Start-Up City — Grade 6 Year-End Capstone

Business progress: 0% complete

📊 Business Dashboard

Startup Budget

$500.00

Unit Price

—

Total Costs

—

Projected Revenue

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Profit / Loss

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🗺️ Your Mission

You have a $500 startup budget and a big idea. Work through 8 phases — each one uses a different Grade 6 math strand. Fill in every calculator, hit Calculate, check your hints if you're stuck, and finish the business plan and checklist at the end. Then print your pitch for investors!

Ratios & Proportional Relationships · 6.RP.1 · 6.RP.3

Product Mix — Ingredient Ratios

Your product requires two key ingredients (or components). Set your recipe ratio, simplify it, and scale it up so you know exactly what to order.

Example: A custom candle uses 3 parts wax : 2 parts fragrance oil. The simplified ratio stays 3 : 2, and a double batch uses 6 : 4.

Ingredient A (parts)

Ingredient B (parts)

Ingredient A name (optional) Ingredient B name (optional)

💡 Need a hint?

To simplify a ratio a : b, find the GCF of a and b, then divide both by it. Example: 6 : 4 → GCF = 2 → simplified is 3 : 2. To scale up, multiply both parts by 2, 3, etc.

Percents · 6.RP.3c

Pricing — Markup, Discount & Sales Tax

Start with your unit cost, apply a markup to earn profit, give a launch discount, then add sales tax. The final price is what customers pay.

Unit cost to produce ($)

Markup % (your profit margin)

Discount % (launch sale)

Sales tax %

💡 Need a hint?

Step 1 — After markup: price = cost × (1 + markup/100). Step 2 — After discount: discounted = price × (1 − discount/100). Step 3 — After tax: final = discounted × (1 + tax/100). All percent conversions use ÷ 100.

Area of Polygons · 6.G.1

Store Layout — Flooring Cost

Your storefront is L-shaped — two rectangles joined together. Find the total floor area, then calculate how much your flooring will cost.

Diagram: Section A is the main showroom. Section B is the back storage/display area. Together they form an L-shape. Area = (A₁ = L₁ × W₁) + (A₂ = L₂ × W₂).

Section A — Main Showroom

Length (ft)

Width (ft)

Section B — Back Display Area

Length (ft)

Width (ft)

Flooring cost ($ per sq ft)

💡 Need a hint?

Area of a rectangle = base × height (length × width). Add the two areas: total = A₁ + A₂. Then multiply by cost per sq ft. Make sure both sections use the same units (feet).

Volume & Surface Area · 6.G.2 · 6.G.4

Packaging — Box Dimensions

Design the box that holds your product. Find the volume (how much fits inside) and surface area (how much cardboard you need), then calculate material cost.

Length (in)

Width (in)

Height (in)

Cardboard cost ($ per sq inch)

💡 Need a hint?

Volume of a rectangular prism: V = l × w × h. Surface area: SA = 2(lw + lh + wh). There are 6 faces — two of each pair (top/bottom, front/back, left/right). Multiply SA by material cost to find total cardboard cost.

Expressions & Variables · 6.EE.2

Revenue Formula — Evaluate Your Expression

Write and evaluate the profit expression: Profit = price × q − fixed costs, where q is the number of units sold.

Expression: P = p × q − C, where p = unit price, q = quantity sold, C = total fixed costs. Bonus: a bulk bonus doubles profit on orders of q² or more units (exponent concept).

Unit price (p) from Phase 2 ($)

Units sold (q)

Fixed costs (C) ($)

💡 Need a hint?

Substitute your values: P = p × q − C. Follow order of operations — multiply first, then subtract. Example: if p = $8.10, q = 50, C = $200, then P = 8.10 × 50 − 200 = 405 − 200 = $205. For the bulk bonus, q² means q × q.

One-Variable Equations · 6.EE.7

Break-Even — How Many Units Must You Sell?

Solve the equation price × x = fixedCosts for x, the minimum number of units you must sell to cover all costs and not lose money.

Selling price per unit ($)

Total fixed costs ($)

💡 Need a hint?

The equation is: price × x = fixedCosts. To solve for x, divide both sides by price: x = fixedCosts ÷ price. Since you can't sell a fraction of a unit, always round UP with Math.ceil(). Check: substitute x back in — price × x ≥ fixedCosts? ✅

Statistics & Data · 6.SP.3 · 6.SP.5

Customer Survey — Analyze Ratings

You surveyed customers on a scale of 1–10. Enter 5–7 ratings, and find the mean (average) and median (middle value) to understand customer satisfaction.

Tip: Mean = sum of all values ÷ number of values. Median = middle number after sorting. These measures of center describe what is typical.

Enter ratings separated by commas (1–10, at least 5 values)

💡 Need a hint?

Sort ratings from least to greatest first. For median with an odd count, pick the middle number. For an even count, average the two middle numbers. Mean = total ÷ count. Compare mean and median — if they're close, your data is balanced!

Integers & Absolute Value · 6.NS.5

Cash Flow — Profit or Loss?

Real businesses track profit and loss as signed numbers. A positive balance means profit. A negative balance means you owe money — a loss. Absolute value shows the magnitude.

Remember: Revenue − Costs = Balance. If costs > revenue, the balance is negative. That means the business lost money this period.

Total revenue earned ($)

Total costs / expenses ($)

💡 Need a hint?

Balance = Revenue − Costs. If the result is positive (+), you made a profit — shown on a number line to the right of zero. If negative (−), you have a loss — to the left of zero. |Balance| is the absolute value (distance from zero, always positive).

★

Final Deliverable

Business Plan — Pitch to Investors

Write your business plan using your real numbers from the phases above. Use the sentence starters below to guide you.

✅ Strand Checklist

Ratios (6.RP.1/3): I found and simplified my ingredient ratio and scaled it up in a table.
Percents (6.RP.3c): I applied markup, discount, and sales tax correctly using ÷100 math.
Area (6.G.1): I calculated the L-shaped store area as two rectangles and found flooring cost.
Volume & Surface Area (6.G.2/4): I found V = l×w×h and SA = 2(lw+lh+wh) for my box.
Expressions (6.EE.2): I wrote and evaluated the profit expression with my own values.
Equations (6.EE.7): I solved price·x = costs for x and verified by substitution.
Statistics (6.SP.3/5): I found the mean and median of my customer ratings and interpreted them.
Integers (6.NS.5): I expressed my profit/loss as a signed number and explained its meaning.

✓

How You Are Scored

Project Rubric

Strand	4 — Expert	3 — Proficient	2 — Developing
Ratios (6.RP)	Ratio simplified correctly using GCF; scaling table complete and accurate; explanation clear	Ratio simplified and table correct	Ratio attempted; minor error in GCF or scaling
Percents (6.RP)	All three percent steps correct to the cent; can explain each ÷100 conversion	Final price correct; steps shown	One step correct; missing a step or rounding error
Geometry — Area (6.G)	L-shape decomposed correctly; both rectangle areas accurate; total and cost correct	Both areas and total cost correct	One rectangle correct; error in sum or cost
Geometry — Vol & SA (6.G)	V and SA both correct with formulas shown; material cost accurate	Both formulas applied correctly	Volume correct but SA error, or vice versa
Expressions & Equations (6.EE)	Expression correctly written and evaluated; break-even solved, verified, and ceiled correctly	Expression and equation both correct	One correct; minor substitution or solving error
Statistics (6.SP)	Mean and median both correct; data interpreted with reference to what is "typical"	Both measures of center correct	One measure correct; minor sorting or calculation error
Communication	Business plan uses every calculated number and clearly connects math to decisions	Business plan references most numbers	Plan is incomplete or numbers are missing/inconsistent