Two Digit Probes Assessment Probe 1 • Form A
2-Digit Strategy Progress Check
Goal Target 80% (4/5)
Score ____ / 5
Student:
Date:
Setting: [ ] 1:1 [ ] Small Grp
Strategy Bank: Combine Tens & Ones Make a Ten / Friendly # Think Addition (Distance) Number Line
1 43 + 35 =
Strategy used: [ ] Tens/Ones [ ] Make Ten [ ] Number Line [ ] Other
2 38 + 27 =
Strategy used: [ ] Make Ten [ ] Tens/Ones [ ] Number Line [ ] Other
3 68 − 25 =
Strategy used: [ ] Decompose Tens/Ones [ ] Number Line Back [ ] Other
4 73 − 48 =
Strategy used: [ ] Think Addition [ ] Count Up [ ] Compensation [ ] Other
5 54 + 39 =
Strategy used: [ ] Make Ten (+40 − 1) [ ] Tens/Ones [ ] Number Line [ ] Other
Scoring Rubric: 4: Independent & efficient strategy 3: Minor prompt needed 2: Model required 1: Counting all / standard only
Independence Level: [ 4 ] [ 3 ] [ 2 ] [ 1 ]
Probe 2 • Form B
2-Digit Strategy Progress Check
Goal Target 80% (4/5)
Score ____ / 5
Student:
Date:
Setting: [ ] 1:1 [ ] Small Grp
Strategy Bank: Combine Tens & Ones Make a Ten / Friendly # Think Addition (Distance) Number Line
1 52 + 36 =
Strategy used: [ ] Tens/Ones [ ] Make Ten [ ] Number Line [ ] Other
2 47 + 28 =
Strategy used: [ ] Make Ten [ ] Tens/Ones [ ] Number Line [ ] Other
3 76 − 32 =
Strategy used: [ ] Decompose Tens/Ones [ ] Number Line Back [ ] Other
4 82 − 59 =
Strategy used: [ ] Think Addition [ ] Count Up [ ] Compensation [ ] Other
5 63 − 27 =
Strategy used: [ ] Think Addition [ ] Decompose Tens/Ones [ ] Constant Diff (+3) [ ] Other
Scoring Rubric: 4: Independent & efficient strategy 3: Minor prompt needed 2: Model required 1: Counting all / standard only
Independence Level: [ 4 ] [ 3 ] [ 2 ] [ 1 ]
Probe 3 • Form C
2-Digit Strategy Progress Check
Goal Target 80% (4/5)
Score ____ / 5
Student:
Date:
Setting: [ ] 1:1 [ ] Small Grp
Strategy Bank: Combine Tens & Ones Make a Ten / Friendly # Think Addition (Distance) Number Line
1 34 + 45 =
Strategy used: [ ] Tens/Ones [ ] Make Ten [ ] Number Line [ ] Other
2 59 + 26 =
Strategy used: [ ] Make Ten (+1 − 1) [ ] Tens/Ones [ ] Number Line [ ] Other
3 87 − 43 =
Strategy used: [ ] Decompose Tens/Ones [ ] Number Line Back [ ] Other
4 64 − 38 =
Strategy used: [ ] Think Addition [ ] Count Up [ ] Compensation [ ] Other
5 46 + 38 =
Strategy used: [ ] Make Ten [ ] Tens/Ones [ ] Number Line [ ] Other
Scoring Rubric: 4: Independent & efficient strategy 3: Minor prompt needed 2: Model required 1: Counting all / standard only
Independence Level: [ 4 ] [ 3 ] [ 2 ] [ 1 ]
Probe 4 • Form D
2-Digit Strategy Progress Check
Goal Target 80% (4/5)
Score ____ / 5
Student:
Date:
Setting: [ ] 1:1 [ ] Small Grp
Strategy Bank: Combine Tens & Ones Make a Ten / Friendly # Think Addition (Distance) Number Line
1 61 + 27 =
Strategy used: [ ] Tens/Ones [ ] Make Ten [ ] Number Line [ ] Other
2 28 + 49 =
Strategy used: [ ] Make Ten (+1 − 1) [ ] Tens/Ones [ ] Number Line [ ] Other
3 79 − 36 =
Strategy used: [ ] Decompose Tens/Ones [ ] Number Line Back [ ] Other
4 91 − 67 =
Strategy used: [ ] Think Addition [ ] Count Up [ ] Compensation [ ] Other
5 75 − 39 =
Strategy used: [ ] Constant Diff (+1) [ ] Think Addition [ ] Tens/Ones [ ] Other
Scoring Rubric: 4: Independent & efficient strategy 3: Minor prompt needed 2: Model required 1: Counting all / standard only
Independence Level: [ 4 ] [ 3 ] [ 2 ] [ 1 ]
Probe 5 • Form E
2-Digit Strategy Progress Check
Goal Target 80% (4/5)
Score ____ / 5
Student:
Date:
Setting: [ ] 1:1 [ ] Small Grp
Strategy Bank: Combine Tens & Ones Make a Ten / Friendly # Think Addition (Distance) Number Line
1 44 + 33 =
Strategy used: [ ] Tens/Ones [ ] Make Ten [ ] Number Line [ ] Other
2 36 + 48 =
Strategy used: [ ] Make Ten (+2 − 2) [ ] Tens/Ones [ ] Number Line [ ] Other
3 95 − 51 =
Strategy used: [ ] Decompose Tens/Ones [ ] Number Line Back [ ] Other
4 85 − 58 =
Strategy used: [ ] Think Addition [ ] Count Up [ ] Compensation [ ] Other
5 57 + 29 =
Strategy used: [ ] Make Ten (+30 − 1) [ ] Tens/Ones [ ] Number Line [ ] Other
Scoring Rubric: 4: Independent & efficient strategy 3: Minor prompt needed 2: Model required 1: Counting all / standard only
Independence Level: [ 4 ] [ 3 ] [ 2 ] [ 1 ]
Strategy Probes Answer Key Teacher Master Guide
2-Digit Strategy Probes Answer Key
Probes 1 – 5 Scoring Guide Mastery Target: 80% (4/5)
IEP Goal: Given two 2-digit numbers, student will write the sum or difference by using a strategy based on place value, properties of operations, or the relationship between addition and subtraction (e.g., combining tens, make a ten, think addition) with 80% accuracy across 3 consecutive probes.
Strategy Independence & Quality Rubric
Level 4: Mastered
Selects & executes mental/visual strategy independently with clear, correct notation.
Level 3: Proficient
Uses strategy accurately with 1 verbal cue or minor self-corrected calculation slip.
Level 2: Emerging
Requires partial modeling, template prompt, or relies on tally/tick marks.
Level 1: Intensive
Counts all by ones, leaves blank, or standard algorithm with place value confusion.
P1 Probe 1 (Form A) • Exemplar Models & Solutions
Key for Student Probe 1
1. 43 + 35 = 78 Combine Tens & Ones
Primary Strategy: Tens: \(40 + 30 = 70\); Ones: \(3 + 5 = 8\); Sum: \(70 + 8 = 78\).
Alternative: Count on by tens from 43 (\(43 \to 53 \to 63 \to 73\)), then add 5 (\(73 + 5 = 78\)).
Ans: 78
2. 38 + 27 = 65 Make a Ten
Primary Strategy: Decompose 27 into \(2 + 25\). Make 40: \(38 + 2 = 40\); Add rest: \(40 + 25 = 65\).
Alternative: Partial sums: \(30 + 20 = 50\); \(8 + 7 = 15\); \(50 + 15 = 65\).
Ans: 65
3. 68 − 25 = 43 Decompose Subtrahend
Primary Strategy: Subtract tens first: \(68 - 20 = 48\); Subtract ones: \(48 - 5 = 43\).
Alternative: Place value split: \(60 - 20 = 40\); \(8 - 5 = 3\); \(40 + 3 = 43\).
Ans: 43
4. 73 − 48 = 25 Think Addition / Distance
Primary Strategy: Missing addend: \(48 + \text{?} = 73\). Jump \(48 + 2 = 50\); \(50 + 23 = 73\). Total: \(2 + 23 = 25\).
Alternative: Constant difference (+2 to both): \(75 - 50 = 25\).
Ans: 25
5. 54 + 39 = 93 Compensation / Friendly 40
Primary Strategy: Treat 39 as 40: \(54 + 40 = 94\); Adjust by subtracting 1: \(94 - 1 = 93\).
Alternative: Decompose 54 into \(53 + 1\); \(1 + 39 = 40\); \(53 + 40 = 93\).
Ans: 93
Two-Digit Operational Strategies • Progress Monitoring Answer Key Page 1 of 3
Answer Key • Probes 2 & 3
Teacher Reference Guide
P2 Probe 2 (Form B) Solutions & Models
All items 1 pt each
1. 52 + 36 = 88 Combine Tens/Ones: \(50 + 30 = 80\); \(2 + 6 = 8\); \(80 + 8 = 88\).
Ans: 88
2. 47 + 28 = 75 Make a Ten: \(47 + 3 = 50\); \(28 - 3 = 25\); \(50 + 25 = 75\). (Or \(60 + 15 = 75\)).
Ans: 75
3. 76 − 32 = 44 Decompose Subtrahend: \(76 - 30 = 46\); \(46 - 2 = 44\).
Ans: 44
4. 82 − 59 = 23 Think Addition: \(59 + 1 = 60\); \(60 + 22 = 82\); \(1 + 22 = 23\). (Or constant diff: \(83 - 60 = 23\)).
Ans: 23
5. 63 − 27 = 36 Think Addition: \(27 + 3 = 30\); \(30 + 33 = 63\); \(3 + 33 = 36\). (Or \(63 - 20 = 43\); \(43 - 7 = 36\)).
Ans: 36
P3 Probe 3 (Form C) Solutions & Models
All items 1 pt each
1. 34 + 45 = 79 Combine Tens/Ones: \(30 + 40 = 70\); \(4 + 5 = 9\); \(70 + 9 = 79\).
Ans: 79
2. 59 + 26 = 85 Make a Ten: \(59 + 1 = 60\); \(26 - 1 = 25\); \(60 + 25 = 85\).
Ans: 85
3. 87 − 43 = 44 Decompose Subtrahend: \(87 - 40 = 47\); \(47 - 3 = 44\).
Ans: 44
4. 64 − 38 = 26 Think Addition: \(38 + 2 = 40\); \(40 + 24 = 64\); \(2 + 24 = 26\). (Or constant diff: \(66 - 40 = 26\)).
Ans: 26
5. 46 + 38 = 84 Compensation: \(46 + 40 = 86\); \(86 - 2 = 84\). (Or \(46 + 4 = 50\); \(50 + 34 = 84\)).
Ans: 84
Qualitative Strategy Indicators to Note in Progress Log:
• Flexibility: Does student switch strategies based on numbers (e.g. 59 triggers "Make 60")?
• Representation: Does student record equations, jumps on open number line, or number bonds?
• Efficiency: Does student compute in chunks of tens rather than single increments?
• Self-Correction: Does student notice when an estimate does not match their calculated value?
Two-Digit Operational Strategies • Progress Monitoring Answer Key Page 2 of 3
Answer Key • Probes 4, 5 & Diagnostics
Teacher Reference Guide
P4 Probe 4 (Form D)
1. 61 + 27 = 88
Tens: \(60+20=80\); Ones: \(1+7=8\); \(80+8=88\).
2. 28 + 49 = 77
Make 50: \(49+1=50\); \(28-1=27\); \(50+27=77\).
3. 79 − 36 = 43
Decompose: \(79-30=49\); \(49-6=43\).
4. 91 − 67 = 24
Think Add: \(67+3=70\); \(70+21=91\); \(3+21=24\).
5. 75 − 39 = 36
Constant Diff (+1): \(76-40=36\).
P5 Probe 5 (Form E)
1. 44 + 33 = 77
Tens: \(40+30=70\); Ones: \(4+3=7\); \(70+7=77\).
2. 36 + 48 = 84
Make 50: \(48+2=50\); \(36-2=34\); \(50+34=84\).
3. 95 − 51 = 44
Decompose: \(95-50=45\); \(45-1=44\).
4. 85 − 58 = 27
Think Add: \(58+2=60\); \(60+25=85\); \(2+25=27\).
5. 57 + 29 = 86
Make 30: \(29+1=30\); \(57-1=56\); \(56+30=86\).
Diagnostic Error Matrix & Targeted Interventions
Observed Student Error
Underlying Misconception
Targeted IEP Strategy Intervention
Subtracts smaller from larger digit (e.g., \(73 - 48 = 35\))
Reverses digits (\(8 - 3 = 5\)) to avoid decomposing or thinking distance.
Introduce open number line / "Think Addition": mark 48 and jump up to friendly 50, then to 73.
Compensates in wrong direction (e.g., \(54 + 39 = 95\))
Adds 1 to make 40, but adds 1 again at the end instead of balancing back.
Use balance scale visual: "We added 1 extra dollar, so we must take that 1 dollar back!"
Place value concatenation (e.g., \(43 + 35 = 708\))
Treats tens sum (70) and ones sum (8) as side-by-side digits instead of place values.
Provide base-ten block mat: trade 7 ten-rods (70) and 8 units, counting aloud "70... 78".
Regrouping omission in addition (e.g., \(38 + 27 = 55\))
Adds \(30+20=50\); adds \(8+7=15\), but drops the new ten and writes 5.
Explicitly practice "Make a Ten": prompt student to move 2 from 27 to 38 first before adding.
Two-Digit Operational Strategies • Progress Monitoring Answer Key Page 3 of 3
Goal Progress Tracker Student Tracker
My Strategy Growth Chart
Target Goal 80% Accuracy (4/5)
Student Name:
School Year / Term:
My Math Mission:
I can solve 2-digit addition and subtraction problems by picking smart strategies (combining tens and ones, making a friendly ten, or thinking addition like distance). My goal is 4 or 5 correct on 3 checks in a row!
Progress Graph • Color in your score for each probe!
Score Bar Goal Line (80%)
Goal: 80% (4/5)
Baseline Date: ____
Probe 1 Date: ____
Probe 2 Date: ____
Probe 3 Date: ____
Probe 4 Date: ____
Probe 5 Date: ____
Strategy Badges to Unlock
10s
Tens & Ones [ ] Unlocked!
+10
Make a Ten [ ] Unlocked!
↔
Think Addition [ ] Unlocked!
☆
Independent Pro [ ] Unlocked!
Student Math Reflection:
Strategy I feel strongest with:
Strategy I want to practice more:
Student Visual Progress Monitoring Tracker • Operation Strategy Squad Page 1 of 2
Teacher IEP Record
IEP Progress Monitoring Data Log
Special Education Tracking Sheet Goal: 80% (4/5) x 3 Probes
Student Name:
Case Manager:
IEP Annual Date:
Reporting Period:
Check
Date
Score
%
Strategies Noted
Level (1-4)
Prompt Level
Met?
Baseline
___/___/___
___ / 5
___ %
T/O • M10 • TA • Standard
[ 1 ] [ 2 ] [ 3 ] [ 4 ]
Ind / Vb / Mod
—
Probe 1
___/___/___
___ / 5
___ %
T/O • M10 • TA • Other
[ 1 ] [ 2 ] [ 3 ] [ 4 ]
Ind / Vb / Mod
[ ] Y [ ] N
Probe 2
___/___/___
___ / 5
___ %
T/O • M10 • TA • Other
[ 1 ] [ 2 ] [ 3 ] [ 4 ]
Ind / Vb / Mod
[ ] Y [ ] N
Probe 3
___/___/___
___ / 5
___ %
T/O • M10 • TA • Other
[ 1 ] [ 2 ] [ 3 ] [ 4 ]
Ind / Vb / Mod
[ ] Y [ ] N
Probe 4
___/___/___
___ / 5
___ %
T/O • M10 • TA • Other
[ 1 ] [ 2 ] [ 3 ] [ 4 ]
Ind / Vb / Mod
[ ] Y [ ] N
Probe 5
___/___/___
___ / 5
___ %
T/O • M10 • TA • Other
[ 1 ] [ 2 ] [ 3 ] [ 4 ]
Ind / Vb / Mod
[ ] Y [ ] N
Retest
___/___/___
___ / 5
___ %
T/O • M10 • TA • Other
[ 1 ] [ 2 ] [ 3 ] [ 4 ]
Ind / Vb / Mod
[ ] Y [ ] N
Qualitative Error Patterns & Strategy Observations
Addition Observations:
[ ] Decomposes both addends into tens & ones reliably
[ ] Recognizes when "Make a Ten" is more efficient
[ ] Retains mental running total when adding tens then ones
[ ] Struggles with regrouping sums greater than 10
Subtraction Observations:
[ ] Reverses smaller/larger digits (e.g. \(73 - 48 = 35\))
[ ] Uses "Think Addition" / distance on number line
[ ] Decomposes subtrahend into tens then ones accurately
[ ] Needs open number line visual support to track jumps
IEP Goal Status & Recommendation:
Overall Goal Status: [ ] Mastered [ ] Progressing [ ] Needs Revision
Consecutive Probes ≥ 80%: [ ] 1 [ ] 2 [ ] 3 (Mastery Met)
Next Instructional Focus: [ ] Fluency [ ] 3-Digit [ ] Generalize
Special Educator Signature:
Date:
Teacher IEP Progress Monitoring Record • Operation Strategy Squad Page 2 of 2
