Group Loops Teacher Guide
Grade 4 Modified Instruction
Group Loops Teacher Guide
Intro to Division via Hands-On Equal Grouping
Lesson Model I Do / We Do / You Do
Targeted Standards
CCSS.MATH.CONTENT.4.NBT.B.6: Find whole-number quotients with up to four-digit dividends and one-digit divisors.
Modified Focus (3.OA.A.2): Partitioning a set of items into equal shares to model division concepts.
Learning Objective
Students will be able to represent a division expression by physically or visually distributing a dividend equally into divisor-defined "loops" to find the quotient.
Warm-Up: Fact Family Spiral (10 mins)
Mental Fluency
Review the inverse relationship of multiplication and division using simple fact families (e.g., \(3 \times 4 = 12\), \(4 \times 3 = 12\), \(12 \div 3 = 4\), \(12 \div 4 = 3\)).
Family 1 2, 5, 10
Family 2 3, 4, 12
Family 3 5, 4, 20
"I Do" - Explicit Modeling (15 mins)
Use the Group Loops Slide 3 & 4 to display the division problem: \(15 \div 3 = ?\)
Model Teacher Script & Teacher Actions:
Say: "Class, today we are going to unlock division using some magic circles I call 'Group Loops'. Division sounds fancy, but it just means sharing fairly. When we see \(15 \div 3\), the first number is \(15\)—that is our big pile of cookies to share. The second number is \(3\). That tells us how many loops (friends) we are sharing with."
Action: Point to the Division Mat. Count out exactly 15 counters (or draw 15 dots) in the "Starting Pile" box. Draw 3 large empty circular loops on your mat.
Say: "Watch me share them out. I must give one to each loop before anyone gets a second one. This keeps it fair. One for Loop A, one for Loop B, one for Loop C. That is 3 used. Let's keep going: 4, 5, 6... [continue until 15 are gone]. Now, look inside just ONE loop. How many dots are in there? Let's count: 1, 2, 3, 4, 5! So, \(15 \div 3 = 5\). Five is our answer, which we call the quotient."
Unit: Foundations of Operations Page 1 of 2
Grade 4 Modified Instruction
Group Loops Teacher Guide
Guided, Partner, and Independent Pacing
Lesson Model Practice & Apply
"We Do" - Guided Practice (15 mins)
Provide each student with their own laminated Group Loops Division Mat and dry-erase markers or counters. Present the problem: \(12 \div 4 = ?\)
Step-by-Step Prompting Sequence:
- Step 1: Identify the Pile. "Touch the number \(12\). Draw or place 12 counters in your Starting Pile. Check your partner's pile. Do they have exactly 12?"
- Step 2: Set the Loops. "Look at the second number, \(4\). How many loops do we need? Let's draw 4 big loops on our mats."
- Step 3: Deal Out Fairly. "Let's deal them one-by-one together. One, one, one, one... Keep going until your pile is empty. Keep it clean and fair."
- Step 4: Find the Quotient. "How many counters are in each loop? Count out loud. Yes, 3! So, \(12 \div 4 = 3\)."
"You Do" - Partner & Independent Work (15 mins)
Partner Play (Peer Support)
Have students work in pre-arranged pairs. One student is the "Dealer" (distributes the counters) and the other is the "Auditor" (double checks equal distribution). Switch roles for each problem.
Target: Worksheet Section B
Independent Assessment
Students complete 3 final division equations independently. They can choose to draw dots in loops or write fact families. This serves as the formative assessment checkpoint.
Target: Worksheet Section C
Accommodation Strategies Checklist
Tactile Focus: Provide plastic tokens or red/yellow counters. Avoid drawings if motor skills are a barrier.
Color Coding: Circle the dividend in blue (total tokens) and the divisor in orange (number of loops).
Pacing Scaffold: Cap dividends at 20. Do not transition to remainders until equal groups is 100% fluent.
Language Support: Keep reinforcing "fair sharing" as the synonym for "division".
Unit: Foundations of Operations Page 2 of 2
Group Loops Slides
Grade 4 Modified Mathematics
Group Loops Division
Learning to divide easily and fairly using visual groups and templates!
Division Intro Interactive Mats
Let's Get Started!
Warm-Up: Fact Families
10 Minutes
2, 5, 10
2 × 5 = 10
5 × 2 = 10
10 ÷ 5 = 2
10 ÷ 2 = 5
3, 4, 12
3 × 4 = 12
4 × 3 = 12
12 ÷ 4 = 3
12 ÷ 3 = 4
5, 4, 20
5 × 4 = 20
4 × 5 = 20
20 ÷ 4 = 5
20 ÷ 5 = 4
Remember: Multiplication and division are a family. They work together!
What is Division?
Fair Share
Rule 1: Division is Sharing
We start with a Total Pile and share them out equally.
Rule 2: Keep it Fair
Every loop gets the same amount. No group is left with less!
Division Vocabulary
12 ÷ 3 = 4
Dividend (The Pile)
Divisor (The Loops)
Quotient (Items in Loop)
When we see ÷, think: "Share this pile into these loops!"
I Do: Watch Me Solve
Model Problem
Equation
15 ÷ 3 = ?
I will share 15 dots into 3 circles, one at a time.
My Mat Visualization
Loop A
5 dots
Loop B
5 dots
Loop C
5 dots
Each loop has exactly 5 dots. So, 15 ÷ 3 = 5!
We Do: Try it Together
Active Participation
Our Expression
12 ÷ 4 = ?
Get Your Mats Ready:
- Count out exactly 12 counters.
- Draw 4 loops on your mat.
- Deal counters 1-by-1.
1
The Dividend (12)
Start with 12 items in your main pile.
2
The Divisor (4)
Identify how many loops you need (4).
3
Fair Share
Distribute into the 4 loops equally.
4
Quotient
Count one loop's items. How many?
Raise your hand when you have the quotient on your mat! 🙋♀️🙋♂️
Partner Play Rules
Collaboration
Group Loops Division Mat
Group Loops Division Mat
Use counters, cubes, or dry-erase markers to share fairly!
Laminate Me
For Dry-Erase!
Step 1 Count Starting Pile
Step 2 Count your Loops
Step 3 Deal 1-by-1 fairly
Step 4 Count items in 1 loop!
1. Starting Pile Workspace (Place dividend counters here first) TOTAL PILE
Put your total count here before sharing!
2. The Group Loops (Share your counters into these circles) DIVISOR LOOPS
Loop 1
Place items inside
Group A
Loop 2
Place items inside
Group B
Loop 3
Place items inside
Group C
Loop 4
Place items inside
Group D
3. Write Your Division Equation Here
Total Pile
÷
Loops Used
=
Items In 1 Loop
Group Loops Practice Worksheet
Division Intro - Modified
Group Loops Practice
Name:
Date:
Section A: Warm-Up - Fact Families
Complete the fact families below. Fill in the missing numbers to match the multiplication and division relationships!
Family 1
2 • 5 • 10
2 × 5 = 10
5 × 2 = 10
10 ÷ 5 =
10 ÷ 2 =
Family 2
3 • 4 • 12
3 × 4 = 12
4 × 3 = 12
12 ÷ 4 =
12 ÷ 3 =
Family 3
5 • 4 • 20
5 × 4 = 20
4 × = 20
20 ÷ 4 =
20 ÷ 5 =
Section B: Guided Practice - "We Do"
Use your Division Mat to solve these equations. Draw the dots inside the circles to show your work!
Problem 1 12 ÷ 4 = ?
Deal 12 total dots into 4 groups. Draw the dots in the loops below:
Items in each loop: [ ____ ]
Final Equation: 12 ÷ 4 =
Problem 2 10 ÷ 2 = ?
Deal 10 total dots into 2 groups. Draw the dots in the loops below:
Items in each loop: [ ____ ]
Final Equation: 10 ÷ 2 =
Group Loops Series Page 1 of 2
Division Intro - Modified
Group Loops Practice
Pacing: You Do
Section C: Partner Play
Switch Roles!
Take turns with your partner being the Dealer and Auditor. Use your Division Mat to solve together.
Partner Match 1
8 ÷ 2 = ____
Dealer: Name ________
Auditor: Name ________
Partner Match 2
16 ÷ 4 = ____
Dealer: Name ________
Auditor: Name ________
Partner Match 3
18 ÷ 3 = ____
Dealer: Name ________
Auditor: Name ________
Section D: Independent Assessment - "You Do"
Solve these division checkups on your own. Circle the correct option.
Question 1
You have 15 tokens. You make 5 equal loops. How many tokens go inside each loop?
A) 2 tokens
B) 3 tokens
C) 4 tokens
D) 5 tokens
Question 2
Which division equation matches sharing 14 blocks into 2 equal loops?
A) 14 ÷ 7 = 2
B) 14 ÷ 2 = 7
C) 2 × 7 = 14
