Fifth Grade · Math · week 29

Composite-solid volumes

Find the volume of a solid figure composed of two non-overlapping rectangular prisms by finding each part's volume and adding.

Some solids are built from two simpler boxes stuck together -- like an L-shaped room or a stepped block. To find the total volume, split the shape into two rectangular prisms, find each volume separately, and add them.

The trick is deciding WHERE to make the split so each piece becomes a clean rectangular prism you already know how to measure.

📋 For the teacher
Teach it (10–15 min):
  • Draw the split line together first, before any multiplying -- deciding where to cut is the real thinking step.
  • Label each piece "Box 1" and "Box 2" and find their volumes completely separately before combining them.
  • Double check that the split does not overlap or leave out any cubes -- the two pieces should account for the whole solid exactly once.
  • Connect this directly to composite-area problems from earlier grades -- the same split-and-add idea, just in 3-D now.
Talk about it:
  • How do you decide where to split a composite solid into two prisms?
  • Why do you find each piece's volume separately before adding?
  • How is this like splitting a composite 2-D shape into rectangles for area?

Mastery looks like: They can split a composite solid into two rectangular prisms, find each volume, and add for the total.

Common stumbles: Splitting the solid in a way that overlaps or misses cubes; adding dimensions across the two boxes instead of adding the two total volumes.

See it visually

Interactive, spoken-aloud tools that show this idea in motion.

AdditionSee groups combine — with counters, blocks, and the number line.try →
Homework for this lessonType it, write it with a stylus, or print it for pencil & paper.open →
Records attendance + 15 min of Math for this learner.
← Back to todayAll coursesYear planner