 + 8 + 10 + 7 + 5 = 35 minutes**. Confirm actual class fit, materials, access and standards requirements with the teacher. The timing and model are original proposals, not observed teaching results.
## Transfer to different cost cards
The original exit model has **F = $15, V = $1 per unit and P = $4 per unit**, retaining the same nonnegative whole-unit/all-sold assumptions. Ask learners to find the break-even quantity and verify it with revenue and cost. Leave their ledger and explanation blank.
The separate teacher key is **$15 ÷ ($4 − $1) = 5 units**. At five, revenue is **$20** and cost **$15 + $5 = $20**, giving zero modeled difference. At four, revenue is **$16** and cost **$19**, giving **−$3**.
Add an explanation question: **What does the calculation establish, and what does it not tell us about buyers?** It establishes equality within the stated model; it supplies no demand evidence. Teacher review is needed for the actual explanation, not automatic grading from a selected quantity.
## Copy a cost-and-revenue lesson brief
Implement the local companion rather than returning a text-only plan. Preserve every numerical fixture and the distinction between illustrative expectations and actual evidence. Any native-runtime or classroom tests mentioned above remain tests to perform in the proper environment; do not mark them passed. Keep edits and practice responses in this open page only, without claiming persistent storage. Provide invalid/missing-input feedback and reset behavior that agree with this specific brief. Do not claim accessibility certification, learning gains, real approvals or test results that were not observed.
Compare q = 4 with q = 6 and ask a teaching colleague to explain the missing per-unit costs before using the packet. Keep printable tasks and actual learner records in the school workflow, and describe break-even as a result of the stated model rather than evidence that a business will make sales.