Rational Detectives Worksheet
Grade 7 Math • Rational Numbers & Operations
Operation Clue Detectives
Learn to spot the right operation in real-world rational number word problems.
Name:
Date:
The Operation Decoder: Match Action to Math
Action: Combining
Clue Words: deposit, gain, increase, combined, altogether, rise, in total.
Rational Clue: Adding a deposit to a negative balance: \(-12 + 25 = 13\)
− Subtraction
Action: Difference
Clue Words: drop, decrease, difference, withdrawal, fall, how much more/less.
Rational Clue: Temperature drop from high to low: \(4.5 - 7.2 = -2.7\)
× Multiplication
Action: Equal Groups
Clue Words: each, per, times, of (a fraction of), repeated change, rate.
Rational Clue: Spending $3.50 each day for 4 days: \(4 \times (-3.50)\)
÷ Division
Action: Equal Split
Clue Words: split equally, divided into, cut into pieces, shared evenly, per one.
Rational Clue: Cutting \(6\frac{1}{2}\) feet of ribbon into \(\frac{1}{2}\)-foot pieces.
3-Step Detective Protocol for Any Problem
1 Circle Numbers & Signs Look for negatives, decimals, or fractions.
2 Underline Action Clue Are items combining, dropping, grouping, or splitting?
3 Set Up the Expression Match the action to \(+\), \(-\), \(\times\), or \(\div\).
Detective Worked Example (Read & Study)
Model
Problem: A scuba diver starts at -14.5 meters below sea level. During her dive, she descends another 8.25 meters. What is her new depth?
Step 1: The Values Starting: -14.5 m
Change: -8.25 m (down)
Step 2: The Clue "Descends another" means going further down. We combine or add the negative distance.
Step 3: Solution \(-14.5 + (-8.25) = \mathbf{-22.75}\)
Answer: \(-22.75\text{ meters}\)
Page 1 of 3 • Rational Operation Detectives • Keep this page handy as a reference!
Part 1: Operation Sorting
Clue Hunt & Operation Match
Student Practice
Page 2 of 3
Directions: Read each word problem. Underline the rational numbers and circle the action clue. Fill in the bubble for the matching operation, then write the math expression.
1 Context: Money & Bank Account
Rational Type: Decimals
Devon’s bank account was overdrawn with a balance of -$24.75. On Friday, he deposited $60.00 into his account. What is Devon’s new account balance?
Operation:
+ (Add) − (Subtract) × (Multiply) ÷ (Divide)
Expression:
2 Context: Weather & Temperature
Rational Type: Signed Decimals
At 6:00 AM, the temperature was -5.8°F. By noon, the temperature rose to 14.2°F. What was the difference between the noon and morning temperatures?
Operation:
+ (Add) − (Subtract) × (Multiply) ÷ (Divide)
Expression:
3 Context: Baking & Fractions
Rational Type: Fractions
A cookie recipe uses \(\frac{3}{4}\) cup of brown sugar for one batch. Marcus needs to make \(2\frac{1}{2}\) batches for the bake sale. How much brown sugar will Marcus need in total?
Operation:
+ (Add) − (Subtract) × (Multiply) ÷ (Divide)
Expression:
4 Context: Woodworking & Measurement
Rational Type: Mixed Numbers
Mr. Alvarez has a pine board that is \(7\frac{1}{2}\) feet long. He wants to cut it into equal shelves that are each \(1\frac{1}{4}\) feet long. How many shelves can he make?
Operation:
+ (Add) − (Subtract) × (Multiply) ÷ (Divide)
Expression:
Detective Hint: Check your 4 answers above. Did you use each of the 4 operations (+, −, ×, ÷) exactly once?
Yes Not Yet
Page 2 of 3 • Rational Operation Detectives • Turn to page 3 for guided solving
Part 2: Step-by-Step Solving
Scaffolded Problem Solving
Student Practice
Page 3 of 3
Follow the guided boxes to solve each problem from start to finish.
A Problem A: Elevation & Decimals
Scaffolded
A research drone is flying at an altitude of 185.5 meters above sea level. Due to high winds, it descends at a steady rate of 12.3 meters every minute. How many total meters did the drone descend after 4.5 minutes?
Step 1: Identify Key Numbers & Action
Rate per minute:
Number of minutes:
Action clue word:
Step 2: Choose Operation
What action is happening?
\(+\) \(-\) \(\times\) \(\div\)
Step 3: Set Up & Calculate
Final Answer:
B Problem B: Fractions & Sharing
Scaffolded
Coach Vance has a \(5\frac{1}{4}\) gallon cooler of water for soccer practice. Each player’s refill bottle holds \(\frac{3}{8}\) gallon. How many full bottles can Coach Vance fill?
Step 1: Identify Key Numbers & Action
Total amount:
Size of each part:
Action clue word:
Step 2: Choose Operation
What action is happening?
\(+\) \(-\) \(\times\) \(\div\)
Step 3: Set Up & Calculate
Final Answer:
Detective Self-Check (How confident do you feel?)
🟢 Master Detective I can spot clue words easily!
🟡 Detective in Training I need the chart to help me.
🟠 Need Clue Support I want to practice with a teacher.
Page 3 of 3 • Rational Operation Detectives • Excellent job decoding operations!
Rational Detectives Answer Key
Teacher Reference & Intervention Guide
Rational Detectives Answer Key
Full solutions, expression setups, and IEP co-teaching intervention notes.
Document Type Answer Key • Page 1 of 2
IEP Instructional Focus: Emphasize identifying the relationship/action first before doing any math. Students with learning disabilities frequently fixate on the numbers and grab whatever operation feels familiar.
1 Devon's Bank Account (Addition)
Correct: Addition (+)
Expression & Answer: -24.75 + 60.00 = $35.25
Devon's new balance is $35.25.
Common Misconception & Tip:
Students see a negative balance and assume they must subtract. Remind them: "A deposit always moves up toward the positive."
2 Morning & Noon Temperatures (Subtraction)
Correct: Subtraction (−)
Expression & Answer: 14.2 - (-5.8) = 14.2 + 5.8 = 20.0°F
The temperature difference is 20.0°F.
Common Misconception & Tip:
Students often compute \(14.2 - 5.8 = 8.4^\circ\text{F}\). Prompt with a thermometer: "From -5.8 up to 0 is 5.8 degrees, then 0 to 14.2 is another 14.2 degrees."
3 Marcus's Brown Sugar Batches (Multiplication)
Correct: Multiplication (×)
Expression & Answer: \(\frac{3}{4} \times 2\frac{1}{2} = \frac{3}{4} \times \frac{5}{2} = \frac{15}{8} = 1\frac{7}{8}\text{ cups}\)
Total needed: \(1\frac{7}{8}\) cups (or 1.875 cups).
Common Misconception & Tip:
The word "in total" prompts many students to add. Point out: "We have multiple equal batches—repeated addition means multiplication!"
4 Pine Board Shelves (Division)
Correct: Division (÷)
Expression & Answer: \(7\frac{1}{2} \div 1\frac{1}{4} = \frac{15}{2} \div \frac{5}{4} = \frac{15}{2} \times \frac{4}{5} = \mathbf{6}\)
Mr. Alvarez can make 6 shelves.
Common Misconception & Tip:
Students may invert the wrong fraction or divide in reverse order. Reinforce the formula: \(\text{Total Length} \div \text{Piece Length} = \text{Pieces}\).
Sorting Verification: The 4 problems on student page 2 map 1-to-1 to each operation: #1 = Addition, #2 = Subtraction, #3 = Multiplication, #4 = Division.
Page 1 of 2 • Teacher Answer Key • Rational Operation Detectives
Teacher Solutions & Strategies
Part 2 Solutions & Differentiation Plan
