Content review: Input → Output Mission
Status: Draft — not approved for publication. Mastery threshold 80% (provisional).
Warm-up · Spy the calculator table
Look at the equation and the two columns. The left column holds the input. The right column shows the output produced by that input. Calculator example: pay = $250 + $10 for each A. A negative number of A’s does not fit this situation.
From original
- Title, body, prompt, choices, both feedback messages (seen on live mission)
⚠ Reconstructed — needs approval
- None
Step 1 · Before the mission
Which row tells us the pay for 7 A’s?
- A. 320 → 7
- B. 7 → 320 ✓
- C. −2 → 230
Answer: 7 → 320
✓ Correct: Yes. Seven is the input, and $320 is the output.
✗ If A: Read left to right: number of A’s → pay.
✗ If C: Read left to right: number of A’s → pay.
Case File 01
Work pay · E(a) = 250 + 10a
You earn $250 for coming to work and $10 for each A a student earns. Seven A’s were earned.
Input a: number of A’s → Output E(a): total pay in dollars
From original
- Scenario
- E(a) = 250 + 10a and E(7) = 320
- Labels
- Table prompt and inputs 1, 7
- Clue and value questions
- Choices A–D
⚠ Reconstructed — needs approval
- Correct letter D (inferred)
- All feedback messages
Step 1 · Build the input-output table
The first row is modeled for you. Add input values 1 and 7, then calculate both outputs from E(a) = 250 + 10a.
Given row: 0 → 250
Answer: 1 → 260; 7 → 320
✓ Correct: Table checks out. Each output came from substituting its input.
✗ Incorrect: Not yet. Multiply the number of A’s by 10 first, then add 250. Check each row on its own.
Step 2 · Identify the clue
In E(7) = 320, is 7 an input or an output?
Answer: Input
✓ Correct: Correct. 7 is the number of A’s — it goes into the rule, inside the parentheses.
✗ Incorrect: Look again. 7 is the number of A’s — it goes into the rule, inside the parentheses. In function notation the input sits inside the parentheses; the output is the result after the equals sign.
Step 3 · Find the missing value
What is your total pay for 7 A’s?
Answer: $320
✓ Correct: Correct. E(7) = 320.
✗ Incorrect: Not quite. Multiply the number of A’s by 10 first, then add 250.
✗ If 70: You found the pay for the A’s only (10 × 7). Don’t forget the $250 for coming to work.
✗ If 260: That’s the pay for 1 A. Substitute 7 for a: 250 + 10(7).
✗ If 1820: Multiply before you add: 10 × 7 = 70, then 250 + 70.
✗ If 257: You added 7 instead of multiplying it by 10. 10a means 10 × a.
Step 4 · Choose the function statement
Remember: the input goes inside the parentheses; the output goes after the equals sign.
- A. E(320) = 7
- B. E(7) = 250
- C. E(10) = 320
- D. E(7) = 320 ✓
Answer: E(7) = 320
✓ Correct: Correct. E(7) = 320 — input inside, output after the equals sign.
✗ If A: This puts the output inside the parentheses. 7 is the input, so it goes inside: E(7). The output 320 goes after the equals sign.
✗ If B: 250 is the starting pay when a = 0. With 7 A’s, the output is 250 + 10(7).
✗ If C: 10 is the rate per A, not the input. The input is the number of A’s: 7.
Case File 02
Hotel tax · T(x) = 0.06x + 4.50
A hotel charges a 6% tax on the room price plus a $4.50 city fee. The room costs $120.
Input x: room price in dollars → Output T(x): total tax in dollars
From original
- T(x) = 0.06x + 4.50 and T(120) = 11.70
⚠ Reconstructed — needs approval
- Scenario wording
- Input/output labels
- Table input values (rows 2–3)
- “Input or output?” question wording
- Missing-value question wording
- Statement answer choices (A–D) and correct letter
- All feedback messages
Step 1 · Build the input-output table
The first row is modeled for you. Add input values 100 and 120, then calculate both outputs from T(x) = 0.06x + 4.50.
Given row: 0 → 4.5
Answer: 100 → 10.5; 120 → 11.7
✓ Correct: Table checks out. Each output came from substituting its input.
✗ Incorrect: Not yet. Multiply the room price by 0.06 first, then add 4.50. Check each row on its own.
Step 2 · Identify the clue
In T(120) = 11.70, is 11.70 an input or an output?
Answer: Output
✓ Correct: Correct. 11.70 is the tax the rule produces for a $120 room — it comes after the equals sign.
✗ Incorrect: Look again. 11.70 is the tax the rule produces for a $120 room — it comes after the equals sign. In function notation the output is the result after the equals sign; the input sits inside the parentheses.
Step 3 · Find the missing value
What is the total tax on a $120 room?
Answer: $11.7
✓ Correct: Correct. T(120) = 11.70.
✗ Incorrect: Not quite. Multiply the room price by 0.06 first, then add 4.50.
✗ If 7.2: You found the 6% only (0.06 × 120). Add the $4.50 fee too.
✗ If 124.5: You added 4.50 to the room price. Multiply by 0.06 first: 0.06 × 120.
✗ If 727.5: 6% is 0.06, not 6. Multiply 120 by 0.06.
✗ If 14.7: Check 0.06 × 120 — it’s 7.20, not 10.20.
Step 4 · Choose the function statement
Remember: the input goes inside the parentheses; the output goes after the equals sign.
- A. T(11.70) = 120
- B. T(120) = 11.70 ✓
- C. T(0.06) = 11.70
- D. T(120) = 4.50
Answer: T(120) = 11.70
✓ Correct: Correct. T(120) = 11.70 — input inside, output after the equals sign.
✗ If A: This puts the output inside the parentheses. 120 is the input, so it goes inside: T(120). The output 11.70 goes after the equals sign.
✗ If C: 0.06 is the tax rate, not the input. The input is the room price: 120.
✗ If D: 4.50 is only the fixed fee. The output for a $120 room includes the 6% tax too.
Case File 03
Delivery · D(m) = 2m + 6
A delivery service charges a $6 base fee plus $2 for each mile. The delivery is 8 miles.
Input m: miles driven → Output D(m): delivery cost in dollars
From original
- D(m) = 2m + 6 and D(8) = 22
⚠ Reconstructed — needs approval
- Scenario wording
- Input/output labels
- Table input values (rows 2–3)
- “Input or output?” question wording
- Missing-value question wording
- Statement answer choices (A–D) and correct letter
- All feedback messages
Step 1 · Build the input-output table
The first row is modeled for you. Add input values 1 and 8, then calculate both outputs from D(m) = 2m + 6.
Given row: 0 → 6
Answer: 1 → 8; 8 → 22
✓ Correct: Table checks out. Each output came from substituting its input.
✗ Incorrect: Not yet. Multiply the miles by 2 first, then add 6. Check each row on its own.
Step 2 · Identify the clue
In D(8) = 22, is 8 an input or an output?
Answer: Input
✓ Correct: Correct. 8 is the number of miles — it goes into the rule, inside the parentheses.
✗ Incorrect: Look again. 8 is the number of miles — it goes into the rule, inside the parentheses. In function notation the input sits inside the parentheses; the output is the result after the equals sign.
Step 3 · Find the missing value
What is the cost of an 8-mile delivery?
Answer: $22
✓ Correct: Correct. D(8) = 22.
✗ Incorrect: Not quite. Multiply the miles by 2 first, then add 6.
✗ If 16: You found the mileage charge only (2 × 8). Add the $6 base fee.
✗ If 64: Multiply before you add: 2 × 8 = 16, then 16 + 6.
✗ If 54: You multiplied 8 by 6 and added 6. The rate per mile is 2.
Step 4 · Choose the function statement
Remember: the input goes inside the parentheses; the output goes after the equals sign.
- A. D(8) = 22 ✓
- B. D(22) = 8
- C. D(2) = 22
- D. D(8) = 6
Answer: D(8) = 22
✓ Correct: Correct. D(8) = 22 — input inside, output after the equals sign.
✗ If B: This puts the output inside the parentheses. 8 is the input, so it goes inside: D(8). The output 22 goes after the equals sign.
✗ If C: 2 is the cost per mile, not the input. The input is the number of miles: 8.
✗ If D: 6 is only the base fee. The output for 8 miles is 2(8) + 6.
Case File 04
Water tank · W(t) = 50 − 5t
A tank holds 50 gallons of water and drains 5 gallons each hour. It has been draining for 6 hours.
Input t: hours draining → Output W(t): gallons left in the tank
From original
- W(t) = 50 − 5t and W(6) = 20
⚠ Reconstructed — needs approval
- Scenario wording
- Input/output labels
- Table input values (rows 2–3)
- “Input or output?” question wording
- Missing-value question wording
- Statement answer choices (A–D) and correct letter
- All feedback messages
Step 1 · Build the input-output table
The first row is modeled for you. Add input values 1 and 6, then calculate both outputs from W(t) = 50 − 5t.
Given row: 0 → 50
Answer: 1 → 45; 6 → 20
✓ Correct: Table checks out. Each output came from substituting its input.
✗ Incorrect: Not yet. Multiply the hours by 5 first, then subtract from 50. Check each row on its own.
Step 2 · Identify the clue
In W(6) = 20, is 20 an input or an output?
Answer: Output
✓ Correct: Correct. 20 is the gallons left that the rule produces after 6 hours — it comes after the equals sign.
✗ Incorrect: Look again. 20 is the gallons left that the rule produces after 6 hours — it comes after the equals sign. In function notation the output is the result after the equals sign; the input sits inside the parentheses.
Step 3 · Find the missing value
How many gallons are left after 6 hours?
Answer: 20
✓ Correct: Correct. W(6) = 20.
✗ Incorrect: Not quite. Multiply the hours by 5 first, then subtract from 50.
✗ If 80: The tank is draining, so subtract: 50 − 5(6).
✗ If 30: 30 gallons drained out (5 × 6). The question asks how many are left: 50 − 30.
✗ If 270: Multiply before you subtract: 5 × 6 = 30, then 50 − 30.
✗ If 44: You subtracted 6 instead of 5 × 6. 5t means 5 × t.
Step 4 · Choose the function statement
Remember: the input goes inside the parentheses; the output goes after the equals sign.
- A. W(20) = 6
- B. W(6) = 50
- C. W(6) = 20 ✓
- D. W(5) = 20
Answer: W(6) = 20
✓ Correct: Correct. W(6) = 20 — input inside, output after the equals sign.
✗ If A: This puts the output inside the parentheses. 6 is the input, so it goes inside: W(6). The output 20 goes after the equals sign.
✗ If B: 50 is the starting amount when t = 0. After 6 hours the output is 50 − 5(6).
✗ If D: 5 is the drain rate, not the input. The input is the number of hours: 6.
Final independent mastery check
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