Volume of Rectangular Prisms

Teacher Guide | Grade 5 Mathematics | FAST Success Kit
Florida B.E.S.T. Standards: MA.5.GR.3.1, MA.5.GR.3.2, MA.5.GR.3.3
@ Learning Objective 5-10 min lesson
Students will: Find the volume of right rectangular prisms by counting unit cubes and by using the formula V = l x w x h. Students will also find the volume of composite figures by decomposing them into rectangular prisms.

Why this matters for FAST: Volume is a major Grade 5 geometry concept. Students must understand that volume measures 3D space in cubic units, apply the formula correctly, and solve problems involving composite shapes made of multiple rectangular prisms.

% Materials Needed
! Common Misconceptions to Address

Misconception #1: Confusing Area and Volume

Students multiply only 2 dimensions (length x width) and give area instead of volume, or use square units instead of cubic units.

How to Address:

"Area covers a flat surface (2D) - like paint on a wall. Volume fills up space (3D) - like water in a fish tank. We need THREE dimensions for volume: length, width, AND height. Our answer is in CUBIC units because we're filling with cubes!"

Misconception #2: Only Counting Visible Cubes

When looking at a 3D model, students count only the cubes they can see and miss the hidden cubes inside or behind.

How to Address:

"Think in layers! Count the cubes in ONE layer (that's length x width), then multiply by how many layers tall (that's the height). A prism that's 3 x 2 x 4 has 6 cubes per layer and 4 layers = 24 cubes total."

The Volume Formulas

V = l x w x h

Volume = length x width x height

OR

V = B x h

Volume = Base area x height

$ Lesson Steps
1

Activate Prior Knowledge (1 min)

Show a flat rectangle. "What do we measure with length x width?" (Area - square units). Now show a box. "What if we want to know how much fits INSIDE this box?" Introduce volume as 3D measurement.

2

Introduce Unit Cubes (2 min)

SAY THIS:

"We measure volume with UNIT CUBES - little cubes that are 1 unit on each side. Volume tells us how many unit cubes fit inside a shape."

Build a 2 x 3 x 2 prism with cubes. Have students count: "How many cubes in the bottom layer? (6) How many layers? (2) Total cubes? (12)"

3

Connect to the Formula (2 min)

Example: Find the volume of a prism that is 4 cm long, 3 cm wide, and 2 cm high

V = l x w x h

V = 4 x 3 x 2

V = 24 cubic cm (or 24 cm3)

Emphasize: "We can also think of this as finding the BASE area first (4 x 3 = 12 square cm), then multiplying by height (12 x 2 = 24 cubic cm). That's V = B x h!"

4

Composite Figures (3 min)

SAY THIS:

"Sometimes we have shapes made of TWO rectangular prisms stuck together. We find the volume of each piece, then ADD them together!"

Show an L-shaped figure. Demonstrate breaking it into 2 rectangular prisms, finding each volume, and adding.

5

Guided Practice (2 min)

Work through together:

  • A box is 5 in x 4 in x 3 in. What's the volume? (60 cubic inches)
  • A prism has volume 36 cubic ft. If l = 3 ft and w = 4 ft, what's h? (3 ft)
  • Composite: Stack a 2x2x3 prism on top of a 4x2x2 prism. Total volume? (12 + 16 = 28 cubic units)
? Check for Understanding

Quick Exit Ticket (Ask the whole class):

"A fish tank is 12 inches long, 8 inches wide, and 10 inches tall. What is the volume?"

A) 30 cubic inches   B) 96 cubic inches   C) 960 cubic inches   D) 960 square inches

Correct answer: C) 960 cubic inches (12 x 8 x 10 = 960, and it must be CUBIC for volume)

& IXL Skills to Assign After This Lesson

Recommended IXL Practice:

Find volume using unit cubes Volume of rectangular prisms Volume: find missing dimensions Volume of composite figures Volume word problems
^ Differentiation & Extension

For struggling students: Have them physically build prisms with unit cubes and count. Use graph paper to draw the "base" and stack layers.

For advanced students: Challenge: "Design a rectangular aquarium with a volume of exactly 120 cubic inches. How many different dimensions could work?" (Find factor combinations of 120)

For home: Send Parent Activity sheet. Families can explore volume with boxes and blocks at home.

FAST Success Kit | Grade 5 | Volume Standards: MA.5.GR.3.1, MA.5.GR.3.2, MA.5.GR.3.3