#4
74
− 38
#5
76
− 32
#6
62
#7
93
− 47
#8
38
#9
81
− 56
#10
59
#11
32
#12
98
− 63
#13
62
− 37
#14
23
#15
47
#16
85
− 51
Student Growth & Mastery Summary Pre-Test vs. Post-Test
Baseline Pre-Test ____ / 16
Final Post-Test ____ / 16
Net Growth + ____ pts
Add (No Regroup) ____ / 4
Add (Regroup) ____ / 4
Sub (No Regroup) ____ / 4
Sub (Regroup) ____ / 4
Mastery Standard: ≥ 13 / 16 (80%+) Status: [ ] Mastered [ ] Targeted Support Needed
Error Pattern 1: Smaller-From-Larger Reversal (Subtraction) High Frequency
Student Work:
62 − 37 = 35
(Does 7 − 2 = 5)
Underlying Misconception: Student believes subtraction is commutative ("always subtract the smaller digit from the larger"), ignoring the whole-part structure.
Targeted Protocol: Use base-ten rods and unit cubes on a place value mat. Ask: "You have 2 cubes. Can you hand me 7? Where can you get more ones?" Practice unbundling 1 ten into 10 ones before computing.
Error Pattern 2: Forgotten Regrouped Ten (Addition) Memory & Routine
Student Work:
48 + 37 = 75
(Writes 5, forgets 10)
Underlying Misconception: Student computes 8 + 7 = 15, writes 5 in ones place, but loses track of the 1 ten bundle when shifting to the tens column.
Targeted Protocol: Teach the "Chimney Ten" visual box directly above the tens column. Model expanded addition: (40 + 8) + (30 + 7) = 70 + 15 = 85.
Error Pattern 3: Over-Regrouping (Non-Regrouping Items) Overgeneralization
Student Work:
42 + 25 = 77
(Carries 1 ten anyway)
Underlying Misconception: Student treats regrouping as an automatic procedure rather than a conditional necessity based on reaching 10 ones.
Targeted Protocol: Sorting sorts! Before computing, student categorizes cards into "Needs Regrouping" vs. "No Regrouping Needed" without calculating. Use rule: "Sum < 10? Leave tens alone!"
Error Pattern 4: Cognitive Overload & Sign Slippage Working Memory
Student Work:
79 − 43 = 122
(Adds on minus sign)
Underlying Misconception: High cognitive demand of two-digit calculation causes student to default to familiar addition routine despite the minus sign.
Targeted Protocol: Establish the 2-second pre-flight routine: "Circle the sign with highlighter. Say 'I am adding' or 'I am subtracting' before touching a number."
Data-Based Decision Rules (RTI / MTSS Intervention Pacing)
3 Consecutive Probes ≥ 80%
Mastery Achieved
Fade intensive support. Transition to bi-weekly maintenance checks and advance to 3-digit operations.
Flat Progress (Below Goal)
Adjust Intervention Intensity
If 3 probes remain flat, modify strategy: increase manipulative practice, reduce group size, or add 10 min/week.
Regrouping Only Below 50%
Target Place Value Concept
Isolate regrouping concept using concrete-representational-abstract (CRA) sequence with physical base-ten blocks.
Double-Digit Progress Monitoring • Error Diagnostics Page 2 of 2
