Two-Digit Addition with Regrouping for Mixed Disability Group

IEP-ALIGNED INTERVENTION LESSON: Two-Digit Addition with Regrouping
Grade 3-4 | Duration: 20 minutes | Group: 4 students | Setting: Co-taught classroom

IEP GOAL CONNECTION:
By May 2025, students will solve two-digit addition problems with regrouping with 80% accuracy across 3 consecutive trials using manipulatives or visual supports as needed.

TARGET SKILL:
Add two-digit numbers with regrouping (e.g., 27 + 38 = 65) using place value understanding and multi-sensory supports

LEARNING BARRIER:
Working memory challenges prevent students from holding multiple steps in mind simultaneously (remembering to regroup while tracking ones/tens). Processing speed barriers make traditional fast-paced instruction overwhelming.

DISABILITY CONSIDERATIONS:

• 2 students with Specific Learning Disabilities (math calculation difficulty)
• 1 student with ADHD (attention/working memory challenges)
• 1 student with Autism Spectrum Disorder (need for predictability, visual structure)

REQUIRED ACCOMMODATIONS:

• Visual supports (place value charts, color-coded tens/ones)
• Concrete manipulatives (base-ten blocks)
• Chunked directions (one step at a time with visual task breakdown)
• Reduced number of practice problems (3-4 instead of 10-12)
• Extended processing time (minimum 5-second wait time after questions)
• Visual schedule showing lesson flow

MATERIALS NEEDED:

• Base-ten blocks (units and rods) - 1 set per student
• Place value mats (laminated, color-coded: blue for tens, yellow for ones)
• Visual step-by-step anchor chart: “Adding with Regrouping”
• Color-coded dry erase markers (blue for tens, yellow for ones)
• Individual whiteboards and erasers
• Visual timer (Time Timer or digital countdown)
• “Trade 10” cards with visual cue
• Number sentences written on index cards (reduced quantity: 4 problems)
• Success tracking chart with stickers
• Visual schedule card showing 4 lesson sections

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HOOK & ACTIVATE (2 minutes): Trading Game

“Today we’re going to be super traders! Raise your hand if you’ve ever traded something - like Pokemon cards, snacks, or toys?”

[Allow brief sharing - use as attention grabber]

“Sometimes when we add numbers, we get SO MANY ones that we need to trade them! Just like trading 10 pennies for 1 dime. Let’s learn how to be expert traders with our numbers.”

Multi-sensory hook:
Hold up 10 unit cubes physically in hand. “How many do I have? Count with me!” Then dramatically trade them for 1 rod. “I just traded 10 ones for 1 ten! We’ll do this with addition today.”

PRE-ASSESSMENT:
“Show me with your fingers: How many ones do you need to make 1 ten?” (Check for understanding of 10:1 relationship - prerequisite skill)

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DIRECT INSTRUCTION WITH MODELING (5 minutes): The “Trade 10” Method

“I DO” (Teacher Model with Think-Aloud):

Display problem on anchor chart: 27 + 38 = ?

“I’m going to talk out loud about everything I’m thinking. Watch my hands and the colors.”

Step 1: Build the first number
[Using blue rods and yellow units on place value mat]
“27 means 2 tens and 7 ones. I’ll put 2 BLUE rods in my tens place [pause, place slowly]. Now 7 YELLOW ones in my ones place [pause, place slowly].”

Step 2: Build the second number
“Now 38. That’s 3 tens and 8 ones. I add 3 MORE blue rods [place] and 8 MORE yellow ones [place].”

Step 3: Check the ones place
“Uh oh! Let me count my ones place: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15! I have 15 ones. That’s MORE than 10. Time to TRADE!”

[Hold up “Trade 10” visual card]

Step 4: Trade 10 ones for 1 ten
“I take 10 yellow ones away [physically remove and place to side]. I trade them for 1 blue ten [place rod in tens column]. Now I have 5 ones left [count remaining]. And I have 1, 2, 3, 4, 5, 6 tens total!”

Step 5: Write the answer
“6 tens and 5 ones = 65. So 27 + 38 = 65!”

Multi-sensory supports in use:

• Visual: Color-coded place value mat (blue/yellow), anchor chart with numbered steps, “Trade 10” card
• Auditory: Think-aloud narration, counting aloud, “Trade 10!” verbal cue
• Kinesthetic/Tactile: Physically placing and removing manipulatives, trading motion
• Predictability: Numbered steps on anchor chart (1, 2, 3, 4, 5) - point to each step

Accommodation implementation:

• Chunked directions: One step at a time, with clear visual cue on anchor chart before each step
• Extended processing time: 5-second pause between each step
• Visual supports: Color-coding makes tens/ones distinction obvious
• Manipulatives: Hands-on base-ten blocks for all students

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GUIDED PRACTICE WITH SCAFFOLDING (7 minutes): “WE DO” Together

Problem: 46 + 27 = ?

“Now YOU have the blocks. We’ll do this problem TOGETHER. I’ll tell you each step, and you do it with me.”

Step 1: “Build 46. How many tens? [Wait 5 seconds] Yes, 4 blue rods. How many ones? [Wait] 6 yellow units. Build it on your mat.”

[Teacher circulates, checks all students, provides hand-over-hand support as needed]

Step 2: “Now ADD 27. Add 2 more tens and 7 more ones.”

[Circulate, check]

Step 3: “Count your ones place with me. Point to each one as we count together: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13!”

Step 4: “Do we need to trade? Thumbs up for yes, thumbs down for no.” [Wait] “Yes! We have more than 10.”

[Hold up “Trade 10” card as visual reminder]

“Take away 10 ones. Count them as you remove: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10. Now trade them for 1 blue ten.”

Step 5: “Count your tens. Count your ones. What’s our answer?” [Wait 5+ seconds]

“46 + 27 = 73! Give yourself a quiet clap!”

Scaffolding prompts:

• Full support: Physical hand-over-hand guidance for placing blocks, pointing to each step on chart
• Moderate support: Pointing to correct place value column, verbal cue “Check the chart”
• Minimal support: “What’s the next step?” while student references chart independently

Error correction protocol:
If student miscounts or forgets to trade:

1. Don’t say “That’s wrong” - instead: “Let’s check together”
2. Go back to concrete: “Let’s count these ones again, touching each one”
3. Use visual: Point to “Trade 10” card and anchor chart step
4. Repeat: “Let’s try that step one more time together”
5. Reinforce: “You fixed it! That’s what good mathematicians do.”

CHECK FOR UNDERSTANDING:

• Visual check: “Point to your tens place” [observe all students]
• Signal cards: “Hold up your ‘Trade 10’ card if we need to trade in this problem: 24 + 32” [Wait - answer: no trade needed]
• Verbal response (randomized): “[Student name], how many ones do we need before we trade?”

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MODIFIED INDEPENDENT PRACTICE (4 minutes):

Level 1 (High Support - Concrete):
Problem: 35 + 29 = ?

Use base-ten blocks with place value mat. Visual step chart available. Teacher/para provides verbal prompts for each step: “What’s step 1?”

Success criteria: Student completes problem with blocks, trades correctly with 1-2 verbal prompts

Level 2 (Moderate Support - Semi-Concrete):
Problem: 48 + 36 = ?

Blocks available as reference, but student draws quick tens/ones on whiteboard using color-coded markers (blue for tens, yellow for ones). Anchor chart available.

Success criteria: Student draws representation and identifies when to trade with minimal prompting

Level 3 (Lower Support - Moving Toward Abstract):
Problem: 57 + 25 = ?

Student solves on whiteboard using numbers, but blocks/mat available if needed. Can reference anchor chart.

Success criteria: Student writes problem, identifies regrouping, attempts solution (accuracy developing)

NOTE FOR CO-TEACHERS:

• General education teacher circulates to monitor on-level students in whole class
• Special education teacher/para stays with intervention group at designated table
• Allow students to choose their entry point (Level 1, 2, or 3) - they know their needs
• Students may complete just 1-2 problems depending on processing speed

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PROGRESS MONITORING CHECK (2 minutes):

Assessment:
Give each student 2 problems on index cards, matched to their level:

1. 44 + 38 = ? (with blocks/mat available)
2. 56 + 27 = ? (with blocks/mat available)

Students solve independently while teacher observes and records.

Accommodations provided:

• Manipulatives available
• Reduced quantity (2 problems instead of 5-10)
• Extended time (2 full minutes for just 2 problems)
• Visual anchor chart visible
• One-on-one check-in with teacher
• Option to verbally explain answer instead of writing

Data collection:
Record level of accuracy AND level of prompting needed

DATA SHEET:

Student Initials	Problem 1: Correct?	Prompt Level	Problem 2: Correct?	Prompt Level	Notes
_____	Yes/No	I/V/P/Ind	Yes/No	I/V/P/Ind
_____	Yes/No	I/V/P/Ind	Yes/No	I/V/P/Ind
_____	Yes/No	I/V/P/Ind	Yes/No	I/V/P/Ind
_____	Yes/No	I/V/P/Ind	Yes/No	I/V/P/Ind

Prompt Level Key: I=Independent, V=Verbal prompt, P=Physical/gestural prompt, Ind=Hand-over-hand

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ADDRESSING THE LEARNING BARRIER:

Barriers identified:

1. Working memory - cannot hold multiple steps in mind
2. Processing speed - needs more time to process each step
3. Abstract reasoning - difficulty with place value concepts without concrete supports

How this lesson removes/reduces barriers:

• Working memory support:

  • Visual anchor chart externalizes the steps (students don’t have to remember sequence)
  • “Trade 10” card serves as visual cue for critical decision point
  • Color-coding reduces cognitive load (no need to remember “which is tens?”)
  • Only 1 step given at a time

• Processing speed support:

  • Minimum 5-second wait time built into every question
  • Reduced number of practice problems (3-4 instead of 10-12)
  • No timed elements
  • Extended 2 minutes for just 2 assessment problems
  • Students work at own pace with manipulatives

• Abstract reasoning support:

  • Concrete manipulatives make place value tangible (can see/touch “ten”)
  • Physical trading action makes regrouping visible
  • Color-coding provides visual discrimination between place values
  • Gradual progression from concrete to semi-concrete (drawing) to abstract (numbers)

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ACCOMMODATION IMPLEMENTATION GUIDE:

Visual supports:
How implemented: Color-coded place value mats (blue tens/yellow ones), numbered anchor chart (1-5 steps), “Trade 10” visual card, visual schedule showing lesson sections
When used: Throughout entire lesson - always visible and referenced

Manipulatives:
How implemented: Base-ten blocks for every student during instruction and practice; available during assessment
When used: Direct instruction (required), guided practice (required), independent practice (available at all levels), assessment (available)

Chunked directions:
How implemented: Teacher gives 1 step at a time, points to step on visual chart, waits for all students to complete step before moving to next
When used: Direct instruction, guided practice; written step-by-step directions on anchor chart for independent reference

Reduced quantity:
How implemented: 3-4 practice problems total instead of 10-12; choose 1 level for independent practice; only 2 assessment problems
When used: Independent practice section, progress monitoring assessment

Extended processing time:
How implemented: Minimum 5-second wait time after every question; 2 full minutes for 2 assessment problems; students work at own pace; visual timer shows time remaining
When used: All sections - built into pacing

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DIFFERENTIATION BY DISABILITY:

For students with Specific Learning Disability (math calculation/reasoning):

• Emphasize concrete-to-representational progression - spend MORE time with manipulatives before moving to drawing/abstract
• Use “touch and count” strategy - physically touch each block while counting to prevent miscounting
• Pre-teach/review place value concepts: “Ten ones equal one ten”
• Provide graph paper for writing numbers to support spatial organization
• Consider 1:1 pre-teaching session before group lesson to build confidence

For student with ADHD (attention, working memory, impulsivity):

• Incorporate movement: “Stand up and trade!” when regrouping (kinesthetic engagement)
• Provide fidget (small manipulative) in non-dominant hand during instruction
• Use attention cues: “Eyes on me” with visual signal before each new step
• Seat near teacher during co-taught lesson to provide proximity support
• Offer choice: “Which problem do you want to try first?” (increases engagement)
• Build in 30-second movement break between guided and independent practice (stand, stretch, wiggle)
• Check in every 2 minutes during independent practice to maintain attention

For student with Autism Spectrum Disorder (need for structure, predictability, processing):

• Provide visual schedule at start: show picture cards for each lesson section
• Use consistent language/routine: ALWAYS say “Trade 10” (don’t vary language)
• Preteach lesson structure: “First we watch, then we do together, then you try alone, then we check”
• Give 30-second warning before transitions: “In 30 seconds, we’ll move to independent practice”
• Minimize sensory distractions: Seat away from noisy areas; use quieter manipulatives (foam blocks instead of plastic if sensitive to sound)
• Provide first/then visual: “First 2 problems, then sticker on success chart”
• Use visual checklist for each problem (check off steps as completed)

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PARAPROFESSIONAL SUPPORT NOTES:

Before lesson:

• Set up 4 place value mats at designated table (color-coded, laminated)
• Place 1 set of base-ten blocks at each seat (4 rods, 20 units per student)
• Have anchor chart visible to all students
• Prepare 4 index cards with assessment problems
• Have success chart and stickers ready
• Set up visual schedule card showing 4 lesson parts
• Position yourself at table with clear sight line to students

During lesson:

• Sit at table WITH students (not behind)
• During “I Do”: Monitor student attention; redirect with gentle touch/visual cue if needed
• During “We Do”: Circulate behind students; provide hand-over-hand support for student who needs physical prompting
• Watch for: miscounting, forgetting to trade, mixing up tens/ones
• For student with ADHD: Provide movement break between sections (stand and stretch)
• For student with ASD: Give 30-second warnings before transitions

How to prompt (most to least intrusive):

1. Full physical: Hand-over-hand guidance placing blocks
2. Partial physical: Touch student’s hand/point to correct location
3. Gestural: Point to anchor chart step or place value column
4. Verbal: “What’s the next step?” or “Check your chart”
5. Verbal reminder: “Remember to trade”
6. Independent: Student works without support

Always try least intrusive prompt first; only increase support if needed.

What to record:

• During guided practice: Note which students need physical vs. verbal prompts
• During assessment: Record correct/incorrect AND prompt level for each problem
• Note any behavioral observations: attention, frustration, engagement
• Track time: Did student complete within 20 minutes?

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SUCCESS CRITERIA:

By end of intervention, students should be able to:

• Build two-digit numbers using base-ten blocks with correct place value (tens in tens column, ones in ones column)
• Identify when regrouping is needed (when ones place has 10 or more)
• Physically trade 10 ones for 1 ten using manipulatives
• Solve at least 1 of 2 two-digit addition problems with regrouping using manipulatives with no more than 1 verbal prompt

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BEHAVIOR & ENGAGEMENT SUPPORTS:

Attention supports:

• Attention cue before each new instruction: “Eyes on me” + visual hand signal
• Proximity: Teacher/para seated AT table, not standing above
• Movement break built in: 30-second stretch between guided/independent sections
• Visual schedule reduces anxiety about “what’s next”
• Keep lesson fast-paced (but with wait time) - don’t linger, maintain momentum

Motivation strategies:

• Gamify: “We’re traders today!” makes math relevant
• Choice: Students choose which level problem to try first
• Success chart: Visual tracking with sticker after completing assessment
• Specific praise: “You remembered to trade without me reminding you!”
• Celebrate mistakes: “Mistakes help our brains grow - let’s fix it together”

Self-regulation supports:

• Visual timer shows time remaining (reduces anxiety)
• Fidget available for student with ADHD
• “Cool down” option: If student gets frustrated, can take 1-minute break with deep breathing
• Work at own pace during independent practice (no pressure)
• Option to verbally explain instead of writing

Reinforcement plan:

• Immediate verbal praise for correct responses: “Yes! You traded!”
• High-five or fist bump after completing assessment
• Sticker on success chart for participation (not just accuracy)
• For student with ASD: Use first/then board (first work, then preferred activity/sticker)
• Group celebration: “Everyone tried hard today - you’re all mathematicians!”

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NEXT STEPS & IEP CONSIDERATIONS:

If student meets success criteria (80%+ accuracy on 2 problems with minimal prompting):

• Next lesson: Gradually reduce manipulative support - move to drawing tens/ones
• Introduce larger numbers (regrouping with numbers in 60s-90s)
• Increase number of problems from 2 to 3
• Begin incorporating regrouping into word problems (application)
• Consider small group re-teaching less intensive (can join larger group with supports)

If student does not meet criteria:

• Prerequisite check: Assess understanding of place value (10 ones = 1 ten) in isolation
• Additional scaffolding:
  • Provide visual “trading mat” that shows 10 ones physically arranged with arrow pointing to 1 ten
  • Use different manipulatives: Try place value disks, linking cubes, or virtual manipulatives
  • Break into smaller chunks: Teach “build numbers” and “trade” as separate lessons before combining
  • Increase frequency: Daily 10-minute practice instead of 3x/week 20-minute lessons
• Simplify: Start with addition that requires regrouping in ones place only (no tens yet): 9 + 5, 8 + 7
• 1-on-1 pre-teaching: Meet individually for 5 minutes before group lesson to preview
• Consider IEP goal modification if: After 4 weeks of intensive intervention with scaffolds, student still below 50% accuracy - may need to adjust goal timeline or modify complexity level

Data documentation for IEP:

• Record progress monitoring results in IEP data tracking system after every lesson
• Collect data 2-3 times per week (every intervention session)
• Graph accuracy over time - look for upward trend across 3+ data points before reducing supports
• Report progress to case manager weekly
• Formal progress report for parents every 4-6 weeks
• Share data at IEP annual review or sooner if goal needs modification

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FAMILY SUPPORT NOTE (Send Home):

“Dear Family,

Today in intervention, your child worked on two-digit addition with regrouping (like 27 + 38) which connects to their IEP goal of solving addition problems with 80% accuracy.

We used base-ten blocks (little cubes and rods) and color-coded place value mats to help them see and touch the numbers. This makes the math easier to understand! When there are more than 10 ones, we “trade” 10 ones for 1 ten - just like trading 10 pennies for 1 dime.

AT HOME TRY THIS:
Use real pennies and dimes! Give your child 2 small groups of pennies (example: 7 pennies + 8 pennies). Have them count all the pennies. If they have 10 or more, help them trade 10 pennies for 1 dime. Count the dimes and leftover pennies together. This is EXACTLY what we do with addition!

What helps your child learn:

• Let them touch and count - Use objects like pennies, beans, or Legos to make math hands-on
• Use colors - Try using two colors (like red and blue) to show tens and ones
• One step at a time - Give 1 direction, wait, then give the next direction
• No rush - Give them extra time to think (count to 5 slowly in your head before expecting an answer)

Today your child showed great effort and successfully used the blocks to solve addition problems! They are making progress toward their goal.

Please contact me if you have questions!”

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TEACHER REFLECTION & NOTES:

Implementation tips:

• Pre-make place value mats by laminating colored paper (blue left side, yellow right side) - reusable
• Store each student’s blocks in a small plastic bin with their name - speeds up distribution
• Keep anchor chart posted on wall after lesson - students can reference during math workshop
• Consider making mini “Trade 10” cards students can keep at desks during all math work
• If co-teaching, decide roles in advance: One teacher leads, other circulates and prompts

Common pitfalls to avoid:

• Moving too fast through steps (remember: processing speed barrier!)
• Assuming students remember steps from yesterday - review anchor chart every lesson
• Allowing students to skip blocks and go straight to abstract - resist this! They need concrete support longer than typical learners
• Forgetting to celebrate mistakes - normalize errors as learning opportunities
• Not collecting data - you MUST have documentation for IEP progress

What to observe during lesson:

• Key indicator of understanding: Student correctly identifies when to trade (10+ ones) without prompt
• Key indicator of engagement: Student voluntarily reaches for blocks/chart to solve problem
• Misconception to watch for: Student adds tens and ones separately but forgets to combine (writes 5 tens and 15 ones as answer instead of regrouping)
• Attention red flag: Student stops tracking the steps on chart, starts playing with blocks off-task

Materials management:

• Prep time: 5 minutes (lay out mats and blocks at table before students arrive)
• Storage: Use gallon Ziploc bags - 1 per student with their blocks, labeled
• Anchor chart: Laminate and use dry erase marker to write problems (reusable)
• Clean-up: Assign student helper to collect blocks - builds responsibility and saves time