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Connect Packing to Multiplying Edge Lengths

Students discover that the number of unit cubes in a rectangular prism equals the product of its three edge lengths (length × width × height). They verify this relationship by comparing cube-counting results with multiplication.

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Connect Packing to Multiplying Edge Lengths

Grade 5 · Volume Formulas and Applications · question 1 of 3

0 of 20

20 rungs. A star at the top.

How many cubes fill the box? Add them layer by layer.

Count the cubes.

How it is taught

0:00 of 3:19

The cubes that fill a box equal length times width times height.

Packing and multiplying the three edges name the same count.

Read it: Volume = length × width × height

A box 4 by 2 by 3 holds 4 × 2 = 8 cubes in its bottom layer, and 3 layers: 8 × 3 = 24. So V = l × w × h = 24 cubic units, and V = B × h: the base's area times the height.

  1. Find the base: length × width, 4 × 2 = 8 square units.
  2. Multiply by the height, which counts the layers: 8 × 3 = 24.
  3. For a solid made of two boxes, find each box's volume, then add them.

The base's area is the number of cubes in one layer.

The height is the number of layers, so base × height counts every cube.

Two boxes that do not overlap each fill their own space, so their volumes add.

V = l × w × h = B × h, in cubic units.

Adding the edges, 4 + 2 + 3, instead of multiplying them.

Volume multiplies: 4 × 2 = 8, then 8 × 3 = 24 cubic units.

A box is 5 by 4 by 3. Its volume is ___ cubic units. — 60. The base is 5 × 4 = 20, and 3 layers: 20 × 3 = 60.

4 × 3 × 2 = 24 cubic units

Look at this box of unit cubes. It's four cubes long, three cubes wide, and two cubes tall. How many cubes fit inside?

Grade 5 · Counting cubes by multiplying length × width × height

Let's start with just the bottom layer. It's four cubes across and three cubes deep.

We could count one by one — but it's faster to multiply.

Four times three is twelve. Each layer has twelve cubes.

Now stack a second layer on top, just like the first.

Twelve cubes per layer, and two layers — twelve times two is twenty-four.

So the volume equals length times width times height — the three edge lengths multiplied together.

Four times three times two is twenty-four cubic units. Packing cubes is the same as multiplying edges!

Now you try. Count the unit cubes packed in this box. How many cubes?

What you see

While they climb, your page writes one true line to ask about tonight, and a short note each Sunday.

MayaGrade 3 · Mathematics
Did you know?

A chessboard has 64 squares — share them out between the 8 rows and each row holds exactly 8.

Today’s goal
1 star — one skill mastered, every rung of its ladder climbed
Climbing now
Divide within 100

An example student.

MayaGrade 3 · Mathematics

Maya earned 2 stars this week — Interpret multiplication as equal groups, which took 6 answers over 3 days before its star landed 3 days ago and Multiply by 6, 7, 8 and 9. Next up: Divide within 100.

An example week.

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