Case Log Answer Key Case Log:
Missing Link
ANSWER KEY / FOR TEACHER USE ONLY
Detective:
LENNY (KEY)
Date:
MAY 12, 2026
Case 01: The Shady Diner
Lunch bill: $15.00. Calculate 7% Tax and 15% Tip.
Tax Investigation
x/15 = 7/100
100x = 105
x = $1.05
Tip Investigation
y/15 = 15/100
100y = 225
y = $2.25
Final Bill: $ 18.30 (15 + 1.05 + 2.25)
Case 02: Tactical Gear
Night Vision Goggles normally cost $240. Current Deal: 30% OFF.
Discount (d): d/240 = 30/100
100d = 7200 → d = 72
Final Price: 240 - 72 = $168.00
Sale Price: $ 168.00
Close the Case
A disguise costs $40.00. Add 5% sales tax.
x/40 = 5/100 → 100x = 200 → x = $2.00 tax
Total = $42.00
Evidence Match:
$42.00
$45.00
NC.7.RP STANDARDS / ANSWER KEY
Case Log #902-K
Proportion Detectives Lesson Plan Proportion Detectives
Lesson Plan: Finding the Missing Link
7TH GRADE | 30 MIN
Learning Objective
Students will identify unit rates and set up proportional equations to solve real-world percentage, tax, and discount problems using cross-multiplication.
NC.7.RP.1-3 Standards
Essential Gear
Best Deal Slide Deck
Case Log Worksheets
Timeline
5 MIN
Warm-Up: Snack Heist
Compare snack packs (5 for $2.50 vs 8 for $3.20). Use unit rates ($/item) to spot the evidence of a better deal.
10 MIN
Mini-Lesson: The Skeleton
Part
Whole
=
%
100
Identify "Whole" (Original Price) and solve using cross-multiplication clues.
10 MIN
Guided Practice: Crime Scenes
Collaboratively solve Case #1 (Tax/Tip) and Case #2 (Discount). Focus on the final step: adding for tax/tip and subtracting for sales.
5 MIN
Cool-Down: Close the Case
Independent attempt at the independent Case Log problem ($40 disguise + 5% tax). Goal: Correct setup and final addition.
Case Tip: Pitfalls
Watch for students who solve for the tax/discount amount but stop there without adding or subtracting to find the total bill.
Extension
"If you have a 10% discount and then 10% tax is added, do you end up at the original price?" Challenge them to prove it with math.
Evidence Evaluation Exit Ticket URGENT
Evidence Evaluation
Exit Ticket: Proportion Case #402
Agent:
A detective's trench coat is $80.00.
1. Set up the Proportion:
=
2. Solve for Sale Price:
Final Price: $ ____________
Cut Along Line
URGENT
Evidence Evaluation
Exit Ticket: Proportion Case #402
Agent:
A detective's trench coat is $80.00.
1. Set up the Proportion:
=
2. Solve for Sale Price:
Final Price: $ ____________
Exit Ticket Answer Key Evaluation Key
Exit Ticket: Case #402 / Teacher Resource
Step 1: Proportion Setup
d
80
=
25
100
Step 2: Cross Multiply & Solve
100 × d = 80 × 25
100d = 2,000
d = $20.00 (Total Savings)
Final Evaluation: Subtract Savings
$80 - $20 = $60.00
Proportion Detective Agency
Exit Ticket Answer Key
Tax Tip and Discount Cheat Sheet Detective Field Guide
Official Agency Proportional Reference
Certified Gear
The Missing Link Formula
Part
Whole
=
%
100
"Multiply across the equals sign, then divide by the lone number!"
Tax
Add to total (+)
x
20
=
7
100
x = $1.40
Tip
Add to total (+)
x
50
=
20
100
x = $10.00
Discount
Subtract (-)
x
80
=
25
100
x = $20.00
Evidence Key
• WHOLE: Price BEFORE the change.
• PART: Tax, tip, or discount amount.
• PERCENT: Always sits above the 100.
Trial Investigation
What is 10% of $60?
60
=
10
100
Final Answer: $ _______________
PROPORTION DETECTIVE AGENCY HQ
NC.7.RP STANDARD COMPLIANT
Spotting the Best Deal Slide Deck Spotting the
Best Deal
Proportion Detective Agency
The Snack Heist
Warm Up
Evidence A
5 Snack Packs
$2.50
Evidence B
8 Snack Packs
$3.20
Which is the "Best Deal"?
The Formula Skeleton
Part
Whole
=
%
100
"The WHOLE is your Original Total."
STEP 1
Multiply Across
x
15
=
7
100
Connect the diagonal clues!
15 × 7 = 105
STEP 2
Divide by Leftover
105
÷
100
Divide your product by the number across from X.
105 ÷ 100 = 1.05
Case 01: Agent Miller
Lunch bill: $15.00. Find 7% Tax & 15% Tip.
Tax Clue
x
15
=
7
100
Tip Clue
y
15
=
15
100
Solve the Mystery
Case 02: Gear Sale
Tactical Gear normally costs $240.
d
240
=
30
100
Subtract Savings from Original!
Case Closed?
Final Clue
A disguise costs $40.00.
A) $42
B) $45
C) $38
Case Results
Answer Key
Case 01
Tax: $1.05
Tip: $2.25
$18.30
Case 02
Off: $72.00
$168.00
Final Clue
Tax: $2.00
Choice A
$42.00
Proportion Case Log Worksheet Case Log:
Missing Link
File: 7-RP-3 / Proportional Investigation
Detective:
Date:
Case 01: The Shady Diner
Lunch bill: $15.00. Calculate 7% Tax and 15% Tip (both on the original bill). Find the total.
Tax Investigation
Investigate
Tip Investigation
Investigate
Final Bill: $ ________________
Case 02: Tactical Gear
Night Vision Goggles normally cost $240. They are currently 30% OFF. Find the final price.
Evidence Room
Sale Price: $ _______________
Close the Case (Solo)
A disguise costs $40.00. Add a 5% sales tax. What is the total cost?
Drafting Space
Evidence Match:
$42.00
$45.00
$38.00
NC.7.RP STANDARDS / PROPORTION DETECTIVE AGENCY
Case Log #902
