Volume with fraction lengths
Find the volume of a right rectangular prism with fractional edge lengths by packing it with cubes whose edge is a suitable unit fraction of a unit (e.g. 1/2 or 1/4), working out the volume of one such cube (a cube with 1/2-unit edges has volume 1/8 cubic unit), counting the cubes and multiplying; show that this gives the same result as multiplying the edge lengths; and apply V = l × w × h and V = B × h with fractional or mixed-number edge lengths in real-world and mathematical problems
Lesson
Set out your lesson
“Volume with fraction lengths means practising the idea at the table with counters or paper models and one clear check. We will demo once, then your child tries.”
Bring to the table
- Paper strips or a folded circle
- Pencil and labels (1/2, 1/4)
Extra for the adult
Worked example. Fold a strip in half: each piece is 1/2 of the whole.
Optional challenge. For Volume with fraction lengths, add one harder example after success.
What to notice. Keep one parent note: examples tried; results; support used. This session samples Volume with fraction lengths, not mastery.
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Teaching approaches
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1 approach
Volume with fraction lengths means practising the idea at the table with counters or paper models and one clear check. We will demo once, then your child tries.
Materials: Paper strips or a folded circle; Pencil and labels (1/2, 1/4). 1. Say the goal of Volume with fraction lengths in plain words once. 2. Adult folds a strip into halves and labels 1/2. 3. Child makes three fair shares (or fraction operations with strips) and names each result. 4. Fresh check: one fresh equal-part or fraction result. Record and stop. Done: three correctly named fraction results. Proof: parent note of examples and results. Stop: End after the fresh check; keep optional challenge for another day.
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Practice this concept
Start practiceVolume with fraction lengths practice
Practice key ideas from Volume with fraction lengths.
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Learning resources
Extra practice links — they do not replace Gakuva’s teaching approach.
BBC Bitesize · Practice link — not the full lesson
KS3 Maths
Before you open · source notes
KS3 Maths supports Volume with fraction lengths. An adult previews and guides; this is a learning page, not a scored quiz.
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Before you openAsk the learner one fact they learned and one question they still have.
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Source, access and review notes
Public BBC Bitesize page. An anonymous GET on 2026-11-12 returned HTTP 200 with no login or payment prompt for this URL. Opening the link does not save practice or assess mastery. An adult should preview and guide the learner.
BBC Bitesize. “KS3 Maths.” External page; Gakuva does not copy, host, embed, or redistribute materials.
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Check understanding
- Show that 8 cubes with 1/2 cm edges fit exactly into a 1 cm cube, so each has a volume of 1/8 cm³
- Pack a 1½ cm × 1 cm × 2½ cm prism with 1/2 cm cubes (3 × 2 × 5 = 30 cubes), find its volume as 30 × 1/8 = 3¾ cm³, and check that 1½ × 1 × 2½ gives the same answer
- Find how much sand fills a box 2¼ ft long, 1½ ft wide and 2/3 ft deep using V = l × w × h (2¼ ft³)
“If your child has a gift box 2½ inches long, 1½ inches wide and 2 inches tall, could they work out its volume — and show why filling it with little half-inch cubes gives the same answer?”
Curriculum record
- Type
- Procedural
- Subject
- Mathematics
- Domain
- Measurement
- Age range
- Ages 11–12
Standards