Unit 1 · Teacher Resource
Unit 1 Projects — Teacher Answer Key
Worked solutions for both versions of the Unit 1 culminating project (Number Sense). Covers Version A: Block Party Planner and Version B: Build-a-Bot Budget Lab.
🎉 Block Party Planner
Standards: 6.NS.2 • 6.NS.3 • 6.NS.4 • $300 budget scenario
1 Phase 1 — Build Identical Goodie Bags (GCF · 6.NS.4)
| Input | Default Value | Worked Solution | Final Answer |
|---|---|---|---|
| Number of stickers | 48 |
Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36 GCF(48, 36) = 12 Each bag: 48 ÷ 12 = 4 stickers Each bag: 36 ÷ 12 = 3 granola bars |
12 goodie bags (4 stickers + 3 bars each) |
| Number of granola bars | 36 |
2 Phase 2 — Sync the Entertainment Schedule (LCM · 6.NS.4)
| Input | Default Value | Worked Solution | Final Answer |
|---|---|---|---|
| DJ hype song every (min) | 6 |
Multiples of 6: 6, 12, 18, 24, 30 …
Multiples of 8: 8, 16, 24, 32 … First common multiple = 24 Verification: 24 ÷ 6 = 4 (4 songs) ✓ 24 ÷ 8 = 3 (3 bursts) ✓ |
Every 24 minutes |
| Bubble machine every (min) | 8 |
3 Phase 3 — Track the Budget to the Penny (Decimal Operations · 6.NS.3)
| Category | Default Amount | Running Total |
|---|---|---|
| Food & drinks | $124.50 | $124.50 |
| Decorations | $38.75 | $163.25 |
| Games & prizes | $67.20 | $230.45 |
| Music & supplies | $45.00 | $275.45 |
| Total spent |
124.50
38.75 67.20 + 45.00 ────── 275.45 |
|
| Remaining budget | $300.00 − $275.45 = $24.55 remaining ✓ Under budget | |
4 Phase 4 — Set a Fair Price Per Person (Division · 6.NS.2 · 6.NS.3)
| Input | Default Value | Worked Solution | Final Answer |
|---|---|---|---|
| Total shared cost | $275.40 |
$275.40 ÷ 36 guests
36 × 7 = 252 275.40 − 252.00 = 23.40 36 × 0.65 = 23.40 → $7.65 per guest Check: 36 × $7.65 = $275.40 ✓ |
$7.65 per guest |
| Number of guests | 36 |
Check: 6 × 24 = 144 ✓
Sample Expert Written Pitch (Final Deliverable)
"In our block party plan, we will make 12 identical goodie bags because GCF(48, 36) = 12 — each bag holds 4 stickers and 3 granola bars with nothing left over. The DJ and bubble machine will sync up every 24 minutes (LCM of 6 and 8), which is when we should schedule the biggest crowd moment. Our total cost is $275.45 — adding $124.50 + $38.75 + $67.20 + $45.00 — which keeps us $24.55 under the $300 budget. Splitting the $275.40 shared cost among 36 guests gives a fair share of $7.65 per person, and we verified this with the division check: 36 × $7.65 = $275.40."
Sample 4 / 3 / 2 Rubric Scoring Notes
Expert (4) responses demonstrate: GCF and LCM both stated correctly with reasoning shown (e.g., listing factors or multiples); budget total accurate to the penny and explicitly under $300; cost-per-guest calculation shown step by step AND the quick-check (144 ÷ 6 = 24) answered correctly; written pitch names every calculated number with correct units and connects each number to its mathematical operation.
Proficient (3): All four numerical answers correct but written pitch may omit one number or reasoning step.
Developing (2): At least two phases attempted; minor decimal/place-value or factor errors; pitch is present but incomplete.
🤖 Build-a-Bot Budget Lab
Standards: 6.NS.2 • 6.NS.3 • 6.NS.4 • $500 budget scenario
1 Phase 1 — Price the Parts Order (Decimal Multiplication · 6.NS.3)
| Part | Unit Price | Quantity | Worked Solution | Line Total |
|---|---|---|---|---|
| Motor | $18.75 | 4 | $18.75 × 4 = (18 × 4) + (0.75 × 4) = 72.00 + 3.00 = $75.00 | $75.00 |
| Wheel set | $6.40 | 6 | $6.40 × 6 = (6 × 6) + (0.40 × 6) = 36.00 + 2.40 = $38.40 | $38.40 |
| Sensor | $12.25 | 3 | $12.25 × 3 = (12 × 3) + (0.25 × 3) = 36.00 + 0.75 = $36.75 | $36.75 |
| Parts subtotal $75.00 + $38.40 + $36.75 = $150.15
|
$150.15 | |||
2 Phase 2 — Split the Cost Fairly (Division · 6.NS.2)
| Input | Default Value | Worked Solution | Final Answer |
|---|---|---|---|
| Total shared cost | $384.00 |
$384.00 ÷ 8 members
8 × 48 = 384 → $48.00 each Check: 8 × $48.00 = $384.00 ✓ |
$48.00 per teammate |
| Team members | 8 |
3 Phase 3 — Organize the Toolkit (GCF · 6.NS.4)
| Input | Default Value | Worked Solution | Final Answer |
|---|---|---|---|
| Screws | 72 |
Factors of 72: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72
Factors of 54: 1, 2, 3, 6, 9, 18, 27, 54 GCF(72, 54) = 18 Each kit: 72 ÷ 18 = 4 screws Each kit: 54 ÷ 18 = 3 bolts |
18 toolkits (4 screws + 3 bolts each) |
| Bolts | 54 |
4 Phase 4 — Are You Under $500? (Budget Check · 6.NS.3)
| Category | Default Amount | Running Total |
|---|---|---|
| Parts subtotal | $160.75 | $160.75 |
| Travel | $210.50 | $371.25 |
| Snacks | $64.80 | $436.05 |
| Total cost |
160.75
210.50 + 64.80 ────── 436.05 |
|
| Remaining budget | $500.00 − $436.05 = $63.95 remaining ✓ Under $500 budget | |
Check: 6 × 16 = 96 ✓
Sample Expert Written Memo (Final Deliverable)
"Coach, our parts subtotal is $150.15 — calculated by multiplying each unit price by its quantity and adding: $75.00 (motors) + $38.40 (wheels) + $36.75 (sensors). Split among 8 team members, each person owes $48.00 for shared costs of $384.00 (÷ 8 = $48.00). Using GCF(72, 54) = 18, we can build 18 identical toolkits, each containing 4 screws and 3 bolts with no leftovers. Our full trip total is $436.05, which is $63.95 under the $500 budget, so I recommend approving this order."
Sample 4 / 3 / 2 Rubric Scoring Notes
Expert (4) responses demonstrate: All three line totals computed correctly with decimal place value maintained; cost-per-share computed correctly AND verified with a multiplication check; GCF of 72 and 54 correctly identified as 18, with kit contents (4 screws, 3 bolts) stated; full budget total ($436.05) compared explicitly to $500 with the remaining ($63.95) named; memo gives a clear recommendation (approve or revise) and cites every number computed.
Proficient (3): All four numerical results correct; memo uses most numbers but may skip the multiplication check or omit one kit-content detail.
Developing (2): At least two phases attempted; minor decimal or GCF errors; memo present but recommendation is vague or numbers are missing.