Multiplication Models Teacher Guide
Resource Room Pull-Out • 40-Minute Plan
Multiplication Models Teacher Guide
Unit 2, Day 5 (Modified) • Modeling Multiplication with Pictures & Diagrams
Standard: 3.OA.3
Setting: Small Group (Pull-Out)
Framework: G-S-T Method
Objective: SWBAT use the GST framework (Groups, Size, Total) to identify, draw, and explain multiplication situations using grouping diagrams, tape diagrams, and number lines.
Key Concept: Multiplication represents totaling objects across equally-sized groups. Factor 1 = Number of Groups (G); Factor 2 = Size of Each Group (S); Product = Total (T).
40-Minute Pacing Schedule
0:00 – 0:08 (8 min) 1. Vocab Launch & GST
0:08 – 0:20 (12 min) 2. Guided Modeling
0:20 – 0:32 (12 min) 3. Scaffolded Practice
0:32 – 0:40 (8 min) 4. Discourse & Stamp
1 Phase 1: Vocabulary First & Choral Practice (8 min)
Pre-teach & Oral Rehearsal
Teach key terms using the exact Uncommon Schools anchor language with choral repetition, gestures, and the visual G-S-T formula:
Multiplication
Totaling objects across equally-sized groups ("times" or "groups of").
Factors (G & S)
Numbers multiplied: 1st factor = Groups (G), 2nd factor = Size (S).
Product (T)
The answer representing the total number (T) across all equal groups.
Teacher Scripted Call-and-Response (Choral Routine)
Teacher: "What does the first factor always represent?" → Scholars: "The number of GROUPS!" (Hold up fingers for groups)
Teacher: "What does the second factor represent?" → Scholars: "The SIZE of each group!" (Cup hands to hold items)
Teacher: "And what does the product represent?" → Scholars: "The TOTAL across all equal groups!"
2 Phase 2: Step-by-Step Modeling of the 3 Diagrams (12 min)
I Do / We Do • 3 × 4 = 12
Deconstruct the 3 models on the pre-charted anchor chart. Have students track along with their finger and label G, S, and T:
1. Grouping Diagram
Definition: Circling objects into equal groups.
Script: "Draw 3 large circles for 3 groups (G). In each circle, draw 4 objects for group size (S). Count: 4, 8, 12. Total is 12 (T)!"
2. Tape Diagram
Definition: A strip of tape partitioned into equal boxes.
Script: "Draw one strip of tape. Break it into 3 equal boxes (G). Put 4 dots in each box (S). Bracket the total as 12 (T)."
3. Number Line
Definition: Skip counting by the size of each group from zero.
Script: "Start at 0. Make 3 jumps (G) of 4 units each (+4, S). Jumps land at 4, 8, 12 (T). Distance from 0 is our product!"
Unit 2, Day 5 Modified • Resource Room Teacher Guide Page 1 of 2
Phases 3 & 4: Guided Practice, Monitoring, & Discourse
Small Group Execution
3 Phase 3: Scaffolded Student Practice & Procedural Laps (12 min)
Worksheet Practice
Students complete partially scaffolded diagrams. Conduct rapid targeted laps around the small group table:
Lap 1: Check GST Labeling
Prompt: "Point to your number sentence. Did you write G, S, and T above the numbers? Which number tells you how many groups to draw?"
Lap 2: Check Diagram Structure
Prompt: "Count your groups out loud. Do you have equal items in every group? Show me your skip count or jump labels (+4, +4...)."
Resource Room Error Bank & Mini-Stamps
Error 1: Inverts Groups & Size (Draws 4 groups of 3 instead of 3 groups of 4)
Questioning: "Look at \(3 \times 4\). What does the first factor represent? (Groups). How many groups do we need? (3). How many items in each? (4)."
Mini-Stamp: "The first factor represents the number of groups. The second factor represents the size of each group."
Error 2: Unequal Groups or Uneven Jumps
Questioning: "Count the dots in box 1. Now count box 2. Are they equal? Can we use multiplication if the groups are not equal?"
Mini-Stamp: "Multiplication can only be used to represent groups that have an equal number in each group."
Error 3: Jumping by 1s on Number Line instead of Group Size
Questioning: "How big should each jump be? Each jump is one whole group! Label the top of each jump with +S (+4)."
Mini-Stamp: "Multiplication models show equal groups. On a number line, each jump is the size of one group."
4 Phase 4: Targeted Discourse & Stamp It! (8 min)
Synthesis & Exit Check
Compare Representations Prompt: "Hold up your tape diagram and your grouping diagram for \(4 \times 5\). Where do you see the 4 groups in the tape diagram? (4 boxes). Where do you see the 4 groups in the grouping diagram? (4 circles). How are they the same?"
Final Lesson Stamp (Have all students chant together):
"Equal groups and multiplication number sentences can be modeled using grouping diagrams, tape diagrams, or number lines, as long as there is a number of groups with an equal number in each group!"
Resource Room Accommodations Built-In:
Pre-drawn circle & tape outlines
GST visual reminder boxes
High visual spacing for motor control
Unit 2, Day 5 Modified • Resource Room Teacher Guide Page 2 of 2
Multiplication Models Student Worksheet
Modeling Multiplication with Pictures & Diagrams
Resource Room Math • Unit 2, Day 5 Modified
Name:
Date:
Key Words & The G-S-T Rule Remember: "Times" means "Groups of"
G
1st Factor
Number of Groups
×
S
2nd Factor
Size of Each Group
=
T
Product
Total in All Groups
Quick Check: Look at the multiplication sentence 3 × 4 = 12
G (Groups) =
S (Size of each) =
T (Total) =
Guided Step-by-Step: 3 Ways to Model 3 × 4 = 12
3 groups of 4 = 12
1. Grouping Diagram Action: Circle objects into equal groups
The 3 groups are drawn. Draw 4 dots in the last circle, then write the count below:
4
4
2. Tape Diagram Action: Break tape into equal boxes
The tape has 3 equal boxes (G). Draw 4 dots in the last box and label the Total (T):
Total (T) =
3. Number Line Diagram Action: Skip count from 0 by the size (+4)
Trace the first two jumps of +4. Draw the 3rd jump of +4 to reach the total:
+4 +4 +4 ? 0 4 8 12
Unit 2, Day 5 Modified • Student Practice Page 1 Keep this reference sheet for Page 2!
Practice & Quick Check: Modeling Multiplication
Step-by-step models for equal groups
Independent / Partner Practice
Problem 1: Model the Sentence 4 × 5 = 20
G =
S =
T =
A. Grouping Diagram (4 groups of 5)
Draw 5 dots in each circle. Write size below:
5
5
B. Tape Diagram (4 boxes of 5)
Write 5 in each box. Label total on top:
Total = [ ]
5
5
C. Number Line Diagram (4 jumps of +5)
Draw 4 jumps of +5 starting at 0. Label each jump (+5):
0 5 10 15 20
Problem 2: Look at this diagram. Write the matching number sentences:
Total = 18
6
6
6
Groups (G) = | Size of each (S) =
