Learning Targets

Standards: CCSS 6.NOS.2 · 6.NOS.3 · 6.NOS.4 Time: ~45 min Materials: This activity (device or printed), scratch paper Grade 6
Teacher Notes (not printed)

Pacing

  • Launch (5 min): Read "The Brief" together. Anchor the job: every kit must be identical and nothing may be left over — that is what makes it a GCF problem, not a division problem.
  • Depot work (30 min): Students complete Task 1 → 6 in order. Task 2 needs the factor trees from Task 1, and Task 5 needs the case count from Task 4, so encourage them to check each task before moving on.
  • Debrief (5–10 min): Compare Task 2 (GCF — cutting a total into equal groups) with Task 3 (LCM — waiting for two cycles to line up). Students routinely swap these; the depot context makes the difference concrete.

Differentiation

  • Level 1 (support): Use the green callouts and the bilingual (EN/ES) prompts. The kit packer and the calendar both let students find the answer by trial before computing it — let them, then ask "how could the factor tree have told you that?"
  • Level 2 (enrichment): Use the purple callouts. Ask students to prove the GCF from the two prime factorizations instead of listing factors, and to explain why LCM(6, 8) is 24 and not 48.

Watch for

  • Task 4: students who write 189.58 instead of "189 cases, 14 cans left." Remainders are cans, not decimals — you cannot ship 0.58 of a case.
  • Task 5: lining up decimal points. $19.20 × 189 is a multi-digit decimal product; encourage estimating first (≈ $19 × 190 ≈ $3,610) so a misplaced decimal stands out.

STEM Connection

  • Relief logistics is real applied number theory: packers use GCF to build identical kits, schedulers use LCM to sync deliveries, and buyers use decimal arithmetic to hold a budget. Same five-step cycle engineers use: Sort → Pack → Schedule → Stack → Cost.
Unit 1 · Math Architect · The Number System (6.NOS.2–4)

Supply Challenge: The Riverbend Relief Depot

You are the packing-line engineer at the Riverbend Relief Depot. A storm hit the county, and the depot has to turn a warehouse full of loose supplies into identical family kits, get them on the right trucks, and pay for it all with $4,000.00. Factor it, pack it, schedule it, stack it, and cost it out.

6.NOS.2 · 6.NOS.3 · 6.NOS.4 Prime Factorization GCF & LCM Decimal Budget STEM Design Challenge
1 · SortBreak each count into its prime factors.
2 · PackUse the GCF to build identical kits.
3 · ScheduleUse the LCM to sync two trucks.
4 · StackDivide to fill cases; read the remainder.
5 · CostWork the decimal budget and sign off.
Depot checks passed: 0 / 12

The Brief

This morning's delivery is on the dock: 84 water bottles, 126 granola bars, and 4,550 canned meals. Every family kit must be exactly the same, and nothing may be left over — that is the rule that makes this a factor problem.

Deliverable 1
Build identical kits with no leftovers.
Deliverable 2
Schedule the two supply trucks.
Deliverable 3
Keep the whole order under $4,000.00.
Level 1 · Support

A factor divides a number with nothing left over. A prime number has only two factors: 1 and itself (2, 3, 5, 7, 11 …). Breaking a number into primes tells you every way it can be split into equal groups.

Español: Un factor divide un número sin dejar residuo. Un número primo solo tiene dos factores: 1 y él mismo. Separar un número en primos te dice todas las formas de hacer grupos iguales.

Task 1 · Sort the Inventory Prime factorization

Click a blue number to split it into two factors. Keep splitting until every branch is green — green means prime and cannot be split again.

Factor tree · 84 water bottles
Factor tree · 126 granola bars
84 =not sorted yet
126 =not sorted yet

Q1.1 — Finish both trees. What is the largest prime factor that 84 and 126 share?

Level 1 · Support

Write both prime lists side by side. Circle the primes that show up in both lists. The biggest circled prime is the answer.

Español: Escribe las dos listas de primos. Encierra los primos que aparecen en las dos listas. El mayor de esos primos es la respuesta.

Task 2 · Pack the Family Kits GCF

Use the packer to try a number of kits. The depot needs the greatest number of identical kits with zero bottles and zero bars left over.

Kit packer · 84 bottles · 126 bars
10 kits
Bottles per kit—
Bars per kit—
Left over—
Leftovers on the dock — not allowed.
Bottles: filled ▪ leftover ▫

Q2.1 — What is the greatest number of identical kits?

kits

Q2.2 — Water bottles in each kit?

bottles

Q2.3 — Granola bars in each kit?

bars

Level 1 · Support

GCF = greatest common factor. From Task 1, 84 = 2 × 2 × 3 × 7 and 126 = 2 × 3 × 3 × 7. Multiply the primes they share: 2 × 3 × 7.

Español: El MCD (máximo común divisor) es el producto de los primos que los dos números comparten: 2 × 3 × 7.
Level 2 · Enrichment

Prove it without listing factors: any number of kits must divide both 84 and 126, so it can only be built from the primes both share. Why does that make 2 × 3 × 7 the largest possible?

Task 3 · Schedule the Trucks LCM

Truck A returns every 6 days. Truck B returns every 8 days. Both were at the depot on Day 0. Click the buttons to mark each truck's days, then find the next day they meet.

Delivery calendar · Day 0 to Day 24
Truck A (every 6) Truck B (every 8) Both trucks
Days both trucks are here—

Q3.1 — After Day 0, what is the next day both trucks are at the depot?

Day

Q3.2 — The depot runs for 72 days. Not counting Day 0, how many times do both trucks arrive together?

times

Level 1 · Support

LCM = least common multiple. Count by 6: 6, 12, 18, 24. Count by 8: 8, 16, 24. The first number in both lists is the LCM.

Español: El mcm (mínimo común múltiplo) es el primer número que aparece en las dos listas: cuenta de 6 en 6 y de 8 en 8.
Level 2 · Enrichment

6 × 8 = 48, but the trucks meet on Day 24. Explain why multiplying the two cycles does not always give the LCM. (Hint: look at the prime factors they share.)

Task 4 · Stack the Cases Multi-digit division

4,550 canned meals arrived. A shipping case holds exactly 24 cans. Use the stacker to fill cases, then answer what the depot supervisor needs to know.

Pallet stacker · 4,550 cans ÷ 24 per case
100 cases
Cans packed—
Cans still loose—
Keep stacking — cans are still loose.

Q4.1 — How many full cases can the depot ship?

cases

Q4.2 — How many cans are left loose after the last full case?

cans

Level 1 · Support

The remainder is cans, not a decimal. You cannot ship 0.58 of a case. Multiply your case count by 24 and subtract from 4,550 to find what is left.

Español: El residuo son latas, no un decimal. Multiplica las cajas por 24 y resta de 4,550.

Task 5 · Work the Budget Decimal operations

Each full case costs $19.20. Pallet wrap for the whole order is a flat $5.20. The depot has $4,000.00. Fill in the cost board.

Line item Math Amount
Full cases of canned meals 189 cases × $19.20 Q5.1
Pallet wrap flat charge $5.20
Money left from $4,000.00 $4,000.00 − (cases + wrap) Q5.2

Q5.1 — Cost of the 189 full cases at $19.20 each.

$

Q5.2 — Add the $5.20 wrap, then subtract from $4,000.00. How much is left?

$

Q5.3 — A case is $19.20 for 24 cans. What does one can cost?

$

Level 1 · Support

Estimate first, then compute. $19.20 is about $19, and 189 is about 190, so the answer should land near $3,600. If your answer is $362 or $36,000, your decimal point moved.

Español: Primero estima. $19 × 190 ≈ $3,600. Si tu respuesta está muy lejos, el punto decimal está mal colocado.
Level 2 · Enrichment

With the $366.00 left over, how many more full cases could the depot buy at $19.20 each — and how much would still be unspent?

Task 6 · Write the Order Slip Distributive property

The order slip lists 84 bottles + 126 bars. Rewrite it as one multiplication using the number of kits. Tap a factor to pull it out front.

84 + 126 = ? × ( ? + ? )

Q6.1 — Using the greatest common factor, complete: 84 + 126 = 42 × ( ___ )

Level 1 · Support

Divide each part by 42: 84 ÷ 42 = 2 and 126 ÷ 42 = 3. Put those inside the parentheses and add them. Check it: 42 × 5 = 210, and 84 + 126 = 210.

Español: Divide cada parte entre 42: 84 ÷ 42 = 2 y 126 ÷ 42 = 3. Suma esos números dentro del paréntesis.

Packing-Line Engineer's Sign-off

When every depot check passes, submit your supply plan. Enter your name in the field below, then press Submit plan & grade to save your score as a PDF or DOC.

Performance Rubric — The Number System (6.NOS.2–4)

Level Score Descriptor
4 — Exceeds 11–12 / 12 Builds both prime factorizations and uses them to justify the GCF and LCM rather than guessing. Divides accurately, explains the remainder as cans, holds the decimal budget, and rewrites the sum with the distributive property.
3 — Meets 9–10 / 12 Finds the GCF, the LCM, the case count, and the budget totals with at most one arithmetic slip. Distinguishes GCF from LCM correctly.
2 — Approaching 5–8 / 12 Completes factor trees and simple division but confuses GCF with LCM, or reports the remainder as a decimal. Partial budget work.
1 — Beginning 0–4 / 12 Few correct answers. Needs reteaching on prime factorization and on what "nothing left over" means. Re-run Tasks 1 and 2 with the Level 1 supports.