Volume with Whole Number Edges
I can find the volume of a rectangular prism with whole-number edges using length × width × height.
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🎯 Content Objective / Objetivo de contenido
I can find the volume of a rectangular prism with whole-number edges using length × width × height.
Today's Flow
Total pacing: ~50 min · Progress bar at top tracks your place
LAUNCH
⏱ ~10 min
⏱️ 3 MIN · THINK-PAIR-SHARE
You are sealing time capsule containers and must know exactly how much each holds. Why do you need three edge measurements (length, width, and height) to find the volume of a container?
Check for Understanding #1
Teacher: If >30% thumbs down, re-teach with a fresh example before moving on.
Time Capsule Project
Your team is building time capsule containers to store class memories. Each container is a rectangular prism, and you need to figure out how much each one can hold. That means calculating the volume using whole number dimensions!
Concept Launch
💡 How do we find the volume of a box?
Volume is the amount of space inside a 3D shape. For a rectangular prism (a box), volume = length × width × height, measured in cubic units.
To find the volume of a box, multiply all three edges: V = length × width × height.
Check for Understanding #2
Teacher: If >30% thumbs down, re-teach with a fresh example before moving on.
Now it's your turn
VOCABULARY
⏱ ~8 min
| Term / Término | Meaning / Significado | Example / Ejemplo | Visual |
|---|---|---|---|
| Volume Volumen |
How much space is inside a solid shape. Cuánto espacio hay dentro de una figura sólida. |
A box 3 × 2 × 4 holds 24 unit cubes, so V = 24 cubic units | |
| Rectangular prism Prisma rectangular |
A solid box shape with six flat rectangle sides. Una figura sólida en forma de caja con seis lados rectangulares. |
A cereal box or shoe box — it has length, width, and height | |
| Cubic units Unidades cúbicas |
The units used to measure space inside, like cubic inches. Las unidades para medir el espacio interior, como pulgadas cúbicas. |
A tiny cube that is 1 in × 1 in × 1 in = 1 in³ (one cubic inch) | |
| Length, width, height Largo, ancho, altura |
How long, how wide, and how tall a box is. Qué tan largo, ancho y alto es una caja. |
V = l × w × h: for a box 5 × 3 × 2, volume = 30 cubic units | |
| Net Plantilla (desarrollo plano) |
A flat shape that folds up into a solid. Una figura plana que se dobla y forma un sólido. |
A cross-shaped pattern of 6 rectangles folds into a rectangular box | |
| Edge Arista |
The line where two flat sides of a solid meet. La línea donde se unen dos lados planos de un sólido. |
A cube has 12 edges — 4 along the top, 4 along the bottom, 4 vertical |
Which Word Fits?
The amount of space inside a three-dimensional solid is its ___.
Use It In a Sentence
Check for Understanding #3
Teacher: If >30% thumbs down, re-teach with a fresh example before moving on.
Turn & Talk — Launch
You are sealing time capsule containers and must know exactly how much each holds. Why do you need three edge measurements (length, width, and height) to find the volume of a container?
👂 Listen For
Students explain volume is three-dimensional, so all three edges (length, width, height) are needed; two measurements only describe one flat face.
Extend: If two containers must have the same volume but different shapes, how could you design them? Justify with an example.
EXPLORE & PRACTICE
⏱ ~18 min
Visual Modeling Workspace
Use the drawing tray below to annotate the visual model. Teacher: say "Click to reveal" on key steps.
Explore Activity
Calculate the volume of each time capsule container. Use V = l × w × h.
✍️ Explore Discourse
Container C holds the most (96 in³) and Container B holds the least (50 in³). What do you notice about the dimensions that make one volume larger than another?
Whiteboard Moment
Show your work clearly. Be ready to explain your thinking to a partner.
Turn & Talk — Explore
In the Fold Shop you fold a flat net into a closed box. How does folding the net help you understand what the volume V = l × w × h actually measures?
👂 Listen For
Students connect the folded net to the 3D space inside, and explain volume counts the unit cubes that fill it, computed as l × w × h.
Extend: Container C (8 × 3 × 4 = 96 in³) holds more than Container B (5 × 5 × 2 = 50 in³). Explain how the dimensions, not just one big edge, decide the volume.
Practice Check A
Two storage bins: Bin A is 8 × 6 × 5 inches. Bin B is 9 × 4 × 7 inches. Which holds more and by how much?
✍️ Show Your Work
Explain why your answer is correct using today's vocabulary.
Practice Check B
What is the volume of a rectangular prism with l = 7 in, w = 3 in, h = 4 in?
✍️ Show Your Work
Explain why your answer is correct using today's vocabulary.
Net Fold Explorer
Complete the interactive activity using today's strategy.
✍️ Justify Your Thinking
Sort each label into the correct box.
A classmate turned in the work below. One step has a mistake. Read every step, find it, name it, and fix it.
Choose ONE option to show what you know — then do it in the workspace below.
Use evidence from today's lesson to complete each frame.
Today's key idea is: "To find the volume of a box, multiply all three edges: V = length × width × height." — and it works because ___.
Because Volume means ___, but a tricky part is ___, so I have to ___.
A common mistake with Volume is ___. It happens because ___, and the fix is ___.
I can prove my answer is correct by ___, using Rectangular prism to check my work.
✍️ TWR · WRITE 3 SENTENCES · 7 MIN
To find the volume of a box, multiply all three edges: V = length × width × height. because ___
To find the volume of a box, multiply all three edges: V = length × width × height. but ___
To find the volume of a box, multiply all three edges: V = length × width × height. so ___
🌱 TWR · GROW THE KERNEL · 6 MIN
Answer these to add detail
Sentence starters (tap to use)
Student Workspace
Calculate the volume of each time capsule container. Use V = l × w × h.
| Container | Length (in) | Width (in) | Height (in) | Volume (in³) |
|---|---|---|---|---|
| Container A | 6 | 4 | 3 | |
| Container B | 5 | 5 | 2 | |
| Container C | 8 | 3 | 4 | |
| Container D | 10 | 2 | 3 |
✏️ Sketch Your Strategy
Differentiation Paths
Step-by-step with a worked model and sentence frames.
What is the volume of a rectangular prism with l = 7 in, w = 3 in, h = 4 in?
Core practice aligned to the standard.
Extension with error analysis or multi-step reasoning.
Partner Activity
Work with your partner on the practice problems at your differentiation path level. Explain each step using math vocabulary.
Check for Understanding #4
Teacher: If >30% thumbs down, re-teach with a fresh example before moving on.
Real-World Connection
🌍 Math in the Wild
A moving company uses rectangular boxes. A large box is 24 inches long, 18 inches wide, and 18 inches tall. A medium box is 18 inches long, 14 inches wide, and 12 inches tall.
✍️ Connection Reasoning
How many more cubic inches does the large box hold than the medium box?
The large box volume is ___ in³ because V = ___ × ___ × ___. The medium box volume is ___ in³. The large box holds ___ more cubic inches.
Turn & Talk — Connect
At the Loading Dock, a large moving box is 24 × 18 × 18 in and a medium box is 18 × 14 × 12 in. Talk through how to find how many more cubic inches the large box holds.
👂 Listen For
Students compute large = 7776 in³, medium = 3024 in³, then subtract to get 4752 in³ more, and reason that you must find each volume before comparing.
Extend: Why can't you decide which box holds more by comparing just one dimension (like length)? Use the two boxes to justify.
CLOSURE & REFLECT
⏱ ~8 min
Today I learned that ___ because ___.
One thing I am still not sure about is ___.
A rectangular prism has l = 11 in, w = 5 in, h = 4 in. What is the volume?
Bonus Exit Check
A time capsule box has a volume of 120 cm³. Its length is 10 cm and width is 4 cm. What is its height?
✍️ Show Your Work
Explain why your answer is correct using today's vocabulary.
Reflection & Self-Assessment
Continue Learning
Launch the Full Interactive Activity
Students continue practice in the HTML lesson engine with auto-check, hints, and differentiation.
Family Connection
Share tonight's family homework and discuss one vocabulary word at home.
Open Family Homework ↗Teacher Notes
⏱️ Pacing Guide
- Launch & vocab: 12 min
- I Do / We Do / You Do: 15 min
- Explore & practice: 15 min
- Connect & closure: 8 min
Total: ~50 min
🎯 Listen For · Common Errors
• Students explain volume is three-dimensional, so all three edges (length, width, height) are needed; two measurements only describe one flat face.
• Students connect the folded net to the 3D space inside, and explain volume counts the unit cubes that fill it, computed as l × w × h.
• Students compute large = 7776 in³, medium = 3024 in³, then subtract to get 4752 in³ more, and reason that you must find each volume before comparing.
• Students change in² to in³ and explain that volume fills 3D space (three edges multiplied), while square units describe the flat area of one face.
Common mistake: A common mistake in Volume with Whole Number Edges is skipping the key idea: "To find the volume of a box, multiply all three edges: V = length × width × height." — always check your work against this rule before you submit.
Answer Key (Teacher Appendix)
Hide this slide during presentation or move to the end of your copy.
✓ Practice 1: Bin B by 12 in³ — Bin A: 8 × 6 × 5 = 240 in³. Bin B: 9 × 4 × 7 = 252 in³. Bin B holds 12 in³ more.
✓ Practice 2: 84 in³ — V = l × w × h = 7 × 3 × 4 = 84 cubic inches.
✓ Practice 3: 3 cm — V = l × w × h → 120 = 10 × 4 × h → 120 = 40h → h = 3 cm.
✓ Practice 4: Cubic inches (in³) — Volume measures 3D space, so it uses cubic units like in³. Square units (in²) are for area, and inches are for length.
✓ Exit ticket: 220 in³ — V = 11 × 5 × 4 = 220 cubic inches. Remember: volume uses cubic units (in³).