Unit 4 · 6.NS.B.2–4

Factory Line: GCF, LCM, Decimals & the Distributive Property

Work on the Factory Line. Package the order by finding factors, multiples, and clean decimal answers.

Learning Target

I can find the Greatest Common Factor (GCF) of two whole numbers.
I can find the Least Common Multiple (LCM) of two whole numbers.
I can add, subtract, and multiply decimals with accuracy.
I can use the Distributive Property to rewrite and solve multiplication expressions.

Standard: CCSS 6.NS.B.2–4 Estimated time: 45–55 minutes Materials: This page, pencil or scratch paper, calculator (optional for check) Branding: Neft Teacher

🍎 Teacher Notes (click to open)

Pacing

Suggested flow: Engage 5 min → Explore 10 min (game/hub) → Explain 12 min → Apply 15 min → Reflect 5 min. Total ≈ 47–55 min.

Grouping

Whole class: Engage — pose the factory problem, take quick guesses before revealing GCF.
Pairs or small groups: Explore links; students can compare what they noticed in the 3D game.
Individual: Explain reading, Apply self-check and graded practice, Reflect writing.

Differentiation — Support

Provide a factor rainbow or T-chart graphic organizer for listing factors (GCF).
Allow a hundreds chart for students who struggle with skip-counting (LCM).
For decimal operations, use graph paper to help students line up place values.
Pair during the Self-Check; encourage think-aloud before selecting an answer.

Differentiation — Challenge

Ask students to find GCF and LCM for three numbers simultaneously (e.g., 12, 18, 24).
Extension: use the Distributive Property to multiply a two-digit decimal (e.g., 3 × 4.7).
Have students write a real-world problem that requires LCM (e.g., scheduling repeating events).

ESOL / Language Supports

Vocabulary list (Explain section) uses plain language — reference it explicitly during whole-class instruction.
GCF vs. LCM: use a memory anchor — "G is for Greatest, so we find the BIG shared factor; L is for Least, so we find the SMALL shared multiple."
Sentence frames for Reflect: "I use GCF when ___ because ___." / "The hardest part was ___, and it helped me to ___."
Allow bilingual dictionaries; translate key terms (factor, multiple, decimal) as needed.

1 · Engage

A real factory problem

A factory packs 24 red parts and 36 blue parts. The boss wants equal boxes with no parts left over. Each box must have the same number of red and the same number of blue.

Think: What is the largest number of boxes you can make? You will solve this kind of problem in this unit.

2 · Explore

Open the tools, then come back

Click each link. Play, read, then return to this page to learn and practice.

3 · Explain

Words you need + worked examples

Factor — a number that divides another with no remainder. (1, 2, 3, 4, 6, 12 are factors of 12.)
GCF (Greatest Common Factor) — the largest factor two numbers share.
Multiple — what you get when you skip-count a number. (5, 10, 15, 20 are multiples of 5.)
LCM (Least Common Multiple) — the smallest multiple two numbers share.
Distributive Property — split one factor, then add: a(b + c) = ab + ac.

GCF of 24 and 36

Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
Biggest shared factor → GCF = 12. So the boss can make 12 equal boxes.

LCM of 4 and 6

Multiples of 4: 4, 8, 12, 16…
Multiples of 6: 6, 12, 18…
Smallest shared multiple → LCM = 12.

Decimals + Distributive Property

Add: line up the dots → 1.40 + 0.75 = 2.15
Multiply: 0.4 × 0.3 = 0.12 (count 2 decimal places)
Distribute: 6 × 47 = 6(40 + 7) = 240 + 42 = 282

Rubric How Your Work Is Scored

Level	Score	What it looks like
4 — Expert	5 / 5 graded + clear reflection	All answers correct with accurate GCF, LCM, decimals, and Distributive Property work; reflection clearly explains the difference between GCF and LCM with a specific example.
3 — Proficient	4 / 5 graded + adequate reflection	Most answers correct; minor computational error; reflection shows understanding of when to use GCF vs. LCM.
2 — Developing	2–3 / 5 graded + partial reflection	Some correct answers; confuses GCF and LCM or makes repeated decimal errors; reflection is brief.
1 — Beginning	0–1 / 5 graded	Answers mostly missing or incorrect; little evidence of understanding factors, multiples, or decimal computation.

5 · Reflect

Write your thinking

Think carefully before you write. Use math vocabulary from the Explain section. Write in complete sentences.

A. How do you know when to use GCF instead of LCM? Use your own words. (Sentence starter: "I use GCF when ___ because ___. I use LCM when ___ because ___.")

B. Which part was hardest for you — GCF, LCM, decimals, or the Distributive Property? What helped you understand it? (Sentence starter: "The hardest part was ___, and what helped me was ___.")

Deliverable: When both text boxes are filled in, press Save as PDF or Save as DOC at the top to submit your completed HyperDoc. Your teacher will see your answers, your score, and your reflection.

🔑 Answer Key — Teacher Only

Graded Practice:

GCF of 24 and 36 = 12 (shared factors: 1,2,3,4,6,12)
LCM of 4 and 6 = 12 (4,8,12… and 6,12…)
1.4 + 0.75 = 2.15 (align: 1.40 + 0.75)
0.4 × 0.3 = 0.12 (4×3=12; 2 decimal places → 0.12)
6 × 47 = 6(40+7) = 240+42 = 282

Self-Check: SC-1 = B (6) · SC-2 = B (15) · SC-3 = B (2.45) · SC-4 = C (212)

Reflect sample answers:

A. "I use GCF when I need to split things into the largest equal groups. I use LCM when I need to find when two things will line up at the same time."
B. "The hardest part was decimals. It helped me to always line up the decimal points before adding."