Unit 10 · Standard 6.G.2
Volume with Whole Number Edges
Key Vocabulary Level 1 support
Picture first, then the word, then a plain-language meaning. Say each word out loud.
A box 3 × 2 × 4 holds 24 unit cubes, so V = 24 cubic units
Volume
How much space is inside a solid shape.
A cereal box or shoe box — it has length, width, and height
Rectangular prism
A solid box shape with six flat rectangle sides.
A tiny cube that is 1 in × 1 in × 1 in = 1 in³ (one cubic inch)
Cubic units
The units used to measure space inside, like cubic inches.
V = l × w × h: for a box 5 × 3 × 2, volume = 30 cubic units
Length, width, height
How long, how wide, and how tall a box is.
A cross-shaped pattern of 6 rectangles folds into a rectangular box
Net
A flat shape that folds up into a solid.
A cube has 12 edges — 4 along the top, 4 along the bottom, 4 vertical
Edge
The line where two flat sides of a solid meet.
Key Ideas & Notes
- 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!
- Calculate the volume of each time capsule container. Use V = l × w × h.
Think About It
- What three measurements do you need to find the volume of a box?
- What does volume tell us about a container?
- How is volume different from the area of one face?
My Notes
Guided Examples
Example 1
What is the volume of a rectangular prism with l = 7 in, w = 3 in, h = 4 in?
Solution: V = l × w × h = 7 × 3 × 4 = 84 cubic inches.
Answer: A. 84 in³
Example 2
A time capsule box has a volume of 120 cm³. Its length is 10 cm and width is 4 cm. What is its height?
Solution: V = l × w × h → 120 = 10 × 4 × h → 120 = 40h → h = 3 cm.
Answer: A. 3 cm
Example 3
Which unit is used for volume?
Solution: Volume measures 3D space, so it uses cubic units like in³. Square units (in²) are for area, and inches are for length.
Answer: A. Cubic inches (in³)
Write About the Math The Writing Revolution
I can explain my work using the words volume, rectangular prism, cubic units, and edge.
1. Kernel Sentence subject + verb
Model: Volume is how much space is inside a solid shape.Volumen es cuánto espacio hay dentro de una figura sólida.
Write a kernel sentence about volume. Use a subject and a verb.Escribe una oración base sobre volumen. Usa un sujeto y un verbo.
2. Sentence Expansion because · but · so
Kernel: Volume matters in mathVolumen importa en matemáticas
Expand the kernel three ways. Add a reason, a contrast, and a result.
Volume matters in math because ___.Volumen importa en matemáticas porque ___.
Volume matters in math, but ___.Volumen importa en matemáticas, pero ___.
Volume matters in math, so ___.Volumen importa en matemáticas, entonces ___.
3. Sentence Types 4 ways to write a math idea
Tell one true fact about volume.Di un hecho verdadero sobre volume.
Volume ___.
Ask a question about volume.Haz una pregunta sobre volume.
How does ___ ?¿Cómo ___ ?
Show excitement about volume.Muestra entusiasmo sobre volume.
Wow, ___ !¡Guau, ___ !
Tell a partner what to do with volume.Dile a un compañero qué hacer con volume.
First, ___ .Primero, ___ .
4. Explain Your Reasoning use a sentence starter
I counted ___ cubes in each layer.Conté ___ cubos en cada capa.
The volume is ___ cubic units.El volumen es ___ unidades cúbicas.
I would find volume to ___.Hallaría el volumen para ___.
Try It
Solve on your own. Check the answer key when you are done.
1. Which unit is used for volume?
- Cubic inches (in³)
- Square inches (in²)
- Inches (in)
- Degrees (°)
2. Two storage bins: Bin A is 8 × 6 × 5 inches. Bin B is 9 × 4 × 7 inches. Which holds more and by how much?
- Bin B by 12 in³
- Bin A by 12 in³
- Bin B by 24 in³
- They hold the same
Stretch Your Thinking Level 2 enrichment
Challenge task — explain your reasoning in full sentences.
A box needs to hold exactly 60 cubic inches. Give three different sets of whole-number dimensions that work. Which set would make the box closest to a cube shape? Why might that matter?
Sentence starter: Option 1: ___ × ___ × ___. Option 2: ___ × ___ × ___. Option 3: ___ × ___ × ___. The ___ option is closest to a cube because ___. This matters because ___.
Reflect — Exit Ticket
A rectangular prism has l = 11 in, w = 5 in, h = 4 in. What is the volume?
- 220 in³
- 55 in³
- 220 in²
- 200 in³
Answer Key & Teacher Guide
- Try It 1: A. 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.
- Try It 2: A. 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.
- Exit Ticket: A. 220 in³ — V = 11 × 5 × 4 = 220 cubic inches. Remember: volume uses cubic units (in³).
Writing (TWR) — what to look for
- Kernel sentence: A complete sentence needs a subject and a verb. Example: Volume is how much space is inside a solid shape.
- Expansion: because gives a reason, but shows a contrast or exception, so shows a result. Answers vary; each must keep the kernel idea and add the correct kind of detail.
- Sentence types: Statement ends with a period, question with "?", exclamation with "!", and a command starts with an action verb (a "bossy" verb).