Operation Detectives Demonstration of Learning
OPERATION DETECTIVES
Demonstration of Learning • TEKS 3.5(B)
Name:
Date:
Score: / 4
Standard: 3.5(B) Represent and solve 1- and 2-step multiplication & division problems within 100 using strip diagrams, arrays, and equations.
Independent Work • 10 min
1
STRIP DIAGRAM MODELING (STAAR Format)
1 Point
Marcus baked 4 batches of cookies. There were 8 cookies in each batch. Then, his family ate 6 cookies. Which strip diagram represents \(c\), the number of cookies Marcus has left?
A Model A
8
8
8
8
6
\(c\) cookies
B Model B
8
8
8
8
6
\(c\)
C Model C
6
6
6
6
8
\(c\)
D Model D
32 cookies
\(c\)
\(c\)
\(c\)
6
2
ARRAY MODELING & EQUATIONS WITH UNKNOWNS
1 Point
Coach Davis organized 36 soccer cones into 4 equal rows for agility practice. He uses the letter \(c\) to represent the number of cones in each row.
Part A: Write a multiplication equation with the letter \(c\) to model this problem:
Part B: Write a division equation that can be used to solve for \(c\):
3
TWO-STEP PROBLEM SOLVING WITHIN 100
2 Points (1 pt Model, 1 pt Answer)
The art teacher bought 6 packs of paintbrushes. Each pack had 5 paintbrushes. Then, she gave 12 paintbrushes to the fifth-grade class. How many paintbrushes does the art teacher have left?
Step 1: Total Paintbrushes (Pack × Brushes)
Show work / equation:
Total = ________
Step 2: Remaining Paintbrushes (Total − Given Away)
Show work / equation:
Left = ________
Final Answer Statement:
The art teacher has paintbrushes left.
Mastery Gauge:
[ 4/4 • Mastered ] [ 3/4 • Proficient ] [ 2/4 • Approaching ] [ 0-1 • Reteach ]
Strategy used:
▢ Strip ▢ Array ▢ Equation
Operation Detectives Teacher Guide
TEACHER SCORING & DIAGNOSTIC GUIDE
TEKS 3.5(B) Readiness Standard • Demonstration of Learning
STAAR Reporting Cat 2
Target Mastery: ≥ 75% (3 of 4 pts)
Standard Deconstruction & Success Criteria
Rigor Level: DOK 2-3
What TEKS 3.5(B) Requires: Students must both represent (using strip diagrams, arrays, and equations with unknown letters) and solve one- and two-step multiplication and division problems within 100. Mastery requires moving beyond basic facts to interpreting structural relationships between equal parts and wholes.
Exemplar Key & Point Allocation (Total: 4 Points)
Q1
Correct Answer: Model B 1 Point
Top bar shows the 4 batches of 8 cookies (\(4 \times 8 = 32\)). Bottom bar splits the 32 into 6 eaten cookies and the remaining unknown \(c\) cookies (\(32 = 6 + c\)).
Q2
Correct Equations: \(4 \times c = 36\) and \(36 \div 4 = c\) (or \(c = 9\)) 1 Point
Full credit requires using the variable \(c\) (or student-defined symbol) showing the inverse relationship between multiplication and division.
Q3
Step 1: \(6 \times 5 = 30\) • Step 2: \(30 - 12 = 18\) paintbrushes 2 Points
1 point for correctly representing/solving the hidden question (total = 30). 1 point for subtracting 12 and writing the final answer: 18.
Diagnostic Misconceptions & What They Reveal
Additive Model Trap (Q1: Chose A)
Student Thinking: Student added 6 instead of subtracting because both quantities are combined in the bottom bracket.
Fix: Annotate "eaten = part removed from whole".
One-and-Done Error (Q3: Answered 30)
Student Thinking: Solved Step 1 (\(6 \times 5 = 30\)) and stopped without addressing the second operation.
Fix: Use two-color highlighting for each step.
Missing Variable (Q2: Used numbers only)
Student Thinking: Writes \(4 \times 9 = 36\) instead of using the letter \(c\) for the unknown quantity.
Fix: Teach that letters act as "placeholders for mystery numbers".
Next-Day Action Plan (Data-Driven Groups)
10-Minute Small Group Protocol
Score 3-4 (Mastered)
Student writes their own 2-step word problem and drafts the matching strip diagram & equation with a variable.
Score 2 (Approaching)
Guided practice with strip diagram sorting cards: match verbal scenarios to part-part-whole vs equal-group models.
