Factor Power Teacher Guide EC Inclusion Push-In Grade 6 Math
Factor Power Push-In Lesson Plan
Topic: Factoring Expressions Using GCF & Distributive Property (6.NS.B.4 & 6.EE.A.3)
Format: Co-Teaching / Small Group
Duration: 45–60 Minutes
Model: Station / Parallel Push-In
Student "I Can" Targets
I can apply knowledge of factors to use the distributive property.I can write an equivalent expression showing the GCF of two addends factored out: \(a + b = G(p + q)\).
Core Scaffolding Strategy
Dual Scaffolds: Factor T-Charts (exhaustive list) \(\rightarrow\) Area Model (reverse generic rectangle) \(\rightarrow\) 4-Step Checklist for \(a(b+c)\).
Co-Teaching Roles & Small Group Push-In Structure
1 Whole Group Hook (8 min)
Gen Ed: Leads warm-up & real-world array hook.EC Push-In: Pre-populates T-charts on whiteboards, scribes visual gestures, checks baseline readiness.
2 Station / Push-In (25 min)
Gen Ed: Facilitates independent / peer station.EC Push-In: Leads targeted small group station with Task Cards, Anchor Chart & Factor Grid Organizer.
3 Debrief & Exit Ticket (10 min)
Gen Ed: Coordinates student share-out.EC Push-In: Administers accommodated exit ticket check & logs progress toward IEP math goals.
4-Level EC Prompting Hierarchy (Push-In Scaffolding Protocol)
Level 1: Independent
"Look at your 4-step checklist. Which step are you on?"
Level 2: Visual Cue
Point to Anchor Chart T-chart or highlight the greatest matching circle.
Level 3: Verbal Prompt
"You pulled out 6. Now divide: What is \(18 \div 6\)? What is \(24 \div 6\)?"
Level 4: Direct Model
Model the area rectangle side lengths: "Side is GCF (6), top lengths are 3 and 4."
personal anchor chart, read aloud when reading is not being assessed, Chunk large task with clear expectations for each segment, Embedded IEP Accommodations & Modifications
• Visual Organizers: Pre-printed T-Charts and split area models.
• Chunked Tasks: Limit to 2 problems per page / single task card at a time.
• Calculation Aids: Multiplication chart / factor reference strip permitted.
• Color-Coding: Green for GCF (outside), Blue/Orange for quotient addends (inside).
Teacher Facilitation Script & Error Matrix
Small Group Push-In Instructional Guide
15-Minute Targeted Push-In Small Group Routine
Phase 1: Connect & Activate (3 Minutes) Model: \(12 + 18\)
"Remember how we use the distributive property like a party host handing out snacks? Now we are doing it in reverse! We want to find the greatest equal group (GCF) that both numbers share."
Action: Have students build T-charts for 12 and 18. Circle all common factors (1, 2, 3, 6). Highlight the largest: 6 .
Phase 2: Area Model Connection (5 Minutes) Visual Scaffold
"Draw a rectangle split in two. The left room has area 12, the right room has area 18. If the shared height is 6, what are the two missing top lengths?"
Action: Guide students to calculate \(12 \div 6 = 2\) and \(18 \div 6 = 3\). Write outside and inside: \(6(2 + 3)\).
Phase 3: Guided Task Card Practice (7 Minutes) Task Cards 1–4
Students rotate through cards using the 4-Step Checklist . Have students verbalize: "GCF on the outside, quotients on the inside!"
Self-Check Checkpoint: Multiply back out using the distributive property: \(6 \times 2 = 12\) and \(6 \times 3 = 18\). Does \(12 + 18 = 30\)? Yes!
Diagnostic Misconception & Rapid Intervention Matrix
Observed Misconception Why EC Learners Make It Instant Push-In Intervention Pulls out common factor, but NOT the Greatest (e.g., \(2(12 + 18)\) instead of \(6(4 + 6)\)). Stops at the first even number/factor found without listing all pairs. "Look inside your parentheses: can 12 and 18 still be divided by another number? If yes, keep finding factors!" Subtracts or guesses inside terms instead of dividing (e.g., \(6(18 - 6) = 6(12)\)). Confuses factoring with subtraction or additive decomposition. Point to the Area Model. "Area = Height \(\times\) Width. To find the top side, divide: \(\text{Area} \div \text{GCF}\)." Forgets the parentheses or puts GCF inside: \(24 + 36 = 12 + 2 + 3\). Working memory overload transitioning from list to algebraic notation. Provide pre-formatted color-coded template: [ GCF ]( [ ] + [ ] ).
Push-In Success Metric: 80%+ accuracy factoring two-digit addends using GCF & Area Model without prompt Level 4.
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Factor Power Anchor Chart Math 6 Visual Reference Anchor Chart
Factoring Expressions with GCF
Use the Distributive Property in Reverse: Write an addition expression as \(G(a + b)\)
\(\star\)
The Golden Formula
\(\text{First} + \text{Second} = \mathbf{\text{GCF}} \Big( \frac{\text{First}}{\mathbf{\text{GCF}}} + \frac{\text{Second}}{\mathbf{\text{GCF}}} \Big)\)
Example: \(24 + 36 = \mathbf{12}(2 + 3)\)
STEP 1 Make Factor T-Charts
List all factor pairs from \(1 \times \text{number}\) up:
Factors of 24
1 • 24 2 • 12 3 • 8 4 • 6
Factors of 36
1 • 36 2 • 18 3 • 12 4 • 9
STEP 2 Find the GREATEST Factor
Circle matching factors and pick the largest one:
Common Factors: 1, 2, 3, 4, 6, 12
Greatest Common Factor: GCF = 12
STEP 3 Fill the Area Model
Put GCF on side; divide to find top lengths:
GCF (Height) 12
\(24 \div 12 = \mathbf{2}\) \(36 \div 12 = \mathbf{3}\)
Area 1 24
Area 2 36
STEP 4 Write Expression & Check
Format: \(\text{GCF}(\text{Length}_1 + \text{Length}_2)\)
12(2 + 3)
Check: \(12 \times 2 = 24\) \(12 \times 3 = 36\) Valid
💡
EC Push-In Memory Hook
"GCF on the OUTSIDE , Quotients on the INSIDE !"
Factor Power Toolkit • Reference Anchor
Factor Grid Graphic Organizer Math 6 Scaffolding Organizer
Factor Grid Graphic Organizer
Name:
Date:
Goal: Write each addition expression as an equivalent factored expression: \(\mathbf{GCF(a + b)}\) Use the 4 Steps & Area Model
1 Factor: \(18 + 24\)
T-Charts 2. GCF 3. Area Model 4. Write & Check
Step 1: Factor Pairs
18
1 • 18 2 • 9 3 • 6
24
1 • 24 2 • 12 3 • 8 4 • 6
Step 2 (GCF): GCF = 6
Step 3: Fill the Area Model (Split Rectangle)
GCF (Height)
6
\(18 \div 6 = \mathbf{3}\) \(24 \div 6 = \mathbf{4}\)
Area: 18
Area: 24
Step 4 Final Expression: 6(3 + 4)
Check: \(6 \times 3 = 18\) \(6 \times 4 = 24\) \(18 + 24 = 42\) ✓
2 Factor: \(15 + 45\)
T-Charts 2. GCF 3. Area Model 4. Write & Check
Step 1: Factor Pairs
15
1 • 15 3 • 5 ——
45
1 • 45 3 • 15 5 • 9
Step 2 (GCF): GCF = ___
Step 3: Fill the Area Model
GCF Side
\(15 \div \text{GCF} = \_\_\_\) \(45 \div \text{GCF} = \_\_\_\)
Area: 15
Area: 45
Step 4 Factored Expression:
____( ____ + ____ )
Page 1 • Factor Grid Graphic Organizer • Push-In Guided Practice
Practice & Reflection
Independent Factor Practice
Use T-Charts & Area Models
3 Factor: \(28 + 42\)
[ ] T-Charts [ ] GCF [ ] Area Model [ ] \(G(a+b)\)
28 42
GCF = _____
28
42
Factored Expression: ____( ____ + ____ )
4 Factor: \(32 + 48\)
[ ] T-Charts [ ] GCF [ ] Area Model [ ] \(G(a+b)\)
32 48
GCF = _____
32
48
Factored Expression: ____( ____ + ____ )
Spot the Error Challenge Is Jordan's answer completely factored?
Jordan was asked to factor \(20 + 30\). Jordan wrote: 5(4 + 6) .
1. Why is 5 NOT the Greatest Common Factor?
2. Write the TRUE factored expression using GCF:
____( ____ + ____ )
Self-Check: How confident do you feel factoring expressions?
🟢 Got it! 🟡 Need quick help 🔴 Need more practice
Factor Match Task Cards Small Group Station Cards
Factor Power Push-In Task Cards
Cards 1–4 • Cut along dashed lines
CARD 1 Tier 1: Guided GCF
Factor the expression using the GCF:
\(16 + 24\)
💡 Scaffold Hint:
• Factors of 16: 1, 2, 4, 8, 16
• Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
What is the factored form? ___( ___ + ___ )
CARD 2 Tier 1: Area Model
Find the missing dimensions:
Factor: \(21 + 35\)
7
21
35
Write equivalent form: 7( ___ + ___ )
CARD 3 Tier 2: Multiple Choice
Which expression is equivalent to \(36 + 48\) using the GCF?
A) \(6(6 + 8)\)
B) \(12(3 + 4)\)
C) \(4(9 + 12)\)
D) \(2(18 + 24)\)
💡 Hint: Check which option pulls out the LARGEST common factor!
CARD 4 Tier 2: Factoring
Complete the 4-step factoring method:
\(27 + 45\)
1. Greatest Common Factor: GCF = ___
2. Divide: \(27 \div \text{GCF} = \_\_\_\) and \(45 \div \text{GCF} = \_\_\_\)
Final Factored Form: ___( ___ + ___ )
Page 1 of 2 • Task Cards 1–4 • Factor Power Small Group Set
Application & Analysis
Factor Power Push-In Task Cards
Cards 5–8 • Cut along dashed lines
CARD 5 Tier 3: Error Analysis
Spot the Mistake:
Marcus factored \(14 + 28\) and got:
\(2(7 + 14)\)
• Why is Marcus's answer NOT completely factored?
• What is the actual GCF of 14 and 28?
Correct Expression: ___( ___ + ___ )
CARD 6 Tier 3: Word Problem
Snack Bag Challenge:
Maya has 24 granola bars and 36 juice boxes . She wants to make identical snack bags with no items left over.
a) What is the greatest number of snack bags she can make? (GCF )
b) Write the distributive expression showing bars + juice per bag.
Distributive Model: ___( ___ + ___ )
CARD 7 Tier 2: Dual Challenge
Factor the expression using the GCF:
\(40 + 64\)
Step 1: GCF of 40 and 64 = ___
Step 2: Quotients inside = \(( \_\_\_ + \_\_\_ )\)
Factored Form: ___( ___ + ___ )
CARD 8 Tier 3: Reverse Match
Factor Match Record Key Student Task Card Log
Factor Power Task Card Recording Sheet
Name:
Date:
Card 1: \(16 + 24\) GCF: ____
Work / T-Chart:
Factored Form: ____( ____ + ____ )
Card 2: \(21 + 35\) GCF: 7
Area Model Top Lengths: \(21 \div 7 =\) ____ , \(35 \div 7 =\) ____
Factored Form: 7( ____ + ____ )
Card 3: \(36 + 48\) Multiple Choice
My Choice (Circle): A | B | C | D
Why? Largest factor pulled out is: ____
Card 4: \(27 + 45\) GCF: ____
Work / Division:
Factored Form: ____( ____ + ____ )
Card 5: Spot the Mistake Marcus: \(2(7+14)\)
Mistake: 7 & 14 still share factor of ____.
Correct Form: ____( ____ + ____ )
Card 6: Snack Bags 24 bars, 36 juice
Greatest number of bags (GCF) = ____
Distributive Model: ____( ____ + ____ )
Card 7: \(40 + 64\) GCF: ____
Work / T-Chart:
Factored Form: ____( ____ + ____ )
Card 8: Reverse Match Expand: \(8(5+7)\)
\(8 \times 5 = \_\_\_\) and \(8 \times 7 = \_\_\_\)
Original Sum: ____ + ____ = 96
Push-In Station Goal: "I can factor expressions using the GCF." Score: ____ / 8 Correct
Teacher Reference
Task Cards Complete Answer Key
EC Push-In Key
Card 1: \(16 + 24\) GCF = 8
Factors: \(16 \rightarrow 1,2,4,\mathbf{8},16\); \(24 \rightarrow 1,2,3,4,6,\mathbf{8},12,24\)
Answer: 8(2 + 3)
Card 2: \(21 + 35\) GCF = 7
Dimensions: \(21 \div 7 = 3\), \(35 \div 7 = 5\)
Answer: 7(3 + 5)
Card 3: \(36 + 48\) Option B
GCF is 12. (A, C, D pull out common factors 6, 4, 2, but not the GREATEST).
Answer: B • 12(3 + 4)
Card 4: \(27 + 45\) GCF = 9
Quotients: \(27 \div 9 = 3\), \(45 \div 9 = 5\)
Answer: 9(3 + 5)
Card 5: Spot the Mistake Actual GCF = 14
Marcus only factored out 2. 7 and 14 share a common factor of 7.
Answer: 14(1 + 2)
Card 6: Snack Bags GCF = 12
Maya makes 12 bags (each with 2 granola bars and 3 juice boxes).
Answer: 12(2 + 3)
Card 7: \(40 + 64\) GCF = 8
Quotients: \(40 \div 8 = 5\), \(64 \div 8 = 8\)
Answer: 8(5 + 8)
Card 8: Reverse Match Check Step
