Mathematics Grade 5 Profit and Loss

Grade 5 Mathematics Study Guide: Profit and Loss

1. The Driving Question

"If you buy a lemonade stand kit for $15 and sell 20 cups at $2 each, how do you know if you actually made money—or lost it? And why does it matter whether you count the cost of the lemons, the cups, or just the kit?"

By the end of this guide, you’ll be able to track every dollar in and out of a real business (even a lemonade stand) and explain exactly how much profit—or loss—you’re left with.

2. The Core Idea — Built, Not Listed

Imagine you’re running a school bake sale. You buy 12 cookies for $6 from the store, then sell each cookie for $1. At the end of the day, you have $10 from sales. Did you make money? To find out, you need to compare two things: 1. Total Revenue: The money you earned from selling ($10).
2. Total Cost: The money you spent to buy the cookies ($6).

The difference between them is your profit (if revenue > cost) or loss (if cost > revenue). In this case, $10 (revenue) – $6 (cost) = $4 profit.

But what if you also spent $2 on napkins? Now your total cost is $6 + $2 = $8. Your profit shrinks to $10 – $8 = $2. Profit isn’t just about sales—it’s about all the money you spend to make those sales happen.

Key Vocabulary:
- Revenue: The total money earned from selling something.
Example: If you sell 5 handmade bracelets at $3 each, your revenue is $15.
- Cost: The total money spent to make or buy the things you sell.
Example: If you buy beads for $4 and string for $1, your cost is $5.
- Profit: Revenue minus cost (when revenue is bigger).
Example: $15 (revenue) – $5 (cost) = $10 profit.
- Loss: Cost minus revenue (when cost is bigger).
Example: If you sell only 2 bracelets for $6 but spent $10 on supplies, you have a $4 loss.

3. Assessment Translation (Grade 5 Formative Work)

How this appears in class:
- Exit tickets: "You buy 10 packs of trading cards for $3 each and sell them for $5 each. What is your profit?" - Show-your-work problems: "A toy store buys 8 action figures for $12 each and sells them for $20 each. If they sell all 8, what is their total profit? Show your steps." - Short constructed response: "Liam sells lemonade for $1.50 a cup. He buys lemons for $4 and cups for $2. If he sells 12 cups, does he make a profit or a loss? Explain how you know."

What a "proficient" response looks like vs. "developing":
| Proficient | Developing | |----------------|----------------| | "Liam’s revenue: 12 cups × $1.50 = $18. His cost: $4 + $2 = $6. Profit: $18 – $6 = $12." | "He makes $12." (No steps shown.) | | "He makes a profit because $18 is more than $6." | "He makes money." (No numbers or explanation.) | | Labels steps clearly (revenue, cost, profit). | Mixes up revenue and cost. |

Model Proficient Response:
"First, I found the revenue: 12 cups × $1.50 = $18. Then, I added the costs: $4 + $2 = $6. Finally, I subtracted cost from revenue: $18 – $6 = $12. Liam made a $12 profit because his revenue was bigger than his cost."

4. Mistake Taxonomy

Mistake 1: Forgetting to include all costs
- Question: "You buy a $10 book and sell it for $15. What is your profit?" - Common wrong answer: "$5 profit." - Why it loses credit: The student only subtracted the book’s cost but forgot other costs (e.g., gas to drive to the store, time spent listing it online).
- Correct approach: "Profit = Revenue – Total Cost. Here, revenue is $15. If the only cost was the book ($10), then profit is $5. But if there were other costs (like $2 for shipping), profit would be $15 – $12 = $3."

Mistake 2: Mixing up revenue and profit
- Question: "A bakery sells 50 cupcakes for $2 each. Their profit is $30. How much did the cupcakes cost to make?" - Common wrong answer: "$100." (Student thinks profit = revenue.) - Why it loses credit: The student confuses revenue ($100) with profit ($30). They didn’t subtract cost from revenue.
- Correct approach: "Revenue = 50 × $2 = $100. Profit = Revenue – Cost. So, $30 = $100 – Cost. Cost = $100 – $30 = $70."

Mistake 3: Ignoring the number of items sold
- Question: "You buy 6 notebooks for $12 and sell each for $3. What is your profit?" - Common wrong answer: "$6 profit." (Student does $12 – $3 = $9, then $9 × 6 = $54, but this is wrong.) - Why it loses credit: The student subtracts the selling price from the total cost instead of multiplying first.
- Correct approach: "Revenue = 6 × $3 = $18. Cost = $12. Profit = $18 – $12 = $6."

5. Connection Layer

1. Within math: Profit and loss → percentages — "If your lemonade stand makes a 20% profit, what does that actually mean for your $50 revenue?" (Understanding profit helps you calculate percentages of earnings.)
2. Across subjects: Profit and loss → economics (social studies) — "Why do stores have ‘sales’? How does lowering prices affect their profit?" (The same math explains why businesses discount items.)
3. Outside school: Profit and loss → allowance or part-time jobs — "If you babysit for $10/hour but spend $3 on snacks for the kids, your ‘profit’ is $7/hour." (You’re already doing this math without realizing it!)

6. The Stretch Question

"If you sell handmade friendship bracelets for $5 each, but the beads cost $2 per bracelet, how many do you need to sell to buy a $50 video game? What if you also have to pay $10 for a booth at the school fair—does that change your answer?"

Pointer toward the answer:
First, find the profit per bracelet: $5 (revenue) – $2 (cost) = $3 profit each. To reach $50, you’d need to sell $50 ÷ $3 ≈ 17 bracelets (since you can’t sell a fraction). But if you add the $10 booth fee, your total cost is now $10 + ($2 × number of bracelets). So, $5 × number of bracelets – ($10 + $2 × number of bracelets) = $50. Solve for the number of bracelets—it’s more than 17! (The answer is 20 bracelets.) The booth fee means you have to sell more to break even.