Grade 10 — Mathematics 10-3 › T3U04 Area & Surface Area

Grade 10 › T3U04 Area & Surface Area › L1
GRADE 10 · ALBERTAOUTCOME AB-MAT10-3-M4

L1 · Area referents; estimating area with square grids

Learning goal

“I can name a referent for common area units (cm², m², in², ft², yd²), choose the right unit for a job, and estimate the area of regular and irregular shapes by counting squares on a grid - full squares whole, partial squares paired.”

Area — the amount of surface a shape covers, measured in SQUARE units: how many unit squares fit inside it. Area answers wear squared units (cm², m², ft²).
Square unit — the tile that does the measuring: a 1 cm x 1 cm square is 1 cm². Change the tile and the count changes - the surface does not.
Referent (for area) — a familiar surface of known area: a thumbnail ≈ 1 cm², a floor tile ≈ 1 ft², a card-table top ≈ 1 m².
Irregular shape — a shape with no area formula (a leaf, a footprint, a pond outline). Its area is found by estimation - usually on a grid.
Worked example

Two jobs: report the area of (a) a postage stamp and (b) a soccer field. Which units? Step 1: Match the unit to the surface. The stamp is a few centimetres across - the cm² tile is the right size: ≈ 25 cm². The field is about 100 m long - the m² tile: ≈ 7000 m². Step 2: The rule: choose the unit so the number lands in a comfortable range (roughly 1 to 10,000). "0.0025 m²" for the stamp and "70,000,000 cm²" for the field are both correct and both useless. Referents that anchor the choices: thumbnail ≈ 1 cm², sheet of paper ≈ 600 cm², bath towel ≈ 1 yd², card-table top ≈ 1 m², floor tile (12 in x 12 in) = 1 ft².

Check yourself — explain it

The area of a sheet of paper is best reported in:

Paired problem — example still visible

Estimate the area of a door using a referent. -> ≈ 2 m² (a door is about 2 m tall and 1 m wide; accept 1.5-2.2 m² with the reasoning stated).

Faded completion — last step is yours

"A floor tile measures 1 ft by 1 ft, so its area is ___ ft². In inches the same tile is 12 in by 12 in, so its area is ___ in²." -> 1; 144

Ready to practise?

10 scored questions with a 3-rung hint ladder. Mastery needs 8/10 plus both gate questions.

Start practice →Take the unit quiz