Integer Medics Slides
Integer Medics
Order of Operations Diagnostic Lab
"Healing broken math, one step at a time."
The Parentheses Puzzle
Patient A
(-4)2
What does this mean?
Patient B
-42
What does this mean?
Are these results the same? Why or why not?
Grand Rounds: Expert Walkthrough
Math with Mr. J
Embedded media
Look for [3:50]
Watch closely how Mr. J handles Multiplication and Division when they appear together.
Funnel Shape
Notice how the problem gets smaller at each step, like a medical funnel.
The "Same Level" Rule
"Multiplication and division are on the same level so to speak, so we solve from left to right."
— Mr. J
Why doesn't Multiplication always come first?
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Left to Right
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Order of Appearance
Mission: Error Analysis Doctor
1
Review 5 "Patient Files" (Math Problems).
2
Some patients are "sick" (they have an error). Use your diagnostic skills to find it.
3
Circle the error and perform corrective surgery (solve it correctly).
Beware of:
- The Multiplication vs. Division trap.
- The (-3)2 vs. -32 sign error.
- Addition before Multiplication.
Post-Op Debrief
Think about the errors you found. Which one do you think is the most common among students?
Error Analysis Doctor Worksheet
Integer Medics
Order of Operations Diagnostic Lab
RESIDENT DOCTOR:
DATE:
Mission: Review each "Patient File" (math problem). If the problem is healthy, write "CLEAN BILL OF HEALTH". If the problem is "sick" (contains an error), circle the mistake and perform "CORRECTIVE SURGERY" in the workspace below.
Part 1: Initial Triage (Warm-up)
1. Solve: \((-4)^2\)
2. Solve: \(-4^2\)
Doctor's Observation: Why are these two results different? Explain the role of parentheses here.
Part 2: The Clinic (Error Analysis)
PATIENT #01 Minor Symptoms
\(12 + 6 \div (-3) \times 2\)
\(12 + (-2) \times 2\)
\(12 + (-4)\)
\(= 8\)
Doctor's Diagnosis (Errors?)
Corrective Surgery (Work Area)
PATIENT #02 Critical Condition
\(40 \div (-4) \times 5\)
\(40 \div (-20)\)
\(= -2\)
Doctor's Diagnosis (Errors?)
Corrective Surgery (Work Area)
PATIENT #03 Critical Condition
\(10 - 3^2 + 5\)
\(10 - 9 + 5\)
\(1 + 5\)
\(= 6\)
Doctor's Diagnosis (Errors?)
Corrective Surgery (Work Area)
PATIENT #04 Stable
\(2 + 4 \times (-5 + 2)\)
\(2 + 4 \times (-3)\)
\(2 + (-12)\)
\(= -10\)
Doctor's Diagnosis (Errors?)
Corrective Surgery (Work Area)
PATIENT #05 Critical Condition
\((-6) + 2 \times 4\)
\((-4) \times 4\)
\(= -16\)
Doctor's Diagnosis (Errors?)
Corrective Surgery (Work Area)
Post-Op Debrief
In your opinion, which of these patients had the most common mistake students make? Why do you think that error happens so often?
Error Analysis Doctor Answer Key
Answer Key
Integer Medics Clinic Guide
TEACHER VERSION
Part 1: Initial Triage
1. Solve: \((-4)^2\)
\(16\)
Explanation: \((-4) \times (-4) = 16\). The negative is squared.
2. Solve: \(-4^2\)
\(-16\)
Explanation: \(-(4 \times 4) = -16\). Only the 4 is squared; the negative is applied after.
Part 2: Clinical Findings
Patient #01: CLEAN BILL OF HEALTH
Diagnosis: Steps were performed correctly following PEMDAS/GEMS.
Step 1: Division (\(6 \div -3 = -2\))
Step 2: Multiplication (\(-2 \times 2 = -4\))
Step 3: Addition (\(12 + -4 = 8\))
Patient #02: SICK (Operation Order Error)
The Error: The student performed multiplication before division. They are on the same level and must be solved Left to Right.
Corrective Surgery:
\(40 \div (-4) \times 5\)
\(\mathbf{-10} \times 5\)
\(= \mathbf{-50}\)
Patient #03: SICK (Wait, actually Healthy!)
Diagnosis: This problem was solved correctly. \(3^2\) is 9, and the subtraction stays.
\(10 - 3^2 + 5\)
\(10 - 9 + 5 = 1 + 5 = 6\)
CLEAN BILL OF HEALTH
*Note: If a student thought this was sick, they likely confused \(-3^2\) with \((-3)^2\).
Patient #04: CLEAN BILL OF HEALTH
Diagnosis: Handled parentheses correctly, then multiplication, then addition.
\(2 + 4 \times (-3)\)
\(2 + (-12) = -10\)
Patient #05: SICK (Precedence Error)
The Error: The student performed addition \((-6) + 2\) before the multiplication \(2 \times 4\). Multiplication must happen first.
Corrective Surgery:
\((-6) + \mathbf{8}\)
\(= \mathbf{2}\)
Common Pitfalls to Watch For
- • Students often think "Multiplication before Division" is a hard rule because 'M' comes before 'D' in PEMDAS.
- • Negative signs attached to exponents are the #1 cause of calculation errors in Algebra 1 and Pre-Algebra.
- • Encourage students to use the "Funnel" method shown in the video to keep their work organized.
