Factor Detectives

Detective Blueprint:

1. Find GCF of both addends  |  2. Factor it out  |  3. Divide each addend by GCF for inside the parentheses

\(18 + 24 = 6(3 + 4)\)

15 + 35

Step 1: GCF(15, 35) = ______

Step 2: Division:

15 ÷ GCF = ___ , 35 ÷ GCF = ___

Factored Form:

___ ( ___ + ___ )

28 + 42

Step 1: GCF(28, 42) = ______

Step 2: Division:

28 ÷ GCF = ___ , 42 ÷ GCF = ___

Factored Form:

___ ( ___ + ___ )

48 + 32

Step 1: GCF(48, 32) = ______

Step 2: Division:

48 ÷ GCF = ___ , 32 ÷ GCF = ___

Factored Form:

___ ( ___ + ___ )

Case File: The Mystery Snack Pack Distribution

REAL WORLD

Detective Jordan is packing identical evidence snack kits for the middle school detective squad. Jordan has 24 granola bars and 36 juice boxes. Every kit must contain the exact same items with none left over.

A. What is the greatest number of identical kits Jordan can make?

Answer: ________ kits

B. How many granola bars and juice boxes go in EACH kit?

Bars: ____   Juices: ____

C. Write an expression representing the total using GCF & Distributive Property:

24 + 36 = ___ ( ___ + ___ )

Factor Detectives Case Complete • Check all work before turning in! Page 2 of 2

Common Misconceptions & Coaching Strategies

Trap 1: The Number 1

Students often label 1 as prime. Coaching: Stress that primes have exactly two distinct factors (1 has only 1 factor: itself).

Trap 2: Premature Stopping

Students stop factor trees at composite numbers (e.g., circling 9 or 4). Coaching: Teach students to ask: "Can this leaf split?"

Trap 3: Incomplete GCF

For \(24 + 36\), students pull out 6: \(6(4 + 6)\). Coaching: Check numbers inside! 4 and 6 still share 2. GCF must leave no common factors.

Factor Detectives Facilitation Guide • NC.6.NS.4 Page 1 of 2: Pacing & Pedagogy

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TEACHER GUIDE: DIFFERENTIATION & COMPLETE ANSWER KEYS

NC.6.NS.4 Official Keys

Multi-Tier Differentiation Strategies

Tier 1: Scaffolding (IEP / ELL)

Provide a multiplication grid and prime checklist (2, 3, 5, 7, 11, 13, 17, 19). Use 2-color counters to build physical rectangular arrays for factor pairs.

Tier 2: On-Target Support

Encourage students to always verify factor trees using inverse multiplication: multiply the prime ends together to see if they rebuild the starting number.

Tier 3: Early Finishers / Extensions

Challenge students to find the GCF of three numbers (e.g., GCF of 24, 36, and 60) and rewrite \(24 + 36 + 60 = 12(2 + 3 + 5)\). Explore Twin Primes.

1. Vocabulary Dossier Quick Check & Warm-Up Keys Handout & Vocab

Warm-Up (Worksheet P1): 19 is Prime; 21 is Composite (\(3 \times 7\)); 31 is Prime; 45 is Composite (\(5 \times 9\)).

Vocab Quick Check: 1. 17 has only factors 1 & 17; 27 has factors 1, 3, 9, 27.  |  2. \(18 = 2 \times 3^2\)  |  3. \(\text{GCF}(12, 18) = 6\).

2. Student Worksheet Page 1 Keys (Factor Trees & T-Charts) Worksheet P1

Tree 48: Expanded: \(2 \times 2 \times 2 \times 2 \times 3\)  |  Exponents: \(2^4 \times 3\)

Tree 54: Expanded: \(2 \times 3 \times 3 \times 3\)  |  Exponents: \(2 \times 3^3\)

Tree 72: Expanded: \(2 \times 2 \times 2 \times 3 \times 3\)  |  Exponents: \(2^3 \times 3^2\)

T-Chart Factors of 20: Pairs: \(1 \times 20, 2 \times 10, 4 \times 5\).
List: { 1, 2, 4, 5, 10, 20 }

T-Chart Factors of 32: Pairs: \(1 \times 32, 2 \times 16, 4 \times 8\).
List: { 1, 2, 4, 8, 16, 32 }

3. Student Worksheet Page 2 Keys (GCF & Distributive Property) Worksheet P2

GCF(28, 42): 28: {1,2,4,7,14,28}; 42: {1,2,3,6,7,14,21,42} ➔ GCF = 14

GCF(36, 60): \(36 = 2^2 \times 3^2\); \(60 = 2^2 \times 3 \times 5\) ➔ Shared: \(2^2 \times 3\) ➔ GCF = 12

Rewrite 15 + 35: \(\text{GCF} = 5\) ➔ \(5(3 + 7)\)

Rewrite 28 + 42: \(\text{GCF} = 14\) ➔ \(14(2 + 3)\)

Rewrite 48 + 32: \(\text{GCF} = 16\) ➔ \(16(3 + 2)\)

Mystery Snack Pack: A. 12 kits  |  B. 2 granola bars, 3 juices  |  C. \(24 + 36 = 12(2 + 3)\)

4. Exit Ticket Official Answer Key Formative Check

1. Factor Tree (40):
\(40 = 2 \times 2 \times 2 \times 5 = \mathbf{2^3 \times 5}\)

2. GCF(18, 30):
Factors of 18: {1,2,3,6,9,18}
Factors of 30: {1,2,3,5,6,10,15,30}
GCF = 6

3. Distributive Rewrite (21 + 35):
\(\text{GCF}(21, 35) = 7\)
Factored form: \(7(3 + 5)\)

Factor Detectives Facilitation Guide • NC Standard NC.6.NS.4 Complete Resource Page 2 of 2: Keys & Support