QUEST 01 (Powers of 10) SOLVED
a) \( 12.85 \times 10^2 = \) 1,285
b) \( 340.2 \div 10^3 = \) 0.3402
a) Move decimal 2 positions right.
b) Move decimal 3 positions left.
QUEST 02 (Decimal Sum) SOLVED
\( 23.4 + 1.98 = \) 25.38
23.40
+ 1.98 → 25.38
QUEST 03 (Product) SOLVED
\( 1.45 \times 0.6 = \) 0.87
145 × 6 = 870
Shift decimal 3 spots → 0.870
QUEST 04 (Division) SOLVED
\( 12.6 \div 0.03 = \) 420
Multiply both by 100:
\( 1260 \div 3 = 420 \)
BOSS BATTLE: THE CRYSTAL SHOPPE SOLUTION
In a classic RPG arcade game, each level crystal costs $4.25. If your guild leader buys exactly 12 crystals, and pays with a $100 bill, how much change should they receive?
Workspace Solution: 1. Cost: \(12 \times 4.25 = \$51.00\)
2. Change: \(\$100.00 - \$51.00 = \$49.00\)
Answer: $49.00 Change
MATH LAUNCHPAD ANSWER KEY • GRADE 6 PAGE 2 OF 4
ANSWER KEY
Level 3 Solutions
REWARD: 150 XP
SCORE: 150/150
TOPIC: Multi-Digit Long Division & Remainders ⚡ Division Completed Without Error
POWER-UP: INTERPRETING REMAINDERS GUIDE
1. Round Up (+1)
Need buses or rooms for everyone. (We must round up here!)
2. Keep Fraction
Splitting continuous measures (e.g. food/sand).
3. Drop Remainder
Counting strictly complete packages / full sets.
QUEST 01 (3-Digit ÷ 2-Digit) SOLVED
\( 936 \div 24 \)
24 goes into 93 three times (72). \(93 - 72 = 21\). Bring down 6 → 216.
24 goes into 216 exactly nine times. \(216 - 216 = 0\).
Quotient: 39
QUEST 02 (4-Digit ÷ 2-Digit) SOLVED
\( 2,688 \div 32 \)
32 goes into 268 eight times (256). \(268 - 256 = 12\). Bring down 8 → 128.
32 goes into 128 exactly four times. \(128 - 128 = 0\).
Quotient: 84
BOSS BATTLE: THE DUNGEON BUS SYSTEM
There are 415 players arriving at the final boss event. Each transport bus can safely hold up to 18 passengers.
a) Solve: How many buses are needed so that every single player gets to go?
b) Interpret: Explain why you decided to either round up, drop, or keep the remainder.
Workspace Solution & Interpretation: \(415 \div 18 = 23\) remainder \(1\). Since we cannot leave the last player behind, we must add an extra bus (\(23 + 1 = 24\) buses total).
Explanation: Round up so the 1 remaining player gets a bus!
Buses Needed: 24 buses
MATH LAUNCHPAD ANSWER KEY • GRADE 6 PAGE 3 OF 4
ANSWER KEY
Level 4 Solutions
REWARD: 150 XP
SCORE: 150/150
TOPIC: Unit Cube Volume & 3D Attributes ⚡ Geometry & Spatial Reasoning Solutions
POWER-UP: GEOMETRY FORMULAS
What is Volume?
Measured in cubic units (\(\text{u}^3\)).
Formula: \(V = l \times w \times h\) or \(V = B \times h\)
Rectangular Prism Traits
QUEST 01 (Volume) SOLVED
Find the volume of a chest that is \(8\text{ ft}\) long, \(4\text{ ft}\) wide, and \(3\text{ ft}\) tall.
\(V = 8 \times 4 \times 3\)
\(V = 32 \times 3 = 96\)
Volume: 96 \(\text{ft}^3\)
QUEST 02 (Attributes) SOLVED
A rectangular prism has how many of each?
• Faces: 6
• Edges: 12
• Vertices: 8
QUEST 03 (Unit Cubes) SOLVED
A block tower is made of 4 layers of unit cubes. Each layer has a length of 5 cubes and a width of 3 cubes. Total cubes?
Volume = Layer base area \(\times\) height = \((5 \times 3) \times 4 = 15 \times 4 = 60\)
Total Cubes: 60 cubes
BOSS BATTLE: THE TROPHY SHIELD SOLUTION
The legendary Grand Arcade Trophy is stored in a glass showcase that is exactly \(5\text{ ft}\) tall. The base area of the showcase is \(14\text{ sq ft}\). What is the total volume of the showcase?
Volume = Base Area \(\times\) height = \(14 \times 5 = 70\)
Answer: 70 \(\text{ft}^3\)
MATH LAUNCHPAD ANSWER KEY • GRADE 6 PAGE 4 OF 4
LVL 3 CHALLENGE
How do we interpret a division remainder? Look closely at the context!
🚍 Round Up: If leaving someone/something behind isn't possible (e.g., transport buses).
🍕 Keep Fraction: If resources are shareable/divisible (e.g., pizzas, food).
🎟️ Drop Remainder: If calculating strictly complete units (e.g., tickets, prize packs).
TOPIC: Multi-digit division with remainders MATH WORKBOOK PAGE 3
LVL 4 CHALLENGE
Volume measures the physical 3D space occupied by a shape. It's measured in cubic units!
Key Formulas:
• Volume = length \(\times\) width \(\times\) height
• Volume = Base Area \(\times\) height
Where Base Area (B) = length \(\times\) width
A rectangular prism is defined by flat faces, straight edges, and sharp vertices.
6 Faces
12 Edges
8 Vertices
TOPIC: 3D solids and unit volumes MATH WORKBOOK PAGE 4
FINAL STAGE
THE BOSS QUESTION
If you double the length of a box while keeping the width and height exactly the same, what happens to the total volume of that box?
It doubles! \( (2 \times l) \times w \times h = 2 \times V \)
✔ Fractions Mastered ✔ Decimals Shifted ✔ Long Division Solved
READY FOR PLAYER ASSESSMENT GAME SYSTEM STAT: COMPLETED
SYS_CHECK: ALL LEVELS UNLOCKED XP: 600/600
YOU UNLOCKED GRADE 6 MATH!
📥 Player Next Steps:
• Hand in your 4-page Math Launchpad Workbook.
• Write down your final score on the front page.
• Get ready for an epic year of 6th grade math adventures!
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