Diagnostic Checkpoint Assessment Form A • Pre-Intervention Baseline
Subtraction Diagnostic Assessment
Name:
Date:
Directions: Solve each subtraction problem using the standard algorithm. Show all trade and regrouping marks clearly.
Skill 1: 3-Digit with Regrouping Item 1
Subtract: $524 - 168$
HTO
524
−168
Target: Unbundling tens & hundreds Score: [ ] 0 [ ] 1
Skill 2: 5-Digit Column Alignment Item 2
Subtract: $68,745 - 24,312$
T-ThThHTO
68745
−24312
Target: Right-to-left 5-digit fluency Score: [ ] 0 [ ] 1
Skill 3: 5-Digit Multi-Regrouping Item 3
Subtract: $43,625 - 18,273$
T-ThThHTO
43625
−18273
Target: Sequential cross-column trades Score: [ ] 0 [ ] 1
Skill 4: Regrouping Across Zeros Item 4
Subtract: $60,000 - 24,357$
T-ThThHTO
60000
−24357
Target: Multi-zero chain trades (9s & 10) Score: [ ] 0 [ ] 1
Baseline Administered By: _________________________
Total Baseline Score: ____ / 4 (____ %)
Form B • Post-Intervention Outcome
Subtraction Mastery Assessment
Name:
Date:
Directions: Show off your skills! Solve each subtraction problem using the standard algorithm and record your regrouping steps.
Skill 1: 3-Digit with Regrouping Item 1
Subtract: $613 - 279$
HTO
613
−279
Target: Unbundling tens & hundreds Score: [ ] 0 [ ] 1
Skill 2: 5-Digit Column Alignment Item 2
Subtract: $79,864 - 35,241$
T-ThThHTO
79864
−35241
Target: Right-to-left 5-digit fluency Score: [ ] 0 [ ] 1
Skill 3: 5-Digit Multi-Regrouping Item 3
Subtract: $52,714 - 26,458$
T-ThThHTO
52714
−26458
Target: Sequential cross-column trades Score: [ ] 0 [ ] 1
Skill 4: Regrouping Across Zeros Item 4
Subtract: $80,000 - 37,429$
T-ThThHTO
80000
−37429
Target: Multi-zero chain trades (9s & 10) Score: [ ] 0 [ ] 1
Intervention Growth Snapshot Pre-Test Score: _____ / 4 ➔ Post-Test Score: _____ / 4
Goal: ≥ 3/4 (75%+)
GROWTH: +_____ %
Diagnostic Tracker Guide MTSS / RTI Tier 3 Coaching Resource
Diagnostic Tracker Guide
Administration Protocol, Master Answer Keys, and Error Analysis Matrix
Assessment Pacing
10–12 Mins (Untimed)
Form A Answer Key (Baseline) Pre-Test
1. $524 - 168$: 356
Trades: 4→14 (from 2T), 1T→11 (from 5H)
2. $68,745 - 24,312$: 44,433
No trades; evaluate comma & column tracking
3. $43,625 - 18,273$: 25,352
Trades: 2T→12 (from 6H), 3Th→13 (from 4TTh)
4. $60,000 - 24,357$: 35,643
Chain trade: 6→5; zeros become 9, 9, 9, 10
Form B Answer Key (Outcome) Post-Test
1. $613 - 279$: 334
Trades: 3→13 (from 1T), 0T→10 (from 6H)
2. $79,864 - 35,241$: 44,623
No trades; evaluate comma & column tracking
3. $52,714 - 26,458$: 26,256
Trades: 4→14, 0T→10, 6H, 2Th→12, 5TTh→4
4. $80,000 - 37,429$: 42,571
Chain trade: 8→7; zeros become 9, 9, 9, 10
Qualitative Diagnostic Error Matrix
Observed Error Pattern Underlying Misconception Target Sequence Link Smaller-from-Larger (Inversion) Subtracts bottom from top when bottom is bigger ($4 - 8 = 4$). Ignores place value integrity. Reinforce Day 1 "More on the Floor" anchor rule. Column Shift / Left-Bias Starts subtracting from left; or misaligns 4-digit subtrahend under 5-digit number. Reinforce Day 2 Place Value Grid & Card Masking. Forgotten Decrement ("Phantom 10") Adds 10 to receiving digit, but fails to cross out and reduce the donor column by 1. Drill Day 3 "Cross - Drop - Trade" 3-beat motor chant. All-Tens Across Zeros Turns every zero into 10 without leaving 9s behind in intermediate columns. Review Day 4 Chain Trade Bucket Brigade model.
MTSS Tier Decision Rules
Score 75%–100% (3–4/4): Mastered. Exit 1:1 Tier 3 to Tier 2 small group maintenance.Score 50% (2/4): Partial Mastery. Administer targeted 1-day mini-booster on missed skill.Score 0%–25% (0–1/4): Persistent Deficit. Recycle CRA base-ten manipulatives; re-teach sequence.
Triple Digit Trade Guide Day 1 • Tier 3 Intervention Guide
Triple Digit Trade Guide
Focus: 3-Digit Subtraction with Regrouping (Tens & Hundreds Unbundling)
1:1 Session Pacing
Target Duration: 20 Mins
Anchor Verbal Pathway
The Rule: "Look at the column. More on top? No need to stop! More on the floor? Go next door and get 10 more!"
Always start in the ones place. Never subtract the smaller number from the larger number if the top is smaller.
Top Error to Watch
Digit Inversion: When subtracting $542 - 278$, writing $8 - 2 = 6$ in the ones place instead of regrouping $4$ tens to $3$ tens and making $12$ ones.
1:1 Direct Instruction Script (20 Minutes)
Phase 1: Concrete / Visual Trade Modeling (4 mins) I DO
Prompt: Place base-ten blocks (or draw place value disks) for $432$."We have 4 hundreds, 3 tens, and 2 ones. We need to take away 156. Can I take 6 ones from 2 ones? No! Where do I go? Next door to the tens! I trade 1 ten for 10 ones. How many tens are left? 3 becomes 2. How many ones now? 10 plus 2 is 12! Now we can subtract."
Phase 2: Guided Practice with Prompt Fading (8 mins) WE DO
Target Problem: Have student write $524 - 267$ in the structured practice mat grid.Teacher Prompt: "Where do we start? (Ones). Read the ones column: 4 minus 7. More on top or more on the floor? (Floor!). What is our action? Cross out the 2 tens, write 1 ten above it. Cross out the 4 ones, write 14. What is $14 - 7$?"
Phase 3: Independent Try & Think-Aloud (5 mins) YOU DO
Student completes Problem 3 ($615 - 288$) completely unassisted while speaking their self-talk aloud. If student hesitates for more than 5 seconds, prompt with: "Check the column rule: more on top or more on the floor?"
Instant Correction Routine
Halt gently: "Freeze right there. Let's look at that column."Compare: "Hold up your fingers: is 4 bigger or is 7 bigger?"Reinforce: "If you have 4 cookies, can I take 7? What do you need to do?"Physical re-draw: Strike through the top number immediately and record traded value in the top box.
Day 1 Mastery Checklist
Identifies need to regroup before subtracting
Correctly decrements neighbor by 1
Adds 10 correctly to receiving digit (e.g. 4 → 14)
Subtracted accurately in all 3 columns
Triple Digit Trade Mat 3
Triple Digit Trade Mat
Day 1: Subtraction with Regrouping (Guided Session)
Name:
Date:
The Subtraction Decision Rule:
More on top? No need to stop! | More on the floor? Go next door and get 10 more!
Start in Ones!
Problem 1 (Model) I DO
Subtract: $432 - 156$
H T O
4 3 2
− 1 5 6
Step: Trade 1 Ten for 10 Ones. 2 becomes 12. Trade 1 Hundred for 10 Tens.
Problem 2 (Guided) WE DO
Subtract: $524 - 267$
H T O
5 2 4
− 2 6 7
Question: In the ones place, is 4 or 7 bigger? Do you need to trade?
Problem 3 (Solo) YOU DO
Subtract: $615 - 288$
H T O
6 1 5
− 2 8 8
Say aloud: Say the rule for each column before you write!
Reverse-Addition Check (Problem 3)
Take your answer and add the bottom number ($288$). Does it equal $615$?
Answer
Bottom #
288
=
Should =
615
Student Daily Reflection
How did regrouping feel today?
🤔
Still Tricky
👍
Getting It!
🚀
Got It Down!
Teacher Initials: _______ | Score: ____ / 3 correct
Triple Digit Trade: Extra Practice Workout
Independent Repetition & Word Problem Application
Target: 4/4 Accuracy
Directions: Use your trade boxes above each column whenever there is "more on the floor."
Practice Item A Regroup Tens & Hundreds
HTO
743
−268
Practice Item B Regroup Tens & Hundreds
HTO
852
−374
Practice Item C Single Trade (Ones Only)
HTO
635
−418
Practice Item D Regroup Tens & Hundreds
HTO
914
−582
Word Problem Challenge
The elementary school library had 521 books on the shelves. During reading month, students checked out 287 books. How many books remain on the shelves?
Vertical Calculation Space:
Five Digit Launch Guide Day 2 • Tier 3 Intervention Guide
Five Digit Launch Guide
Focus: 5-Digit Subtraction with NO Regrouping (Alignment & Place Value Mastery)
1:1 Session Pacing
Target Duration: 20 Mins
Instructional Intent & Key Concept
Struggling learners often get lost navigating 5 columns. Day 2 isolates column discipline , ten-thousands place value , and comma placement without the cognitive load of regrouping.
Core Rule: "Stack by place value, start on the far right (ones), and drop the comma between the thousands and hundreds."
Left-to-Right Habit
Watch for students starting at the ten-thousands place because "it's first." Explicitly enforce covering columns and working strictly right-to-left .
Step-by-Step 1:1 Coaching Routine
Phase 1: Place Value Naming & Stacking Alignment (5 mins) I DO
Teacher Action: Write $58,746 - 23,124$ horizontally."Before we touch a pencil to subtract, we read the number: 58 thousand, 746. Let's line up each digit into its home: Ten-Thousands (TTh), Thousands (Th), Hundreds (H), Tens (T), and Ones (O). Where does our subtraction always start? In the ones! 6 take away 4 is 2." Model column by column.
Phase 2: Guided Column Tracking with Visual Masking (7 mins) WE DO
Technique: Use an index card to cover the other 4 columns. Reveal one column at a time from right to left.Target Problem: $87,954 - 34,621$"Slide the card: Ones column: 4 - 1 = 3. Tens: 5 - 2 = 3. Hundreds: 9 - 6 = 3. Where does our comma drop? Right after the thousands!"
Phase 3: Independent Execution & Comma Rule Check (5 mins) YOU DO
Student independently calculates Problem 3 ($96,875 - 42,310$). Student must point to each column, state the value ("8 hundreds minus 3 hundreds is 5 hundreds"), and insert the comma accurately.
The "Jagged Column" Fix
When students write without a grid, digits drift sideways. If a student writes digits crookedly, immediately transition them to the vertical grid lines on the practice mat. Clean alignment prevents 70% of algorithmic calculation errors.
Day 2 Fluency Check
Lines up 5 digits with proper place-value alignment
Executes right-to-left without left-digit bias
Correctly places comma between thousands & hundreds
Solves with 100% calculation accuracy
Target: Confident right-to-left automaticity before Day 3 regrouping.
Five Digit Launch Mat 5
Five Digit Launch Mat
Day 2: 5-Digit Subtraction (Guided Session)
Name:
Date:
Gold Rule Keep digits in their columns! Always start at the Ones on the right.
Remember the Comma!
Problem 1 (Model) I DO
T-Th Th H T O
58746
− 23124
3
5
6
2
2
Result: 35,622 (Read: 35 thousand, 622)
Problem 2 (Guided) WE DO
T-Th Th H T O
87954
− 34621
Write your answer with a comma: __________________
Problem 3 (Independent Check) YOU DO
T-Th Th H T O
96875
− 42310
Self-Prompt Questions:
Did I start in the ones place?
Is $5 - 0 = 5$ or $0$?
Did I place the comma after 3 digits from the right?
Alignment Detective: Which Stacking is Correct?
Look at $45,892 - 3,421$. Circle the letter of the setup that aligns place values correctly:
Choice A
4 5 , 8 9 2
3 is under 5 (Thousands)
Choice B
4 5 , 8 9 2
3 is under 4 (Ten-Thousands)
Alignment & Comma Placement Mastered
Student Sign-off: [ ] Ready for Regrouping! Score: ____ / 3
Five Digit Launch: Extra Practice Workout
Alignment Fluency & Multi-Digit Stamina
Target: 4/4 Clean Columns
Directions: Subtract carefully from right to left. Don't forget to write the comma between thousands and hundreds!
Practice Item A 5-Digit by 5-Digit
T-ThThHTO
86597
−34261
Practice Item B Watch Alignment! (4-digit)
T-ThThHTO
47698
−5234
Practice Item C Zeros in Answers
T-ThThHTO
58349
−26108
Practice Item D Large Digits
T-ThThHTO
95786
−61432
Stadium Ticket Challenge
A city stadium has 68,950 total seats. For Friday's big game, fans have purchased 45,720 tickets. How many seats are still unsold?
Vertical Calculation Space (Align Columns!):
Unsold Seats:
Big Number Bridges Guide Day 3 • Tier 3 Intervention Guide
Big Number Bridges Guide
Focus: 5-Digit Subtraction with Regrouping across Adjacent Place Values
1:1 Session Pacing
Target Duration: 20 Mins
The "Cross - Drop - Trade" 3-Beat Routine
Every time there is "more on the floor," teach this precise motor sequence:
1. CROSS Slash neighbor digit
2. DROP Write new amount (-1)
3. TRADE Add 10 to current digit
The "Phantom 10" Trap
Students often change 3 to 13 in the ones place, but forget to cross out the 5 in the tens place, essentially inventing 10 out of nowhere. Never let them trade until the slash is made.
Step-by-Step 1:1 Intervention Script (20 Minutes)
Phase 1: Multi-Step Regrouping Model (5 mins) I DO
Problem: $64,283 - 27,156$ (Trades in Ones and Thousands)."Watch my hands: I go to the ones. 3 minus 6. More on floor! 1. CROSS the 8. 2. DROP it to 7. 3. TRADE: 3 becomes 13. $13 - 6 = 7$. Tens: $7 - 5 = 2$. Hundreds: $2 - 1 = 1$. Now look at thousands: 4 minus 7. More on the floor! 1. CROSS the 6 ten-thousands. 2. DROP to 5. 3. TRADE: 4 becomes 14. $14 - 7 = 7$. Ten-thousands: $5 - 2 = 3$. Answer: 37,127."
Phase 2: Guided Practice with Verbal Chanting (8 mins) WE DO
Problem: $73,541 - 38,265$ (Regrouping across multiple columns)."Student, put your finger on the ones column. Chant with me: 'More on top or floor?' (Floor!). Chant the 3 beats: 'Cross, Drop, Trade!' What is our new number? Yes, 11! Subtract. Now move left to tens: we have 3 minus 6. Floor again! Repeat the chant!"
Phase 3: Solo Mastery with Self-Monitoring (5 mins) YOU DO
Student completes Problem 3 ($52,834 - 19,452$) completely independently. Student performs addition check immediately beneath.
What If Student Double-Trades?
Some students trade when the top number is already larger (e.g. $7 - 5$, they cross 7 and write 17).Intervention cue: Tap the decision card: "Look closely! Is the top bigger? Yes! Stop! Do not trade if you have enough!"
Day 3 Observation Log
Executes Cross-Drop-Trade without skipping drops
Does NOT regroup when top digit is larger
Handles multiple trades in a single problem
Verifies answer using addition inverse
Target: Student self-corrects without teacher prompting.
Big Number Bridges Mat 3
Big Number Bridges Mat
Day 3: 5-Digit Subtraction with Regrouping (Guided Session)
Name:
Date:
3-Beat Chant 1. CROSS the neighbor → 2. DROP by 1 → 3. TRADE: Add 10!
Start in Ones
Problem 1 (Model) I DO
T-Th Th H T O
5
14
7
13
6 4 2 8 3
− 27156
3
7
1
2
7
Answer: 37,127
Problem 2 (Guided) WE DO
T-Th Th H T O
73541
− 38265
Hint: In ones ($1-5$), trade from tens. In tens ($3-6$), trade from hundreds!
Problem 3 (Independent Try) YOU DO
T-Th Th H T O
52834
− 19452
Check the rule:
Ones: $4 - 2$. Is there more on the floor?No! $4 > 2$, so just subtract: $4 - 2 = 2$. Do NOT trade here!
Addition Proof (Problem 3)
Check your answer by adding it to $19,452$:
Your Answer
Subtrahend
19,452
=
Should Equal
52,834
Intervention Milestone
Can you do Cross-Drop-Trade without reminders?
Need Help
Almost Solo
100% Solo!
Teacher Notes: __________________________ | Score: ____ / 3
Big Number Bridges: Extra Practice Workout
Independent Multi-Column Trades & Applied Distance Problem
Target: 4/4 Multi-Trades
Directions: Use the 3-beat chant: 1. Cross neighbor, 2. Drop by 1, 3. Trade (add 10). Always start at the ones!
Practice Item A Trades in Tens & Thousands
T-ThThHTO
64825
−28371
Practice Item B Trades in Ones & Thousands
T-ThThHTO
83492
−47836
Practice Item C Multiple Sequential Trades
T-ThThHTO
71643
−35289
Practice Item D Trades in Tens & Ten-Thousands
T-ThThHTO
92514
−38162
Flight Mileage Challenge
A cargo plane flew 34,250 miles during July and 18,635 miles during August. How many more miles did the airplane fly in July than in August?
Zero Zone Breakthrough Guide Day 4 • Tier 3 Intervention Guide
Zero Zone Breakthrough Guide
Focus: 5-Digit Subtraction Regrouping Across Multiple Zeros
1:1 Session Pacing
Target Duration: 20 Mins
The "Chain of Trades" Verbal Pathway
The Big Question: "Can we borrow from a zero? No, its bank account is empty!"
The Solution: Travel left until we find the first digit with value. Bring value back one column at a time: it becomes a 10, then immediately trades 1 to the next neighbor, leaving behind a 9 !
The "All Tens" Fallacy
Struggling students will often change ALL zeros to 10s (e.g., in $50,000$, writing $10, 10, 10, 10$). Reiterate: each zero can only give away 1 if it has 10, leaving 9 in its place!
1:1 Intervention Protocol (20 Minutes)
Phase 1: Direct CRA "Bucket Brigade" Model (5 mins) I DO
Problem: $50,000 - 23,471$"Look at the ones place: $0 - 1$. More on the floor! We look to tens: empty ($0$). Hundreds: empty ($0$). Thousands: empty ($0$). Where is the money? In the ten-thousands ($5$)!
Phase 2: Guided Chain Tracking (8 mins) WE DO
Target Problem: $40,502 - 18,367$ (Zeros interspersed with numbers)."Put your pencil on ones: $2 - 7$. Can we borrow from tens? It has 0! Where do we go? To hundreds! It has 5! Slash 5 $\rightarrow$ 4. Tens gets 10. Now slash 10 $\rightarrow$ 9. Ones becomes 12! What is $12 - 7$?"
Phase 3: Independent Capstone Challenge (5 mins) YOU DO
Student solves Problem 3 ($70,000 - 34,682$) independently. Crucial: Student must perform the addition check immediately to prove their answer before celebrating!
The "Drop the Bottom" Error ($0 - 4 = 4$)
If student writes $0 - 4 = 4$, immediately place an empty bowl in front of them:"There are 0 candies in this bowl. Take 4 candies out." When they hesitate: "You can't! You must get candies from another bowl first!"
4-Day Cumulative Exit Criteria
Day 1: 3-Digit regrouping mastered (≥80%)
Day 2: 5-Digit column alignment & commas
Day 3: Multi-column Cross-Drop-Trade routine
Day 4: Chain trade across zeros with addition check
Zero Zone Breakthrough Mat 4
Zero Zone Breakthrough Mat
Day 4: Regrouping Across Zeros (Guided Session)
Name:
Date:
The Zero Secret Zeros have no value! Travel left to find a number. Middle zeros become 9s , only the target ones digit gets 10 !
Problem 1 (Model) I DO
T-Th Th H T O
4
9
9
9
10
5 0 0 0 0
− 23471
2
6
5
2
9
Answer: 26,529
Problem 2 (Guided) WE DO
T-Th Th H T O
40502
− 18367
Notice: In ones ($2-7$), trade from 5 in hundreds! Tens becomes 9, ones is 12!
Problem 3 (Mastery Final Boss!) YOU DO
T-Th Th H T O
70000
− 34682
Checklist:
Cross the 7 to make 6
Middle zeros become 9s
Far right zero becomes 10
Subtract every column
Reverse Proof (Problem 3)
Add your answer back to $34,682$ to prove it equals $70,000$:
Your Answer
Subtrahend
34,682
=
Target
70,000
Official Subtraction Master!
Successfully conquered 3-Digit Trades, 5-Digit Alignment, Multi-Trades, and the Zero Zone!
Student: ___________________ Interventionist: ___________________ PASSED ⭐️
Zero Zone Breakthrough: Extra Practice Workout
Chain Regrouping Fluency & Playground Fund Problem
Target: 4/4 Zero Accuracy
Directions: Remember the chain rule: Middle zeros become 9s; only the target ones place gets 10!
Practice Item A 4 Consecutive Zeros
T-ThThHTO
50000
−18346
Practice Item B Interspersed Zeros
T-ThThHTO
40020
−16385
Practice Item C Large Zero Minuend
T-ThThHTO
90000
−45678
Practice Item D Alternating Non-Zero Digits
T-ThThHTO
60405
−28179
Playground Fund Challenge
A community raised $50,000 to build a modern inclusive playground. They spent
