Factory Line: GCF, LCM, Decimals & the Distributive Property
Standard 6.NS.B.2-4 · Grade 6 Math
You are the line manager at the Factory Line packing plant. Use
factors, multiples, and decimal math to pack every order with no
leftovers and no mistakes.
Learning Target
I can find the greatest common factor (GCF) of two whole numbers and use it to rewrite sums with the distributive property (6.NS.B.4).
I can find the least common multiple (LCM) of two whole numbers to solve real-world problems (6.NS.B.4).
I can add, subtract, multiply, and divide multi-digit decimals fluently (6.NS.B.2–3).
Standards: 6.NS.B.2, 6.NS.B.3, 6.NS.B.4Estimated Time: 50–60 minutesMaterials: This page, pencil/paper for factor lists, calculator (optional for decimals)Product: Factory Line Report (4 answers with work shown) + saved quiz PDF/DOC
Teacher Notes (not printed in student view)
Pacing
Key Words + Introduction: ~8 min | Process / game phase: ~20 min | Report writing: ~12 min | Self-Check: ~8 min | Quiz + Reflection: ~10 min. For classes new to the distributive property with GCF, add 5–8 minutes to the Process phase and do a live example together before students work independently.
Grouping
Works well individually or in pairs. Pairs should both write their own reports. For small groups (3–4), assign each student one concept (GCF, LCM, distributive property, decimals) to become the "expert" and teach the others.
Differentiation — Support
Provide a blank factor-pair T-chart for students to list factors of each number side-by-side to find GCF visually.
Provide a hundreds/times chart or allow calculator use for decimal multiplication.
Pre-highlight the Key Words section and have students read it aloud before starting.
Reduce the report to 2 items (GCF + decimal) for students working below grade level.
Differentiation — Challenge
Challenge: "Write an expression using the distributive property with the GCF of 30 and 45, then verify it equals the original sum."
Ask: "A factory restocks two machines at different intervals. Machine A restocks every 8 days; Machine B every 12 days. If they both restock today, when is the next time they restock on the same day?" (LCM = 24)
Have students create their own real-world GCF or LCM word problem, solve it, and write the answer key.
ESOL / Language Supports
Key sentence frames: "The GCF of ___ and ___ is ___ because ___." | "The LCM of ___ and ___ is ___ because ___." | "I rewrote ___ + ___ as ___ × ( ___ + ___ )."
The Key Words section (section 2) uses plain definitions with numeric examples — review it together before assigning the process.
Post a decimal-alignment visual (place value chart) at the front of the room.
Allow home-language computation notes alongside English explanations.
Assessment Notes
The Self-Check section gives instant formative feedback on GCF, LCM, and distributive property. The NTKit quiz covers all four skills and can be saved as PDF/DOC. Use the rubric (section 7) to score the written Factory Line Report.
1. Introduction
Welcome to the Factory Line! A packing plant must put
items into boxes the smart way. You will think like a line manager and
ask:
What is the biggest equal group I can make? When will two machines
finish at the same time? What is the total cost in dollars and cents?
In this WebQuest you will use the
greatest common factor (GCF), the
least common multiple (LCM), the
distributive property, and
decimal operations (add, subtract, multiply, divide)
to keep the line running.
2. Key Words
Read these first. You will use them throughout the WebQuest.
Factor — a number that divides another number with no leftover. Factors of 12: 1, 2, 3, 4, 6, 12.
Greatest Common Factor (GCF) — the biggest factor that two numbers share. GCF of 12 and 18 = 6.
Multiple — a number you get by counting by another number. Multiples of 4: 4, 8, 12, 16…
Least Common Multiple (LCM) — the smallest multiple that two numbers share. LCM of 4 and 6 = 12.
Distributive Property — pull out the GCF, then write the sum as a product. Example: 12 + 18 = 6 × (2 + 3).
Decimal — a number with a point, like 4.75. Line up the decimal points when you add or subtract.
3. Your Task
By the end you will build a short
Factory Line Report that shows:
One GCF you found (the biggest equal group of two item amounts).
One LCM you found (when two machines line up again).
One distributive property rewrite using the GCF (example: 12 + 18 = 6 × (2 + 3)).
One decimal total (add or multiply money amounts).
Then you will complete the Self-Check questions and the
Check Your Understanding quiz, and save it with your
name as a PDF or DOC.
Deliverable: Written Factory Line Report (4 answers with work shown) + saved quiz PDF/DOC with your name.
4. Process — Follow the Steps
Find a GCF. List the factors of each number. Circle
the biggest one they share. Example: 12 = (1,2,3,4,6,12), 18 =
(1,2,3,6,9,18). Shared biggest = 6. This is the
biggest equal group with no leftovers.
Find an LCM. Count by each number until you hit the
same number. Example: 4 → 4,8,12; 6 → 6,12. First match =
12. This tells you when two machines finish together.
Use the distributive property. Pull out the GCF.
Example: 12 + 18. The GCF is 6, so 12 + 18 = 6 × (2 + 3) =
30.
Do decimal money math. Line up the decimal points
to add or subtract. To multiply, multiply like whole numbers, then
count decimal places. Example: 3 boxes × $4.25 =
$12.75.
Play the game. Open
Unit 4 — Factory Line (link below). Pack the orders by
choosing the right GCF, LCM, and decimal totals.
Write your report. Write your four answers from the
Task section. Show your work for each.
Self-Check your knowledge. Try the three practice
questions below — get instant feedback before the real quiz.
Take the quiz. Type your name in the top bar,
answer the 6 quiz questions, click Check My Answers, then
Save as PDF or DOC.
ESOL tip: "Greatest" = biggest. "Least" = smallest.
"Factor" = divides evenly. "Multiple" = skip-count. Keep the decimal
point in a straight line.
Answer each question, then click Check to see if you are right. You get instant feedback and a hint. These do not count toward your final grade.
List factors of each number. Find the biggest one they share. Type a number only.
Skip-count by 3 and by 5 until you hit the same number. Type a number only.
GCF of 20 and 30 is 10. Divide: 20 ÷ 10 = 2, 30 ÷ 10 = 3. What is 2 + 3? Type a number only.
7. Evaluation — How You Are Graded
Factory Line Rubric — 4 Levels
Skill
4 — Manager
3 — On Track
2 — Slow Line
1 — Restart
GCF
Correct GCF with factor lists for both numbers shown; biggest shared factor identified.
Correct GCF; factor list for one number shown.
Attempted; minor error (found a common factor but not the greatest).
Not attempted or GCF concept missing.
LCM
Correct LCM with skip-counting or multiples list for both numbers shown.
Correct LCM; one list of multiples shown.
Attempted; minor error (found a common multiple but not the least).
Not attempted or LCM concept missing.
Distributive Property
Correctly rewrites sum as GCF × (a + b) with GCF identified and both quotients shown.
Correct rewrite; GCF identified.
Attempted; error in one quotient or GCF choice.
Not attempted or property misapplied.
Decimal Operations
Correct decimal answer; decimal points aligned or place values tracked; label included.
Correct decimal answer; minor label missing.
Attempted; one place-value or alignment error.
Not attempted or decimal point misplaced throughout.
Quiz Score
6 of 6 correct.
4–5 of 6 correct.
3 of 6 correct.
2 or fewer correct.
8. Check Your Understanding
Type your name in the bar at the top first. Answer all 6. Then click
Check My Answers.
Your score and results appear in the panel at the top. Use
Save as PDF or Save as DOC there to
turn in your work.
9. Reflection
Think about what you learned in this WebQuest. Write 2–3 sentences to answer:
How does finding the GCF help a packing line manager (or anyone splitting things into equal groups) in real life?
What was the hardest concept — GCF, LCM, the distributive property, or decimals? What strategy helped you the most?
Deliverable reminder: Submit your Factory Line Report (4 answers with work shown) AND save this quiz page as a PDF or DOC with your name before turning in.
10. Conclusion
Great work, line manager! You used the GCF and
LCM, the distributive property, and
decimal operations to pack every order with no
leftovers. These same skills help in real life: splitting items into
equal groups, planning when two events line up, and adding up money at
the store.
Next shift: keep practicing in the Factory Line game to pack faster
with zero mistakes.
Neft Teacher · Grade 6 Math · Unit 4 · 6.NS.B.2-4
🔒 Teacher Answer Key — click to expand (do not share with students)
Self-Check Answers
SC Q1:12. (Factors of 24: 1,2,3,4,6,8,12,24. Factors of 36: 1,2,3,4,6,9,12,18,36. GCF = 12.)
SC Q2:15. (Multiples of 3: 3,6,9,12,15. Multiples of 5: 5,10,15. LCM = 15.)
GCF: "Factors of 12: 1,2,3,4,6,12. Factors of 18: 1,2,3,6,9,18. GCF = 6. I can pack 6 items per group with no leftovers."
LCM: "Multiples of 4: 4,8,12. Multiples of 6: 6,12. LCM = 12. The two machines will finish at the same time every 12 minutes."
Distributive Property: "12 + 18 = 6 × (2 + 3) = 6 × 5 = 30. I pulled out the GCF (6) and divided each part."
Decimal Total: "3 × $4.25. I multiplied 3 × 425 = 1275, then placed the decimal point 2 places from the right: $12.75."
Sample Reflection (strong response)
"Finding the GCF helps a packing manager split items into equal groups with no leftovers — like dividing 12 red and 18 green apples into bags of 6. The hardest part was the distributive property because I had to remember to divide both numbers by the GCF. Writing out the factor lists step-by-step helped me the most."