App Pricing Engine — Unit 6 Culminating Project

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📊 Your Mission

Two streaming apps — StreamPro and StreamBasic — are competing for customers. Your manager asked you to investigate their pricing expressions, prove which expressions are equivalent, apply the distributive property, and calculate real costs for a chosen number of months. Work through four phases, fill every box, and finish with a pricing memo.

Equivalent Expressions · 6.EE.4

Are These Pricing Expressions Equal?

StreamPro advertises its family plan two ways: 2(x + 3) and 2x + 6. Your job is to verify these are equivalent by testing any value of x. If both expressions always give the same result, they are equivalent!

Test it: Enter any value for x (number of extra features). The calculator evaluates both expressions and confirms whether they are equal.

Value of x (try several!)

Need a hint?

For x = 5: 2(5 + 3) = 2 × 8 = 16. 2(5) + 6 = 10 + 6 = 16. They match! Try x = 0, x = 10, x = 100 — they will always match because these expressions are equivalent (that is what 6.EE.4 means).

Distributive Property · 6.EE.3

Expand the Discount Expression

StreamBasic offers a discount: a(b + c) where a is the discount rate, b is the base price, and c is a service fee. Use the distributive property to expand and simplify. Enter your own values for a, b, and c.

Distributive property: a(b + c) = a·b + a·c
Multiply the factor outside the parentheses by each term inside.

Factor a (discount multiplier, 1–5)

Term b (base price)

Term c (service fee)

Need a hint?

For a = 3, b = 8, c = 4: 3(8 + 4) = 3·8 + 3·4 = 24 + 12 = 36. You distribute the 3 to each term inside the parentheses. Both ways give the same answer: 3 × 12 = 36. ✓

Evaluate a Cost Expression · 6.EE.2c

Calculate the Real Cost

StreamPro costs 9.99n + 4.50 dollars, where n is the number of months subscribed. The 4.50 is a one-time setup fee. Substitute your chosen n and evaluate — respecting order of operations (multiply before adding).

Order of operations: In 9.99n + 4.50, multiply 9.99 × n first, then add the setup fee 4.50.

Number of months (n, 1–24)

Need a hint?

At n = 6: first, 9.99 × 6 = 59.94 (multiplication first!). Then 59.94 + 4.50 = 64.44. The setup fee is added only once at the end. Total cost = $64.44 for 6 months.

Compare Plans & Quick Check · 6.EE.2c · 6.EE.4

Which Plan Costs Less?

Compare StreamPro (9.99n + 4.50) vs StreamBasic (7.50n + 12.00) for the same number of months. Which is cheaper in the short term? Which is cheaper long-term? Then pass the quick-check.

StreamPro: 9.99n + 4.50 | StreamBasic: 7.50n + 12.00
Enter the same n for both to compare.

Number of months n (1–24)

Quick check: Using the distributive property, evaluate 3(4 + 2). What is the answer?

Your answer (3(4 + 2))

★

Final Deliverable

Write Your Pricing Memo

Write a 3–5 sentence pricing memo to your manager. Explain your findings using real numbers and expressions from your calculations above.

Analyst Checklist

I tested 2(x + 3) and 2x + 6 for the same x and confirmed they are equivalent.
I applied the distributive property to expand a(b + c) step by step.
I evaluated 9.99n + 4.50 using correct order of operations (multiply before adding).
I compared both plans for the same n and identified which costs less.
My pricing memo gives a clear recommendation backed by real numbers.

✓

How You Are Scored

Project Rubric

Category	4 — Expert	3 — Proficient	2 — Developing
Equivalent Expressions (6.EE.4)	Equivalence verified for multiple x values with reasoning	Equivalence confirmed for one x value	Attempted but result was incorrect
Distributive Property (6.EE.3)	Expansion shown step by step and result verified both ways	Expansion is correct	Minor distribution error
Evaluating & Order of Operations (6.EE.2c)	Cost calculated correctly; order of operations explained	Cost value is correct	Attempted but operation order wrong
Communication	Memo clearly recommends a plan using every computed value	Memo uses most computed values	Memo is vague or missing key numbers