Volume of Rectangular Prisms
Name Period
Objectives / Objetivos
Content Objective: I can find the volume of a rectangular prism, including ones with fractional edge lengths, using base area × height.
Language Objective: I can explain my work using the words volume, rectangular prism, dimensions, and base area.
Key Idea / Idea clave
Volume of Rectangular Prisms with Fractional Edges. Formula: V = l × w × h = B × h. 1. Convert mixed numbers to improper fractions before multiplying. 2. Multiply numerators across, multiply denominators across: V = (l · w · h). 3. Simplify the fraction and label with cubic units
I Notice / Observo
- What are the three measurements of the time capsule?
- What does volume measure — length, area, or space inside?
I Wonder / Me pregunto
- What if we made the capsule taller but narrower — would the volume change?
Vocabulary / Vocabulario
| Term / Término | Definition / Definición |
|---|---|
| Volume of Rectangular Prisms Volumen de prismas rectangulares | The space inside a rectangular prism. Formula: V = Bh = l × w × h. El espacio dentro de un prisma rectangular. Fórmula: V = Bh = l × w × h. |
| Volume Volumen | How much space is inside a solid shape. Cuánto espacio hay dentro de una figura sólida. |
| Rectangular prism Prisma rectangular | A solid box shape with six flat rectangle sides. Una figura sólida en forma de caja con seis lados rectangulares. |
| Cubic units Unidades cúbicas | The units used to measure space inside, like cubic inches. Las unidades para medir el espacio interior, como pulgadas cúbicas. |
| Dimensions Dimensiones | How long, how wide, and how tall a shape is. Qué tan largo, ancho y alto es una figura. |
| Base area Área de la base | The area of the bottom of a solid. Volume = base area × height. El área del fondo de un sólido. Volumen = área de la base × altura. |
Practice Preview / Vista previa de práctica
Read each task. Show your work in the spaces provided and explain how you know.
1. What is the volume of a rectangular prism with l = 4 in, w = 3 in, h = 5 in?
- A 12 in³
- B 24 in³
- C 60 in³
- D 60 in²
Answer:
2. A rectangular shipping container is 8 feet long, 4 feet wide, and 3 feet tall. It is half full of boxes. How many cubic feet of space are left? Draw and label a bar model to support your calculation.
3. Find the missing dimension or volume for each container.
Complete each empty cell. Show your reasoning below.
| Container | Length | Width | Height | Volume |
|---|---|---|---|---|
| Box A | 12 in | 5 in | 3 in | |
| Box B | 7 cm | 4 cm | 168 cm³ | |
| Box C | 8 ft | 5 ft | 240 ft³ |
4. Find the Volume Error
Which step has the mistake, and what should it be?
Reflection / Reflexión
One thing I learned today / Una cosa que aprendí hoy: