Square Sleuths Slides
Square Sleuths
Solving the Case of the Faulty Quadratics
What's the Mistake?
Evidence #001
Solve: \(x^2 + 6x = -5\)
\(x^2 + 6x + 9 = -5\)
\((x + 3)^2 = -5\)
\(x + 3 = \pm \sqrt{-5}\)
Spot the "Glaring Error"
- Look closely at the second line.
- Is the "balance" maintained?
The Expert Witness
Justin explains the "Breaking Rules" segment (0:00 - 1:50)
WATCH
Embedded media
Key Quote
"You can't introduce a new operation on one side WITHOUT also doing it to the other side."
Listen For
- • Expression vs. Equation
- • The Balance Rule
- • The +9 Correction
Your Mission
1
Examine the Cases
You have 5 solved problems on your worksheet. Some are clean; some are crimes against math.
2
Identify the Error
If there's a mistake, circle it and explain what went wrong.
3
Fix the File
Re-solve the problem correctly in the space provided.
Detective's Warning
Watch out for the "Sneaky Three": Sign Errors, Balancing Blunders, and Square Root Slips.
Most Wanted Errors
CRITICAL
The One-Sided Add
Adding the constant to the left side but forgetting to add it to the right side.
COMMON
The Binomial Flip
Using the wrong sign in the binomial. Example: \(x^2 - 6x + 9\) becomes \((x+3)^2\).
FREQUENT
The Negative Forget
Forgetting that a square root gives both positive and negative results (\(\pm\)).
Debrief
"Which mistake did you see most often?"
"Which one is the easiest to accidentally make?"
"What strategy can you use to double-check your work?"
Note to Self
Write one specific tip on your worksheet to your "Future Self" about how to avoid your most common mistake.
Case Closed.
Square Sleuths Worksheet
Square Sleuths
Case File: Completing the Square Errors
Agent Name:
Date:
Detective Instructions:
Analyze the solved equations below. Some contain a single mathematical "crime" (error). If you find an error, circle it, describe the mistake, and re-solve the problem correctly. If the work is correct, write "Case Solved" in the description.
CASE #101 Evidence File
Solve: \(x^2 + 8x = 20\)
\(x^2 + 8x + 16 = 20\)
\((x + 4)^2 = 20\)
\(x + 4 = \pm\sqrt{20}\)
\(x = -4 \pm 2\sqrt{5}\)
Detective's Notes:
Corrective Action:
CASE #102 Evidence File
Solve: \(x^2 - 10x = -9\)
\(x^2 - 10x + 25 = -9 + 25\)
\((x - 5)^2 = 16\)
\(x - 5 = 4\)
\(x = 9\)
Detective's Notes:
Corrective Action:
CASE #103 Evidence File
Solve: \(x^2 + 4x = 5\)
\(x^2 + 4x + 4 = 5 + 4\)
\((x + 2)^2 = 9\)
\(x + 2 = \pm 3\)
\(x = 1, -5\)
Detective's Notes:
Corrective Action:
CASE #104 Evidence File
Solve: \(x^2 - 6x = 7\)
\(x^2 - 6x + 9 = 7 + 9\)
\((x + 3)^2 = 16\)
\(x + 3 = \pm 4\)
\(x = 1, -7\)
Detective's Notes:
Corrective Action:
CASE #105 Evidence File
Solve: \(x^2 + 12 = 8x\)
\(x^2 - 8x = -12\)
\(x^2 - 8x + 16 = -12 + 16\)
\((x - 4)^2 = 4\)
\(x - 4 = \pm 2 \rightarrow x = 6, 2\)
Detective's Notes:
Corrective Action:
NOTE TO SELF
Reflect on the errors you found today. What is the one thing you want to remind your "Future Self" to avoid when completing the square?
Square Sleuths Teacher Guide
Teacher Facilitation Guide
Square Sleuths • 9th Grade Algebra
Duration: 45-50 min
Learning Objective
Students will analyze and correct common misconceptions in completing the square, specifically focusing on balancing equations, sign errors in binomials, and square root operations.
Materials Needed
- • Square Sleuths Slide Deck
- • Square Sleuths Student Worksheet
- • Video: "Solving Equations by Completing the Square"
Lesson Timeline
0-5 min
Hook: The Evidence File
Display Slide 2. Show the solved problem with the glaring error. Ask students to talk to a partner: "What happened to the balance?" Avoid giving the answer immediately; let them find the missing +9 on the right side.
5-10 min
Expert Witness: Video Segment
Play the video from 0:00 to 1:50. Use Slide 3 to set the context. Focus on the narrator's explanation of why "breaking rules" (adding terms to expressions) is fixed once it becomes an equation (balancing both sides).
10-30 min
The Mission: Find the Error
Students work individually or in pairs on the worksheet. Circulate and listen for misconceptions. Are they catching the sign error in Case #104? Are they recognizing the correct work in Case #103 and Case #105?
30-40 min
The Debrief: Discussion
Use Slide 6 to guide the conversation. Ask: "Which crime was the most common across the worksheet?" Focus on why these errors happen (e.g., forgetting \(\pm\) is usually due to rushing to the answer).
40-45 min
Closing: Note to Self
Students complete the "Note to Self" section on their worksheet. This is their personal metacognitive anchor for future homework/tests.
Answer Key: Square Sleuths Cases
Case #101: The Balancing Blunder
Error: 16 was added to the left side, but not the right side.
Correct: \((x+4)^2 = 20 + 16 \rightarrow (x+4)^2 = 36 \rightarrow x+4 = \pm 6 \rightarrow x = 2, -10\)
Case #102: The Square Root Slip
Error: Forgot the \(\pm\) symbol when taking the square root of 16.
Correct: \(x - 5 = \pm 4 \rightarrow x = 5 \pm 4 \rightarrow x = 9, 1\)
Case #103: CASE SOLVED
The work is correct as shown.
Case #104: The Binomial Flip
Error: Sign error in binomial factoring. \(x^2 - 6x + 9\) factors to \((x - 3)^2\), not \((x + 3)^2\).
