Tutorpip← About this lessonOpen the sheet →Download PDF
Grade 6 · Maths · Lessons
Filling a box with little cubes
📦box🧊small cubes➗fractions✖️edges
Cubes with fraction edges.
The big ideaSmall cubes fill a box with fraction edges. Count them, or multiply the edges: it is the same volume.

How it works

Small cubes with fraction edges can fill a box. Count them, or multiply the edges: it is the same volume.

A half-unit cube is 1/2 on each edge, so it takes 8 of them to make 1 cubic unit.

Multiply length times width times height, even when the edges are fractions.

4 × 5 = 20
A layer of 5 by 4 half-unit cubes: 20 cubes.

Example 1: Count the cubes

  1. A box takes 5 by 4 by 1 half-unit cubes.
  2. 5 × 4 × 1 = 20 cubes.
  3. Each cube is 1/8 of a cubic unit, so it is 20/8 = 2 1/2 cubic units.

Example 2: Multiply the edges

  1. A box has edges 1 ft, 2/3 ft and 5/3 ft.
  2. 1 × 2/3 × 5/3 = 10/9.
  3. 10/9 is 1 1/9 cubic feet.

Example 3: Same volume

  1. The same box counted by third-foot cubes gives 30 cubes.
  2. 30 cubes of 1/27 each is 30/27.
  3. 30/27 is 1 1/9: the same volume.

Words to know

volume
How much space a solid takes up.
unit cube
A cube with edges of 1 unit.

Watch out

Try it

  1. A box is 2 by 3 by 4 unit cubes. What is its volume?
  2. How many half-unit cubes make 1 cubic unit?
  3. Edges 1/2, 1/2 and 4. Volume?
  4. Edges 3/2, 2 and 2. Volume?
Answers: 1. 24 cubic units · 2. 8 · 3. 1 cubic unit · 4. 6 cubic units
For grown-upsPack a box with building blocks of two different sizes and compare the counts.
Open these notes on screenScan the code, or go to tutorpip.com.