Two Step Takedown Slides
2
Math Investigators • Grade 5
Problem-Solving Strategies
Model • Represent • Solve
Two-Step Takedown
Uncover the hidden question, build visual bar models, and write bulletproof equations to crack complex problems.
Find Hidden Clues
Draw Tape Diagrams
Write Multi-Step Math
Concept Briefing • The Big Idea
01 / 07
Every Two-Step Problem Has a Hidden Question
You can't jump straight to the finish line! Before you can answer the problem's final question, there is an invisible question you must answer first.
STEP 1: The Hidden Clue
What must you know first?
Find the missing total, difference, or group size needed before solving the final goal.
STEP 2: The Final Mission
Answer what was asked!
Take your answer from Step 1 and use it with the remaining information to reach the final answer.
Pro Tip: If you only do one math calculation, you stopped halfway through!
The Toolkit • The 4-Step Blueprint
02 / 07
How Problem Solvers Attack Every Problem
1
Read & Hunt
Circle given numbers and underline the final question.
Clue Hunt
2
Model It
Draw a bar model or tape diagram to see the parts and whole.
Tape Diagram
3
Write Math
Form equations for Step 1 and Step 2 using letters for unknowns.
Equation
4
Solve & Check
Compute accurately and ask: does this answer make sense?
Sense Check
Consistent diagrams build problem-solving confidence! Next: Let's investigate Case File #1 →
Case File 01 • Multiplication → Subtraction
03 / 07
The Situation
Marcus bought 6 packs of mechanical pencils with 8 pencils in each pack. He gave 15 pencils to his classmates. How many pencils does Marcus have left?
Visual Bar Model
Step 1: Total Pencils Bought (6 equal groups of 8)
8
8
8
8
8
8
Total = 48 pencils
Step 2: Remove Given Pencils
Gave 15
Left: ?
Step 1: Hidden Question
How many pencils did Marcus buy altogether?
6 × 8 = 48 pencils
Step 2: Final Question
How many pencils are left after giving away 15?
48 - 15 = 33 pencils left
Single Equation: (6 × 8) - 15 = 33
Notice how parentheses group the first step: (6 × 8) comes before subtracting!
Case File 02 • Addition → Division
04 / 07
The Situation
The 5th-grade baking club baked 84 chocolate cookies and 60 sugar cookies. They packed all cookies equally into 6 gift boxes. How many cookies were in each box?
Visual Bar Model
Step 1: Combine All Cookies
84 Chocolate
60 Sugar
Total Cookies = 144
Step 2: Split 144 Cookies into 6 Boxes
?
?
?
?
?
?
Step 1: Hidden Question
How many cookies were baked in total?
84 + 60 = 144 cookies
Step 2: Final Question
How many cookies are placed in each of the 6 boxes?
144 ÷ 6 = 24 cookies per box
Single Equation: (84 + 60) ÷ 6 = 24
Key Observation: You must add first to find the total BEFORE dividing among the boxes!
Investigator Alert • Common Traps to Avoid
05 / 07
Avoid the 3 Biggest Two-Step Traps!
The "One-and-Done"
Doing only the first calculation and writing it down as the final answer.
Fix: Check if your answer answered the actual prompt question!
Wrong Order
Multiplying or dividing before finding the needed sum or difference.
Fix: Use parentheses ( ) to force Step 1 to happen first!
Number Grabbing
Picking the first two numbers in the story and randomly adding them together.
Fix: Sketch a quick bar model before writing any numbers!
Always ask: "Did I find the hidden step, or did I stop at step one?" • Step 1 ≠ Final Answer
Team Challenge • Guided Investigation
06 / 07
Mission Prompt
Maya had $75 saved. She earned $45 mowing lawns. Then, she bought 3 video games that cost $25 each. How much money does Maya have remaining?
Question 1
What is the total money Maya had?
$75 + $45 = $120 total
Question 2
How much did Maya spend?
3 × $25 = $75 spent
Final Result
How much money is left?
$120 - $75 = $45 remaining
Can you write this as one grand equation? ($75 + $45) - (3 × $25) = $45
Mission Debrief • Investigator Checklist
07 / 07
Ready for the Independent Worksheet?
✓
Identify the Hidden Step
Ask yourself: "What do I have to calculate before I can answer the question?"
✓
Sketch a Quick Bar Model
Tape diagrams show whether parts are being combined, multiplied, or split.
✓
Show Both Equations Clearly
Label Step 1 and Step 2 so your mathematical thinking is crystal clear!
Grab your pencil • You are ready to crack every case! Detective Mode: Active
Two Step Takedown Worksheet
Grade 5 Math • Operations & Problem Solving
Two-Step Takedown: Case File Worksheet
Identify the hidden question, sketch a bar model, and write equations to solve each case.
Name:
Date:
Score:
The 4-Step Plan: 1 Find Hidden Question • 2 Sketch Bar Model • 3 Write Equations • 4 Check & Label Units
CASE 01
The Book Fair Mystery
Multiplication → Subtraction
The 5th-grade class bought 7 boxes of chapter books for the school library. Each box contained 12 books. Before placing the books on shelves, they discovered that 16 books had torn covers and needed repairs. How many undamaged books were ready for the shelves?
Step 1: Write the Hidden Question:
Bar Model Representation (Label parts):
12
12
12
12
12
12
12
Total Books: [ ] Torn: 16 | Undamaged: ?
Step 1 Equation:
Step 2 Equation:
Final Answer:
CASE 02
Field Day Relay Teams
Addition → Division
At Field Day, there are 68 fifth graders and 52 fourth graders participating in the relay races. The coaches combine all students and divide them equally into 8 relay teams. How many students are on each relay team?
Draw Your Bar Model / Diagram:
Step 1 Equation (Hidden Step):
Step 2 Equation (Final Answer):
Final Answer:
Two-Step Takedown • Independent Practice Page 1 Turn over for Cases 03, 04, and the Detective Challenge →
Part 2
Advanced Investigations & Error Analysis
Student Name:
CASE 03
Art Room Clay Sculptures
Multiplication → Addition
Ms. Rivera bought 5 packs of red clay with 18 sticks in each pack. She also had a leftover bin with 35 sticks of blue clay. She needs a total of 150 sticks of clay for an art project. How many sticks of clay does she have in total right now?
Draw Your Bar Model:
Step 1 Equation:
Step 2 Equation:
Final Answer:
CASE 04
The Apple Orchard Delivery
Two Step Takedown Answer Key
Teacher Reference • Grade 5 Mathematics
Two-Step Takedown: Master Answer Key
Complete bar model representations, multi-step equations, and instructional coaching notes.
Curriculum Alignment CCSS.MATH.5.OA.A.1 • 5.NBT.B.5/6
Grading Rubric per Case: 1 pt: Hidden Question Identified • 1 pt: Accurate Bar Model • 1 pt: Equations Labeled • 1 pt: Correct Final Value & Units
CASE 01 KEY
The Book Fair Mystery (7 boxes × 12 books - 16 torn)
Answer: 68 undamaged books
Step 1 Hidden Question:
"How many books did the 5th-grade class buy in all?"
Bar Model Representation:
12
12
12
12
12
12
12
Total: 7 × 12 = 84 books 84 - 16 = 68
Step 1 Equation: 7 × 12 = 84 (total books)
Step 2 Equation: 84 - 16 = 68 (undamaged books)
Single Expression: (7 × 12) - 16 = 68
Common Misconception: Students often subtract 16 from 12 (impossible) or multiply 16 by 7. Ensure they see the 16 torn books come from the total collective stock.
CASE 02 KEY
Field Day Relay Teams (68 fifth + 52 fourth ÷ 8 teams)
Answer: 15 students per team
Step 1 Hidden Question:
"How many total students are participating in Field Day?"
Bar Model Representation:
68 (5th Grade)
52 (4th Grade)
15
15
15
15
15
15
15
15
Step 1 Equation: 68 + 52 = 120 (total students)
Step 2 Equation: 120 ÷ 8 = 15 (students per team)
Single Expression: (68 + 52) ÷ 8 = 15
Order of Operations Trap: Without parentheses, 68 + 52 ÷ 8 would divide 52 by 8 first (6.5), then add 68 = 74.5! Emphasize why the total must be grouped first.
Teacher Guide • Page 1 of 2 Solutions for Cases 03, 04, and Error Analysis on Page 2 →
Part 2 Key
Advanced Cases & Error Analysis Solutions
Teacher Scoring Guide
CASE 03 KEY
Art Room Clay Sculptures (5 packs × 18 + 35 blue)
Answer: 125 sticks of clay
Model & Hidden Step:
Hidden Q: "How many sticks of red clay were bought?"
5 packs × 18 = 90 red sticks
