You are the lead designer at a game studio. Use the power of expressions to build a scoring system that is balanced, fair, and mathematically sound — then document it in a design report.
Your studio is launching Quest Blaster, a multiplayer adventure game. You need to design the scoring engine — the formulas that calculate how many points players earn. Work through four phases. Each one uses a real expression skill: exponents, writing algebraic expressions, evaluating with order of operations, and deciding which formula is fairest. Fill every box, hit Calculate or Check, then complete the design document and checklist at the end.
In Quest Blaster, reaching a new level multiplies your score. The formula is score = baselevel. Enter a base point value and a level number; the calculator shows the expanded form and the total score.
An exponent means repeated multiplication. 34 = 3 × 3 × 3 × 3. Start with the base and multiply it by itself as many times as the exponent says. Count the factors — there should be exactly exponent of them.
Players collect coins during a level. The studio wants a coin bonus expression: multiply the number of coins by a rate, then add a flat starting bonus. You write the algebraic expression, then the calculator confirms it.
"3 points for each coin" means 3 times c, written as 3c. "Plus a 50-point bonus" means + 50. Put them together: 3c + 50. The coefficient 3 is the rate; 50 is the constant term.
The studio's elite scoring formula is 2x² + 5 where x is the player's power level. Substitute your value of x and evaluate — respecting order of operations (exponents before multiplication before addition).
At x = 3: first, 3² = 9. Then 2 × 9 = 18. Finally, 18 + 5 = 23. So 2(3)² + 5 = 23. Always do exponents before multiplication, and multiplication before addition.
Two designers propose scoring formulas. Compare them for the same player level x to decide which gives a more balanced result. Then pass the quick-check to prove your order-of-operations skills.
Write a short design document (3–5 sentences) explaining your scoring engine choices. Use the real numbers and expressions you calculated above.
| Category | 4 — Expert | 3 — Proficient | 2 — Developing |
|---|---|---|---|
| Exponents (6.EE.1) | Expanded form and value both correct; reasoning explained | Value is correct | Attempted with an exponent error |
| Writing Expressions (6.EE.2a) | Expression written correctly and coins problem explained | Expression written correctly | Expression has a minor error (wrong coefficient or missing constant) |
| Evaluating & Order of Operations (6.EE.2c) | 2x² + 5 evaluated correctly at chosen x; steps shown | Final value correct | Attempted but order of operations error |
| Communication | Design doc clearly justifies every formula choice with real numbers | Design doc uses most computed numbers | Design doc is unclear or missing key numbers |