Plan a panel with fractional side lengths

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.

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.

Answer: 1/6

Teacher response: Six equal half-by-third tiles fill a square metre; this panel uses one.

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

Answer: 2/5

Teacher response: Six of fifteen equal tiles cover the panel: 6/15 = 2/5 square metre.

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.

Answer: 1 1/8

Teacher response: The longer side includes more than one metre: 3/2 × 3/4 = 9/8 square metres.

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.

Answer: 2/3

Look for:

• Uses square units for area and explains the unit tile.
• Distinguishes an area calculation from an actual fitting claim.

Teacher response: Twenty of thirty equal tiles cover the panel, so the area is 20/30 = 2/3 square metre.

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

Answer: No. Shape and side lengths also matter. For example, a 1 m by 1/2 m sheet and the worked 3/4 m by 2/3 m panel both have area 1/2 square metre, but the uncut sheet does not contain the panel in either edge-aligned orientation.

teach-1. 3 minutes: Ask learners to distinguish the edge length they can trace from the area they can shade.

teach-2. 4 minutes: Draw the 4-by-3 reference grid and mark the six tiles used by the panel. Label a tile's area.

teach-3. 5 minutes: Choose a support or core item, then compare its product with the dimensions before attempting the challenge.

teach-4. 3 minutes: Complete the independent area check and describe why area alone does not prove an uncut sheet fits.

misconception. Add 3/4 and 2/3 because both lengths belong to the panel.

Teacher response: Ask what the result must measure. Trace one side for length, then shade the inside for area. Counting small equal tiles explains why two length factors produce square units.

support. Give a unit-square grid already divided into the needed rows and columns; identify one tile before counting the selected region.

extend. Find a different pair of side lengths with area 1/2 square metre and compare whether the same uncut sheet fits.