A hands-on 5th-grade mathematics lesson where students act as freight logistics engineers to model, calculate, and optimize rectangular prism volume using unit cubes and formulas.
Always label volume with cubic units (\(\text{m}^3, \text{ft}^3, \text{cm}^3\))!
Advanced Cargo 05 / 07
Composite Crates: Decompose to Conquer
When cargo containers are welded or stacked into L-shapes, follow the 3-step blueprint method:
1
Slice It
Draw a line to split the composite solid into 2 distinct right rectangular prisms: Prism A & Prism B.
2
Calculate Both
Identify the separate dimensions for each prism. Compute: \(V_A = l_A \times w_A \times h_A\) \(V_B = l_B \times w_B \times h_B\)
3
Combine Total
Add the volumes together to find total cargo space: \(V_{\text{total}} = V_A + V_B\)
Pro Tip: Whether you slice horizontally or vertically, the total volume remains identical!
Hands-On Protocol 06 / 07
Freight Station Protocol
Team Responsibilities
• Blueprint Drafter: Sketches layers and records dimensions.
• Cargo Loader: Packs physical unit cubes onto the freight grid.
• Quality Inspector: Verifies formula calculation and units.
Mission Objectives
1. Build Bay 1 & Bay 2: Match the blueprint specifications.
2. Record Base & Layers: Complete the logistics table.
3. Double-Deck Challenge: Pack and decompose the composite crate.
Cubes must touch face-to-face with no overhangs or internal gaps!
Mission Debrief 07 / 07
Core Logistics Takeaways
1
Volume is the measure of 3D interior space, packed without gaps or overlaps using unit cubes.
2
Calculate volume using \(V = l \times w \times h\) or \(V = B \times h\), always tagged with cubic units.
3
To find composite volume, decompose into non-overlapping rectangular prisms and add their volumes.
Ready for the Cool-Down Inspection Ticket! END OF LAB PRESENTATION
The cargo hold crane has a maximum safe loading volume limit of \(45\text{ cubic units}\). Can Bay Gamma be safely hoisted into the hold? Explain your reasoning using your calculated total volume.
2. Logistics Re-Engineering Challenge:
Could you pack all of Bay Gamma's total unit cubes into a single standard rectangular prism with a height of \(2\text{ units}\)? What would the length and width be? Show your design.
Cargo Crafters • Logistics Blueprint Lab Page 2 of 2
Work:
Height: \(\text{cm}\)
Section 4: Composite Freight Solids & Word Problems
10. Stepped Modular Cargo Container DECOMPOSE INTO 2 PRISMS
A welded freight module consists of two joined sections: Prism 1: \(6\text{ m long} \times 2\text{ m wide} \times 3\text{ m high}\). Prism 2: \(4\text{ m long} \times 2\text{ m wide} \times 2\text{ m high}\).
Warehouse Bay 7 needs to store 40 identical supply boxes. Each box has dimensions of \(2\text{ ft long}\), \(1\text{ ft wide}\), and \(3\text{ ft high}\). The total storage capacity of Bay 7 is \(300\text{ ft}^3\). Will all 40 boxes fit in Bay 7? Show all calculations and explain your engineering decision.
Can all 40 boxes fit? (Circle): YES NO
Total Boxes Volume: \(\text{ft}^3\)
Cargo Crafters • Student Practice Worksheet Page 2 of 2
7. Cargo Hold Deck
\(V = B \times h\)
\(V = 36 \times 3\)
Volume = \(108\text{ m}^3\)
8. Missing Height
\(h = V \div B\)
\(h = 120 \div 24\)
Height = \(5\text{ ft}\)
9. Unknown Dimension
\(B = 5 \times 3 = 15\)
\(h = 90 \div 15\)
Height = \(6\text{ cm}\)
Worksheet Section 4: Composite Solids & Word Problem
10. Stepped Modular Cargo Container Total = \(52\text{ m}^3\)
