The Snack Pack Factory
The factory floor runs on three kinds of number sense: long division for the big pallet counts, decimal arithmetic for the invoices, and GCF/LCM for pack sizes and truck schedules — with the distributive property packing 36 + 24 into 12(3 + 2).
Common Core standards covered
- 6.NS.B.2Fluently divide multi-digit numbers using the standard algorithm.
- 6.NS.B.3Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.
- 6.NS.B.4Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1–100 with a common factor as a multiple of a sum of two whole numbers with no common factor. For example, express 36 + 8 as 4(9 + 2).
© Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved.
Teacher-facing overview
Big idea: Fluently divide multi-digit numbers and operate on multi-digit decimals with the standard algorithms; find GCF and LCM; use the distributive property to express a sum with a common factor as a multiple of a sum.
Student target: “I can compute multi-digit quotients and decimal results with the standard algorithms, find GCF and LCM with meanings attached, and rewrite a common-factor sum in distributive form.”
Success criteria: I can run long division on multi-digit numbers and check by multiplying back. · I can add, subtract, multiply, and divide decimals with the point placed by reasoning. · I can find GCF (biggest equal grouping) and LCM (first alignment) and say which a problem wants. · I can express a sum like 36 + 24 as GCF × (sum with no common factor).
Essential question
Equal packs with nothing left over, trucks that arrive together, invoices to the cent — what do factors, multiples, and place value each control?
Learning target: I can compute multi-digit quotients and decimal results with the standard algorithms, find GCF and LCM with meanings attached, and rewrite a common-factor sum in distributive form.
Success criteria
- I can run long division on multi-digit numbers and check by multiplying back.
- I can add, subtract, multiply, and divide decimals with the point placed by reasoning.
- I can find GCF (biggest equal grouping) and LCM (first alignment) and say which a problem wants.
- I can express a sum like 36 + 24 as GCF × (sum with no common factor).
Why this matters
6.NS.B is the fluency backbone of middle school: long division powers the decimal conversions of Grade 7, decimal operations price everything from Food Truck Friday onward, and GCF/LCM are the first taste of number STRUCTURE — the distributive identity 36 + 24 = 12(3 + 2) is the exact move that becomes factoring expressions in Unit 7 and beyond. Estimation-first keeps every algorithm honest.
Students should already be able to
- Multiplication facts and multi-digit multiplication.
- Whole-number division with remainders.
- Decimal place value.
Vocabulary to define explicitly
- Greatest common factor (GCF)
The largest number dividing both — the biggest equal grouping.
Example: GCF(36, 24) = 12: twelve identical packs, none left over.
Not an example: 12 is not a factor 'of the pair's sum' — it divides EACH number separately.
🔒 3 more terms with examples and non-examples — Least common multiple (LCM), Distributive form, Place-value reasoning — are defined in the full lesson. See plans →
Where this shows up outside the classroom
Assessment plan
Formative — for feedback during the lesson
- Warm-up option hunt.
- Board estimates and checks.
- The third-item extension.
Summative — the graded evidence: The exit ticket (division, GCF+identity, LCM, decimal product), scored with the four-criterion rubric.
The task students work on
The Snack Pack Factory ships fair snacks. THE PACKING LINE: 36 granola bars and 24 fruit bars into identical packs, nothing left — all options, then the biggest, then the packing written as a distributive identity. THE PALLET COUNT: 8,568 bars arrive in cases of 24 — how many cases? THE TRUCK SCHEDULE: the granola truck comes every 6 days, the fruit truck every 8 — when do they meet again? THE INVOICE DESK: 2.5 kg of nuts at $3.20/kg; a $84.50 balance minus a $37.25 payment; four labels at $19.75; a $91.80 order split across 12 packs. Estimate first at every desk.
Factory board — estimate before algorithm.
| Station | Job | Estimate | Exact |
|---|---|---|---|
| Packing | GCF(36, 24) and the pack contents | ||
| Packing | distributive form of 36 + 24 | ||
| Pallet | 8,568 ÷ 24 | ||
| Schedule | LCM(6, 8) | ||
| Invoices | 2.5 × 3.20; 84.50 − 37.25; 19.75 × 4; 91.80 ÷ 12 |
Anticipated student strategies
Complete listings build the GCF/LCM meanings, estimates anchor the algorithms, and the distributive identity ties structure to the packing everyone just did.
- Factor-pair listing. The student lists factor pairs of both numbers and circles common ones: 1, 2, 3, 4, 6, 12.
The complete route — every common pack size appears, and the greatest gets crowned rather than guessed.
🔒 2 more anticipated strategies with select-and-sequence guidance are in the full lesson. See plans →
Lesson script
Common factors: 1, 2, 3, 4, 6, 12. Twelve packs is the champion — GCF. Each pack: 36÷12 = 3 granola, 24÷12 = 2 fruit. Name the meaning: GCF is the biggest equal grouping.
Listen for: Leftovers appear the moment either bar type doesn't split evenly — 'common' is the requirement, 'greatest' is the choice.
Long division narrated place by place — how many 24s in 85 (3), in 136 (5), in 168 (7).
- Factored form: GCF outside, no common factor left inside.
- Estimate brackets the quotient before the algorithm speaks.
Listen for: If it did, the GCF outside wasn't greatest — the inside is the packs' contents reduced completely.
🔒 The remaining 4 steps — fully scripted with teacher-says lines, discourse questions, look-fors, and interventions — are in the full lesson. See plans →
Misconceptions and how to respond
- “GCF of 36 and 24 is 6 — I found a common factor and stopped.” 6 works, but 12 packs also work and are more. GREATEST means the search finishes: list all pairs, or check the inside of your identity shares no factor.
- “LCM(6, 8) = 48 — just multiply.” — the teacher response is in the full lesson.
- “2.5 × 3.20: multiply, then count decimal places — 0.800.” — the teacher response is in the full lesson.
- “12(3 + 2) = 36 + 2.” — the teacher response is in the full lesson.
🔒 Every misconception ships with a tested classroom response. See plans →
Scaffolded practice
The workbook follows gradual release rather than a page of blank prompts: 1 fully worked, 1 partially completed, then 4 independent.
- I doPack 36 granola and 24 fruit bars: all options, the GCF packing, and the distributive identity.
🔒 5 more prompts across all three release tiers are in the full lesson. See plans →
Worked solutions and scaffolds for every prompt are in the downloadable kit, included with membership. See plans and pricing.
Exit ticket
- 1,512 bars in cases of 12: how many cases?
🔒 3 more exit-ticket questions are in the full lesson. See plans →
Worked answers, the completed answer tables, and the scoring rubric are in the downloadable kit, included with membership. See plans and pricing.
Printable handouts in the kit
All handouts are in Printable_Handouts.pdf inside the kit download.
Materials and classroom resources
Student experience
Students enter through a low-floor prompt, build or sketch a model, test a strategy, revise their thinking, collaborate, and present a final solution. The task remains accessible while allowing for sophisticated reasoning.
Detailed facilitation notes
- Step 1: Find all common pack sizes; crown the greatest. Ask: “What do you notice?”, “What could you try next?”, and “How can you prove that?”
- Step 2: Write the packing as a distributive identity. Ask: “What do you notice?”, “What could you try next?”, and “How can you prove that?”
- Step 3: Align the truck schedules with the LCM. Ask: “What do you notice?”, “What could you try next?”, and “How can you prove that?”
- Step 4: Run the invoices: decimal add, subtract, multiply, divide. Ask: “What do you notice?”, “What could you try next?”, and “How can you prove that?”
Differentiation and inclusion
Support: Factor-pair charts scaffold GCF/LCM; extend with the big-pallet division and the three-item packing.
Language support: “I started by…”, “My model shows…”, and “I know my answer is reasonable because…”.
Extension: Require a second solution, alter a condition, or have students write a challenge for another group.
Accessibility: Manipulatives, enlarged visuals, oral response choices, partner reading, and reduced-copy student pages.
Assessment plan
Formative checks: Strategy choice, accuracy, representation, collaboration, and explanation.
End evidence: One GCF packing with its distributive form, one LCM schedule, and one multi-step decimal invoice.
Mastery: The student completes the task accurately and explains the strategy with limited prompting.