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MathematicsFractionsAges 10–11

Area with Fractions

Find the area of a rectangle with fractional side lengths by tiling with unit-fraction squares; show that the area equals the product of the side lengths

Lesson

Set out your lesson

Find fractional rectangle areas with truly square unit-fraction tiles, and distinguish side length from area.

Before teaching

Use this short check, then start teaching.

Activity

Check rectangle area using mt_eiB3-6pu6a and fraction multiplication using mt_AabJisinfi. Ask whether a side unit and a square-area unit mean the same thing before proceeding. Canonical ages are 10–11, not a readiness guarantee. These activity checks are inferred; source availability is not mastery.

Policy

Check learner readiness directly; prerequisite availability is not attainment.

Printer, credit, and teaching notes

Check learner readiness directly; prerequisite availability is not attainment.

Instructions

Use the supplied screen sheets or print only the active sheet. A pencil and scrap paper are enough; no printer, purchase, cutting, cooking, food handling or personal disclosure is required. Read Show first, then use Together with support. Put Show and adult keys aside before Try. Stories are fictional; no activity is evidence until the learner actually attempts it. Allow drawing, pointing, oral explanation or adult scribing; record the support actually used. Scribed mathematics is not independent handwriting. Pause or return to a prerequisite when needed, without treating uncertainty as failure.

Teach The Idea

Area counts square units. To tile a fractional rectangle with squares, choose one common side subdivision for both dimensions. A square tile with side 1/n metre has area 1/n² square metre. Different horizontal and vertical subdivisions can give useful rectangular cells, but do not call them squares. Count tiles and multiply by each tile’s area.

Teaching Procedure

Read the Show model aloud while tracing the relevant unit. In Together, invite an attempt before giving the private hint. Ask the learner to explain why the operation fits. For Try, remove worked material and let the learner choose a representation. Discuss mistakes after recording the attempt, then retry another day if useful.

Models And Materials

Supplied fixed-unit models make partition size, equal sharing or square-area units visible. Learner diagrams are blank scaffolds or stated givens, not worked answers. Screen or paper drawing serves the purpose; no digital interactive is needed.

Use the complete materials on screen or print only the current sheet. Keep adult guidance out of learner view.

Next: Show

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Family records and proof options

Keep a record of your learning

Save photos, notes, and attendance. Export a proof packet for compliance or portfolio reviews.

Learning resources

Extra practice links — they do not replace Gakuva’s teaching approach.

PhET Interactive Simulations · Practice link — not the full lesson

Build a Fraction

Open practice (new tab)
Before you open · source notes

Build a Fraction supports hands-on exploration for Area with Fractions. Not every lab worksheet.

Free interactive page, no sign-in required for the tested path.

Before you open

Ask the learner what they changed in the sim or page and what they observed.

Opening this link does not save learning or assess mastery.

Source, access and review notes

Public PhET Interactive Simulations 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.

PhET Interactive Simulations. “Build a Fraction.” External page; Gakuva does not copy, host, embed, or redistribute materials.

Unknown — link only

Check understanding

  • Tile a 2/3 × 3/4 rectangle with 1/12 squares and count to find area = 6/12 = 1/2
  • Explain why the number of unit-fraction tiles equals the product of the two fractions
  • Calculate the area of a rectangle with sides 1 1/2 and 2/3 using fraction multiplication
“If a piece of fabric is 2/3 m long and 3/4 m wide, can your child work out its area — and explain how tiling it with tiny fraction-squares shows the same answer as multiplying?”

Curriculum record

Type
Representational
Subject
Mathematics
Domain
Fractions
Age range
Ages 10–11

Standards

ccss-math:5.NF.4.b