Area Model Monitoring Guide
Teacher Facilitation Tool
Lesson 31 Monitoring Laps Protocol
Topic: Multiply Two-Digit Multiples of 10 by Two-Digit Numbers (Area Model & Partial Products)
Bluebonnet G4 • Module 3
Circulation Time: 10 Minutes
Objective: Partition an area model, compute 2 partial products, and add vertically.
Lap 1: Setup Lap 2: Partial Prod. Lap 3: Addition
1
Lap 1: Area Model Setup & Decomposition (Minutes 0–3)
Target: Problems 1–3
What to Look For
- Multiple of 10 on left side (e.g., 20, 50, 60).
- 2-digit factor split into Tens and Ones (22 → 20 and 2; NOT 2 and 2).
- Partition divides box into 2 unequal rooms (wide tens, narrow ones).
Common Error Alert
Place Value Drop: Writes single digits at top (e.g., "4" and "1" instead of "40" and "1" for 41).
Flipped Factor: Splitting the multiple of 10 instead of the mixed factor.
15-Sec Verbal Prompt
“Say this number in expanded form: what is 41? (40 + 1). Great, write 40 above the big room and 1 above the small room!”
Flag student for Intervention Sheet if stuck after prompt.
2
Lap 2: Partial Products & Tens × Tens Logic (Minutes 3–6)
Target: Problems 2–5
What to Look For
- Correct expression inside each room: \(50 \times 40\) and \(50 \times 1\).
- Unit Form: \(5\text{ tens} \times 4\text{ tens} = 20\text{ hundreds} = 2,000\).
- Two zeros recorded for tens × tens plus base product zeros.
Common Error Alert
Zero Confusion: Writing 200 instead of 2,000 for \(50 \times 40\) because \(5 \times 4 = 20\) already ends in zero.
Unit Error: Thinking tens × tens = tens (e.g., \(20 \times 20 = 40\)).
15-Sec Verbal Prompt
“What is 1 ten times 1 ten? (1 hundred). So 5 tens times 4 tens is 20 hundreds. How do we write 20 hundreds? (2,000). Double check your zeros!”
3
Lap 3: Vertical Recording & Column Addition (Minutes 6–9)
Target: Problems 4–7
What to Look For
- Partial products written vertically alongside model.
- Strict column alignment: ones over ones, tens over tens, hundreds over hundreds.
- Correct sum matching the total area inside the model.
Common Error Alert
Misaligned Columns: Writing 180 under 4,200 with the 1 under thousands instead of hundreds.
Omitted Addend: Only writing down the larger partial product.
15-Sec Verbal Prompt
“Draw vertical grid lines through your ones, tens, and hundreds places before you add. Do your ones line up with ones?”
Problem Set Progression & Pacing
Q1–Q3 (Provided Frame): Models are outlined. Focus on decomposition and partial product calculation.
Q4–Q5 (Student Draws): Students draw and partition their own rectangle. Check proportions.
Q6–Q9 (Mental/Vertical): Visualizing model and recording numerical partial products directly.
Bluebonnet Learning G4 • Module 3 Lesson 31 Page 1 of 2: Monitoring Protocol Pacing: 10 Min Problem Set Circulation
Lesson 31 Circulation Roster & Action Tracker
Record live observations during 10-minute Problem Set circulation
✓ = Independent • = Minor Prompt ! = Intervention
| Student Name | Lap 1: Setup
Decomp. / Dimens. | Lap 2: Partial Prod.
Tens × Tens zeros | Lap 3: Addition
Vertical Alignment | Action / Debrief Pull Note |
| --- | --- | --- | --- | --- |
| 1. | | | | |
| 2. | | | | |
| 3. | | | | |
| 4. | | | | |
| 5. | | | | |
| 6. | | | | |
| 7. | | | | |
| 8. | | | | |
| 9. | | | | |
| 10. | | | | |
Fast Tier-2 Interventions: If a Student Cannot Set Up the Model
Action 1 (Model Frame):
Provide the Area Model Intervention Worksheet. Have student point to the multiple of 10 and write it on the left height.
Action 2 (Number Bond Anchor):
Draw a quick number bond beside the problem: e.g., \(22\) branches into \(20\) (tens) and \(2\) (ones) before writing them above each room.
Fast Check Key (Problems 1–5)
1. \(20 \times 22\) 400 + 40 = 440
2. \(50 \times 41\) 2,000 + 50 = 2,050
3. \(60 \times 73\) 4,200 + 180 = 4,380
4. \(80 \times 32\) 2,400 + 160 = 2,560
5. \(70 \times 54\) 3,500 + 280 = 3,780
Targeted Debrief Question
“Why does \(50 \times 40\) result in three zeros (\(2,000\)) while \(60 \times 70\) has two zeros (\(4,200\))?”
Core Takeaway: \(5 \times 4 = 20\) has an inherent zero; tens × tens adds 2 more place value zeros.
Group Pull Rule: If ≥3 students miss setup on Lap 1, pull to small group table immediately.
Bluebonnet Learning G4 • Module 3 Lesson 31 Page 2 of 2: Observation Grid Post-Lesson: Use data to group students for Lesson 32
Area Model Intervention Worksheet
Visual Math Scaffold • G4 Lesson 31
Area Model Builder: Step-by-Step Multiplication
Decompose factors, set up the rectangle, and multiply with confidence
Name:
Date:
The 4-Step Area Model Setup Blueprint
1 Side Factor
Find the multiple of 10. Put it on the left height.
Example: \(30\)
2 Split the Top
Split the other 2-digit number into Tens and Ones.
\(25 = 20 + 5\)
3 Multiply Rooms
Big: tens × tens = hundreds
Small: tens × ones = tens
\(600\) and \(150\)
4 Add Vertically
Line up place values (O, T, H) and add.
\(600 + 150 = 750\)
Worked Model: \(30 \times 25\) Reference Guide
Number Bond
25
↙ ↘
20 5
Height 30
20 5
\(30 \times 20\) 600
\(30 \times 5\) 150
H T O
6 0 0
+ 1 5 0
7 5 0
Problem 1 Solve \(20 \times 22\)
Guided Frame: Follow Steps 1 to 4
1. Decompose
22
↙ ↘
20
2
Tens & Ones
2 & 3. Fill the Area Model
Height 20
20 (tens)
2 (ones)
\(20 \times 20\)
\(20 \times 2\)
4. Add
H T O
Problem 2 Solve \(50 \times 41\)
Fill in the missing dimension labels and solve
Decompose 41
41
↙ ↘
____
____
tens & ones
Label and Multiply
Height
Tens: [ ]
Ones: [ ]
\(50 \times \text{____}\)
\(50 \times \text{____}\)
Add Vertically
Th H T O
Bluebonnet Learning G4 • Module 3 Lesson 31 Page 1 of 2: Guided Blueprint Remember: 1 ten × 1 ten = 1 hundred!
Practice: Build Your Own Area Model
Draw your rectangles, partition into tens and ones, and compute partial products
Goal: Set up without hints!
Problem 3 Solve \(60 \times 73\)
Decompose 73 → [ ] + [ ]
Area Model (Label the height and top):
Tens room:
Ones room:
Vertical Solution:
Th H T O
Problem 4 Solve \(80 \times 32\)
Draw your partition line and labels
Draw Area Model Here:
Vertical Solution:
Th H T O
Problem 5 Solve \(70 \times 54\)
Challenge Problem
Draw & Label Area Model:
Vertical Solution:
Th H T O
My Self-Check:
Multiple of 10 on the left Split tens and ones across top Counted zeros (tens × tens = hundreds) Aligned columns to add
Bluebonnet Learning G4 • Module 3 Lesson 31 Page 2 of 2: Independent Practice Success: Decomposing numbers makes multi-digit multiplication simple!
