Independent Challenges & Error Detective
Target Time: 25 Minutes
Level 2: Multi-Step Challenges (Watch for Exponents & Left-to-Right Rules!)
Funnel down line by line
Problem 4 Exponent First
\( 20 - 2 \times 3^2 \)
Hint: \( 3^2 = 3 \times 3 \)
Answer:
Problem 5 TRAP ALERT: Left-to-Right!
\( 18 \div 3 \times 2 \)
Do NOT do \( 3 \times 2 \) first! Go left to right.
Answer:
Problem 6 Grouping & Division
\( 8 + (15 - 3) \div 4 \)
Show funnel steps below:
Answer:
Problem 7 3 Operations
\( 5 \times (2 + 4) - 10 \)
Show funnel steps below:
Answer:
Level 3: Error Detective • Find & Fix the Mistake
Each student below got the wrong answer!
Case A: Jayden's Work Wrong Answer: 4
\( 14 - 8 + 2 \)
\( \rightarrow 14 - 10 = \mathbf{4} \) ❌
1. What mistake did Jayden make?
2. Correct funnel solution:
Case B: Maya's Work Wrong Answer: 14
\( 2 + 3 \times 4 \)
\( \rightarrow 5 \times 4 = \mathbf{20} \) ❌
1. What mistake did Maya make?
2. Correct funnel solution:
Self-Check Checklist:
Underlined 1 step at a time Solved M/D from Left to Right Solved A/S from Left to Right
How ready do you feel for the Exit Ticket?
1: Need Help 2: Getting There 3: Confident 4: Master!
Teacher prompt: "The small exponent tells you how many times to repeat the base. Write out the repeated multiplication first before solving!"
Misconception 3
Mental Juggling (No Funnel)
Student tries to hold numbers in memory and writes only the final number.
Teacher prompt: "Underline ONE piece only. Drop the rest down like an anchor. If I don't see the inverted triangle, the mission isn't valid!"
Grade 6 Intervention Module: Order of Operations Page 1 of 2 • Solutions on Next Page →
Step-by-Step Solutions & Actionable Post-Assessment Rubric
Teacher Reference
Packet Page 1 Solutions: Guided Try & Level 1 Foundation
Guided Fill-In
\( 20 - 4 \times (1 + 2) \)
\(= 20 - 4 \times \mathbf{3} \)
\(= 20 - \mathbf{12} \)
\(= \mathbf{8} \)
Problem 1
\( 12 + \underline{4 \times 3} \)
\(= \underline{12 + 12} \)
\(= \mathbf{24} \)
Multiplication first.
Problem 2
\( 24 - \underline{18 \div 2} \)
\(= \underline{24 - 9} \)
\(= \mathbf{15} \)
Division first.
Problem 3
\( \underline{(9 - 4)} \times 5 \)
\(= \underline{5 \times 5} \)
\(= \mathbf{25} \)
Grouping first.
Packet Page 2 Solutions: Level 2 Challenges & Error Detective
Problem 4
\( 20 - 2 \times \underline{3^2} \)
\(= 20 - \underline{2 \times 9} \)
\(= \underline{20 - 18} \)
\(= \mathbf{2} \)
Problem 5 (Trap!)
\( \underline{18 \div 3} \times 2 \)
\(= \underline{6 \times 2} \)
\(= \mathbf{12} \)
(Not 3!)
Problem 6
\( 8 + \underline{(15 - 3)} \div 4 \)
\(= 8 + \underline{12 \div 4} \)
\(= \underline{8 + 3} \)
\(= \mathbf{11} \)
Problem 7
\( 5 \times \underline{(2 + 4)} - 10 \)
\(= \underline{5 \times 6} - 10 \)
\(= \underline{30 - 10} \)
\(= \mathbf{20} \)
Case A (Jayden's Mistake): \( 14 - 8 + 2 \)
Error: Jayden added \( 8 + 2 = 10 \) first because of the "A before S" misconception. Addition and subtraction have equal priority and must be solved left to right.
Correct: \( \underline{14 - 8} + 2 = 6 + 2 = \mathbf{8} \)
Case B (Maya's Mistake): \( 2 + 3 \times 4 \)
Error: Maya moved strictly left to right, adding \( 2 + 3 = 5 \) before multiplying. Multiplication has higher priority than addition.
Correct: \( 2 + \underline{3 \times 4} = 2 + 12 = \mathbf{14} \)
Exit Ticket Answer Key (2 Points Each / 6 Total)
Q1: Grouping First
\( 6 \times \underline{(9 - 5)} \)
\(= 6 \times 4 = \mathbf{24} \)
1 pt for step, 1 pt for answer.
Q2: Left-to-Right Tiebreaker
\( \underline{24 \div 6} \times 3 \)
\(= 4 \times 3 = \mathbf{12} \)
Trap check: \( 24 \div 18 \) = 0 pts.
Q3: Exponent & Subtract
\( 30 - \underline{2^3} \times 2 \)
\(= 30 - \underline{8 \times 2} = 30 - 16 = \mathbf{14} \)
\( 2^3 = 8 \) (not 6).
Actionable Post-Lesson Grouping
Score 5-6 (Mastery): Ready for Grade 6 core curriculum. Extension: nested brackets \( \{ [ \ ( \ ) \ ] \} \) and variables.
Score 3-4 (Approaching): Schedule 5-minute warm-up check on Left-to-Right tiebreakers. Provide highlighters for operation tiers.
Score 0-2 (Intensive): Small-group manipulative intervention using operation hierarchy cards and two-step index card strips.
Operation Rescue Facilitator Guide Grade 6 Math Intervention • CCSS 6.EE.A.1
