Word Problem Roadmap ReferenceCase File: Fraction Action Evidence Analysis & Decoding Guide Ref No: 027-FRACT The Investigator's Protocol 1 Inspect the Evidence Read the problem carefully. Highlight the numbers and underline the question. What exactly are you trying to solve? 2 Identify the Unknown Define what your answer represents. Is it a total amount? A remaining piece? A specific share of a group? 3 Gather the Clues Look for "Operation Keywords." Multi-step problems often hide clues like "half of what remains" or "the total of both shares." 4 Map the Mission Draw a bar model or write an equation. For multi-step problems, you might need two equations to find the final answer. Decoding the Keywords ADDITION (+) Combined Together Sum Total SUBTRACTION (−) Left over Difference Remaining How much more MULTIPLICATION (×) "OF" (fraction of a set) Times Product Each / Every Confidential Pro-Tip: In multi-step fraction problems, "of the remainder" or "of what was left" means you MUST subtract the first amount before multiplying by the next fraction! Property of Detective Math Academy Operational Guide: FRACTION-01
Case Breakdown OrganizerCase Breakdown Organizer Operational Protocol: Fraction Forensics Investigator: Date: The Transcript (Word Problem) Key Evidence (Numbers & Fractions) The Objective (What are we solving for?) Visual Evidence (Bar Model or Diagram) Decoding Chamber (Show Your Work) Step 1: First Operation Step 2: Second Operation The Final Verdict Case Solution with Units
Fraction Files WorksheetUnsolved Cases: Fraction Files Status: Active Investigation • Classification: Multi-Step Agent: Date: Mission Briefing Apply your investigator's protocol to decode these multi-step mysteries. Show all your "evidence" (calculations) in the work areas provided. LEVEL 1 Case #101: The Baker's Delivery "I started with 48 muffins," the baker reported. "First, I delivered \(\frac{1}{3}\) of them to the cafe. Then, I delivered 12 more muffins to the school. How many muffins are left in my van?" Work Space (Step 1) Work Space (Step 2) Final Verdict: LEVEL 2 Case #205: The Garden Plot "My garden is 60 square feet," the gardener said. "I used \(\frac{2}{5}\) of the garden for tomatoes and \(\frac{1}{4}\) of the garden for peppers. The rest is for flowers. How many square feet of the garden are for flowers?" Work Space (Step 1) Work Space (Step 2) Final Verdict: LEVEL 3 Case #309: The Secret Inheritance "There was $120 in the safe," the witness stated. "The first heir took \(\frac{1}{4}\) of the money. Then, the second heir took \(\frac{1}{3}\) of the remaining money. How much money is still in the safe?" Work Space (Step 1) Work Space (Step 2) Final Verdict: Fraction Detective HQ Case File: WORD-PROB-01
Fraction Action SlidesOperation: Fraction Action Case File: Decoding Word Problems Mastering Multi-Step Fraction Challenges Detective Math Academy • Level 1 Clearance The Investigator's Protocol 1 Inspect Evidence Highlight fractions and underline the final question. 2 Identify the Goal Is it a "fraction of a total" or a "fraction of a remainder"? 3 Map the Mission Sketch a bar model to visualize the hidden parts. 4 Execute & Verify Solve step-by-step and check if your answer is reasonable. Critical Clue: The Wording Standard Fraction "Sarah has 20 apples. She gives \(\frac{1}{4}\) to Tim." Calculation: \(\frac{1}{4} \times 20\) Fraction of Remainder "Sarah has 20 apples. She gives 4 to Tim, then \(\frac{1}{4}\) of what remains to Ben." Step 1: \(20 - 4 = 16\) Step 2: \(\frac{1}{4} \times 16\) Always ask: "Is this fraction of the ORIGINAL TOTAL or the NEW AMOUNT?" Live Training: Case #042 Status: In Progress "The local library has 120 books on display. \(\frac{2}{5}\) are Mystery. 20 of the remaining books are Biographies. How many books are NOT Mystery or Biographies?" Investigation Step 1: Find the Mystery books: \(\frac{2}{5}\) of 120 Investigation Step 2: Think: Subtract them from the total... Investigation Step 3: Then subtract the biographies. You Are Ready for the Field Open your Fraction Files Worksheet. Use your Roadmap to decode the keywords and show your evidence in every work area. Look for Keywords Draw Your Models Double Check Units
Fraction Files Answer KeyAnswer Key: Fraction Files Classification: Top Secret • Teacher Resource Only Case File: WORD-PROB-01-KEY Level 1 Solution Case #101: The Baker's Delivery Step 1: The First Delivery \(\frac{1}{3} \times 48 = 16\) muffins Operation: Multiplication of fraction by whole number. Step 2: The Final Count \(48 - 16 = 32\) (after cafe) \(32 - 12 = 20\) muffins Operation: Successive subtraction. CORRECT VERDICT: 20 Muffins Level 2 Solution Case #205: The Garden Plot Step 1: Calculate Vegetable Areas Tomatoes: \(\frac{2}{5} \times 60 = 24\) sq ft Peppers: \(\frac{1}{4} \times 60 = 15\) sq ft Operation: Multiple fractions of the same total. Step 2: Find the Difference Total used: \(24 + 15 = 39\) sq ft Flowers: \(60 - 39 = 21\) sq ft Operation: Subtraction from initial total. CORRECT VERDICT: 21 sq ft Level 3 Solution Case #309: The Secret Inheritance Step 1: First Heir's Share \(\frac{1}{4} \times 120 = \$30\) \(120 - 30 = \$90\) (The Remainder) Key point: Must find remainder before step 2. Step 2: Second Heir's Share \(\frac{1}{3} \times 90 = \$30\) \(90 - 30 = \$60\) Operation: Fraction of the remaining amount. CORRECT VERDICT: $60 Teacher Note: Misconception Alert In Case #309, students commonly try to find \(\frac{1}{3}\) of the original $120. Remind them that the phrase "of the remaining money" act as a redirect—they must perform a subtraction operation before they can move to the next fraction calculation.
