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: ~45 min · Progress bar at top tracks your place
LAUNCH
⏱ ~10 min
⏱️ 3 MIN · THINK-PAIR-SHARE
Your time capsule container is a rectangular prism. To find how much it can hold, why do you need three measurements (length, width, and height) instead of just one or two?
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 how much space is 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
Your time capsule container is a rectangular prism. To find how much it can hold, why do you need three measurements (length, width, and height) instead of just one or two?
👂 Listen For
Students explain that volume is three-dimensional, so all three edges (length, width, height) are needed; two measurements only give area of one face.
Extend: Could two time capsules have the same volume but different shapes? 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
Container C is 8 × 3 × 4 and Container B is 5 × 5 × 2. How did you count or multiply the unit cubes to find each volume, and which holds more?
👂 Listen For
Students compute Container C = 8 × 3 × 4 = 96 in³ and Container B = 5 × 5 × 2 = 50 in³, and conclude C holds more by connecting volume to multiplying all three edges.
Extend: Container B (50 in³) has a larger length and width than Container D (10 × 2 × 3 = 60 in³), yet D holds more. Explain how that is possible.
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
A rectangular prism has length 8 cm, width 5 cm, and height 4 cm. What is its volume?
✍️ 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
A moving company's large box is 24 × 18 × 18 in and its medium box is 18 × 14 × 12 in. Talk through how you would 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 just compare one dimension (like length) to decide which box holds more? 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 box has a volume of 72 in³. Its base is 6 in by 4 in. 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: ~45 min
🎯 Listen For · Common Errors
• Students explain that volume is three-dimensional, so all three edges (length, width, height) are needed; two measurements only give area of one face.
• Students compute Container C = 8 × 3 × 4 = 96 in³ and Container B = 5 × 5 × 2 = 50 in³, and conclude C holds more by connecting volume to multiplying all three edges.
• 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 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: 160 cm³ — V = l × w × h = 8 × 5 × 4 = 160 cm³.
✓ Practice 3: 3 in — Height = V ÷ (l × w) = 72 ÷ (6 × 4) = 72 ÷ 24 = 3 in.
✓ Practice 4: 84 in³ — V = l × w × h = 7 × 3 × 4 = 84 cubic inches.
✓ Exit ticket: 220 in³ — V = 11 × 5 × 4 = 220 cubic inches. Remember: volume uses cubic units (in³).