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Fraction Classroom · 2.5.0 · Student pages

Plan a panel with fractional side lengths

Produce a coverage record that separates fractional side lengths from square units and checks a material-area claim.

Anonymous group code: __________   Date: __________

A square-metre reference has twelve equal tiles; the panel selects six. Side lengths are in metres and coverage is in square metres.QuantityMeaningValueSmall tile1/4 m × 1/3 m1/12 square mSelected tiles3 columns × 2 rows6Panel area6 × 1/12 square m1/2 square m
A square-metre reference has twelve equal tiles; the panel selects six. Side lengths are in metres and coverage is in square metres.

Build the idea

model. A rectangular display panel is 3/4 metre wide and 2/3 metre high. What area needs covering?

  1. Name the reference square: it is 1 metre by 1 metre. The panel's width and height are lengths, while the requested coverage is an area.
  2. Partition the reference into 4 equal columns and 3 equal rows. One small tile has dimensions 1/4 metre by 1/3 metre, so twelve tiles fill one square metre.
  3. Select 3 columns and 2 rows. The panel contains 3 × 2 = 6 tiles, each with area 1/12 square metre; the total is 6/12, or 1/2 square metre.
  4. Check with multiplication: 3/4 × 2/3 = 6/12. Both side lengths are below one metre, and the area fits within the reference square. Adding the side lengths would measure a length, not coverage.

Worked example: 1/2 square metre. Divide a square metre into fourths across and thirds vertically. Each tile is 1/12 square metre; the panel contains six such tiles.

Practise and explain

Try p1–p3 with a partner. Use a drawing and label your units. Try e1 independently before comparing responses.

p1. Support: a panel is 1/2 m wide and 1/3 m high. Enter its area in square metres and identify one matching unit tile.

p2. Core: a panel is 2/3 m wide and 3/5 m high. Enter its area in square metres.

p3. Challenge: a rectangle is 1 1/2 m long and 3/4 m wide. Enter its area in square metres and explain why the result can exceed one.

e1. Independent check: a panel is 4/5 m wide and 5/6 m high. Enter the area in square metres and show a tiled or multiplication check.

Transfer the idea

transfer. A sheet and a panel have equal areas. Does that alone prove the sheet can cover the panel without cutting or gaps?