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Finding Volume by Multiplying

A 50-minute Grade 5 lesson deriving the volume formula from layers of cubes, so that length times width times height is a conclusion rather than a rule to remember.

Finding Volume by Multiplying is a free 50-minute Grade 5 maths lesson plan for Common Core standard 5.MD.C.5 — find volume by multiplying. It is timed across 5 sections, gives the exact wording to use where the wording carries the mathematics, names 3 misconceptions with the teaching move that addresses each, and ends with an exit ticket and a printable worksheet with its answer key.

Grade:
Grade 5
Length:
50 minutes
Standard:
5.MD.C.5

Grade 5 · Measurement & Data

5.MD.C.5

Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume.

Objective

Students will be able to find the volume of a rectangular prism by multiplying, and solve problems including finding a missing dimension.

Students are successful when they can

  • Calculates volume as length times width times height.
  • Explains the formula as layers of a base area.
  • Finds a missing dimension from a given volume.

What you need

  • Interlocking cubes
  • Open boxes with labelled dimensions
  • Problem cards including missing-dimension cases
  • The printable practice sheet linked at the end of this plan

The lesson

Warm-up — one layer at a time

6 min
  1. Build a single layer 5 by 3 and count the cubes: 15.
  2. Ask how many for four such layers, without building them. Sixty.

Teach — the formula is layers

15 min
  1. Build a 5 by 3 by 4 prism. The base layer is 5 × 3 = 15 cubes, and there are 4 layers.
  2. So 15 × 4 = 60 cubic units, which is 5 × 3 × 4.
  3. Say it: the formula is the base area multiplied by the height, and the base area is itself a multiplication.
  4. Turn the prism on its side and recalculate. Same 60, whichever face you call the base.
  5. Now reverse it: a prism has volume 72 and a base of 6 by 3. The height is 72 ÷ 18 = 4.
  6. Do a real problem: a tank 40 cm by 25 cm by 30 cm — how many litres, given 1,000 cubic cm is a litre.
“You are not memorising three letters multiplied together. You are counting one layer and then counting the layers.”

Guided practice — forwards and backwards

14 min
  1. Pairs find volumes from dimensions, checking one by building it.
  2. They then solve missing-dimension problems by dividing.
  3. Finally they find the volume of a solid made from two joined prisms.

Independent practice

12 min
  1. Students complete a volume by multiplying page.
  2. Answers that add the dimensions or use only two of them are the diagnostic errors.

Close

3 min
  1. A prism has volume 120 and a base area of 20. What is the height?
  2. Six, and the division is the formula run backwards.

What goes wrong, and why

Each of these is a reasoning error rather than carelessness. The fix addresses the reasoning.

Multiplies only two of the three dimensions.

Why: The area formula is familiar and takes two numbers, so the third gets left out when the shape looks like a rectangle in the drawing.

Fix: Build it. Two dimensions give one layer, and the prism is visibly more than one layer thick.

Adds the three dimensions.

Why: Three numbers and an unclear operation, with addition as the default fallback.

Fix: Check against a counted build. 5 + 3 + 4 is 12 and the solid has 60 cubes, so addition is not what the shape is doing.

Finds a missing dimension by dividing the volume by one side only.

Why: The base area has not been computed first, so the division is by a length rather than by an area.

Fix: Write the base area as a separate line before dividing. Volume divided by base area gives the height; volume divided by a length does not.

If they are not there yet

  • Build every prism and count by layers before multiplying.
  • Work with dimensions of 2, 3 and 5 so the arithmetic is not competing with the structure.

If they finish early

  • Find the volume of a compound solid made from two prisms.
  • Find all prisms with whole-number dimensions and a volume of 36.
  • Convert a volume in cubic centimetres to litres.

Exit ticket

A box is 8 cm by 4 cm by 3 cm. Find its volume. Another box has volume 90 cubic cm and a base of 5 by 3 — what is its height?

What to look for: 96 cubic cm and 6 cm. An answer of 32 to the first means one dimension was dropped; 18 to the second means the volume was divided by a length rather than the base area.

Printable practice for 5.MD.C.5

Free to print and copy, answer key included. Each sheet can generate a fresh set of problems for a retake.

Questions about Finding Volume by Multiplying

How long does the Finding Volume by Multiplying lesson take?

50 minutes, split across 5 timed sections: warm-up 6 min, teach 15 min, guided practice 14 min, independent practice 12 min, close 3 min. The minutes are stated per section and add up to the stated length, so the plan can be cut or extended at a section boundary rather than abandoned halfway.

Which standard does Finding Volume by Multiplying teach?

CCSS.MATH.CONTENT.5.MD.C.5 — 5.MD.C.5, Measurement & Data for Grade 5: “Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume.” In plain terms, find volume by multiplying.

What do I need to teach this lesson?

Interlocking cubes, open boxes with labelled dimensions, problem cards including missing-dimension cases and the printable practice sheet linked at the end of this plan. Everything listed is either ordinary classroom equipment or a free printable from this site — there is nothing to buy and nothing to prepare beyond photocopying.

What mistakes should I expect in this lesson?

Three, each a reasoning error rather than carelessness: multiplies only two of the three dimensions; adds the three dimensions and finds a missing dimension by dividing the volume by one side only. The plan gives the thinking behind each one and the teaching move that addresses the thinking rather than the symptom.

How do I know whether the lesson worked?

The exit ticket asks: “A box is 8 cm by 4 cm by 3 cm. Find its volume. Another box has volume 90 cubic cm and a base of 5 by 3 — what is its height?.” 96 cubic cm and 6 cm. An answer of 32 to the first means one dimension was dropped; 18 to the second means the volume was divided by a length rather than the base area. That tells you whether the class needs a reteach or a thirty-second conversation before you plan tomorrow.

Is there a worksheet to go with Finding Volume by Multiplying?

Yes — 2 printable 5.MD.C.5 worksheets, linked at the end of the plan and free like the rest of the site. Each one comes with an answer key and 25 versions, so the practice after the lesson can be a different paper on every desk.

Is Finding Volume by Multiplying free to use?

Yes. The plan, its printables and their answer keys are free to read, print and photocopy for your own class, with no account and no email capture. It was last reviewed on 5 September 2026. Please do not resell it or republish it as your own.

Last reviewed 2026-09-05. Aligned to 5.MD.C.5 of the Common Core State Standards for mathematics.