Grade 10 — Mathematics 10-3 › T3U02 Imperial Measurement

GRADE 10 · ALBERTAOUTCOME MAT10-3-M2

L1 · The imperial system: units, relationships, and fractions

Learning goal

“I can describe how the imperial system grew out of everyday objects, name its units for length, capacity, mass and temperature with their relationships, and explain why imperial measurements are written as fractions.”

Imperial system — the older measurement system built from body parts and everyday containers; still used daily in the United States and on Canadian job sites.
Foot (ft) — the length unit that began as an actual human foot; now defined as exactly 12 inches.
Yard (yd) — 3 feet; historically the distance from a king's nose to his outstretched fingertip.
Fractional measurement — a measurement written as a whole number plus a fraction, like 5 3/8 in - the normal way imperial lengths are read off a tape.
Worked example

Imperial units were not designed on a desk; they grew out of bodies and trade. The inch was a thumb's width (three barleycorns long, by law), the foot was a foot, the yard a king's reach. Because nobody coordinated them, the relationships are whatever history left behind - and they are PROVIDED, never derived: Length: 1 ft = 12 in, 1 yd = 3 ft (= 36 in), 1 mi = 1760 yd. Capacity: 1 cup = 8 fl oz, 1 pt = 2 cups, 1 qt = 2 pt, 1 gal = 4 qt. Mass: 1 lb = 16 oz, 1 ton = 2000 lb. Temperature: degrees Fahrenheit (°F), water freezing at 32°F and boiling at 212°F. Say it plainly: SI asks 'how many tens?'; imperial asks 'what's the relationship THIS time?' - and the reference strip answers it.

Check yourself — explain it

Imperial conversions are harder to do in your head than SI conversions because...

Paired problem — example still visible

Using the reference strip: how many inches are in 1 yard, and how many cups are in 1 quart? -> 1 yd = 3 ft x 12 in = 36 in; 1 qt = 2 pt x 2 cups = 4 cups

Faded completion — last step is yours

"Chain it: 1 gal = 4 qt, and 1 qt = 4 cups (from the paired problem), so 1 gal = ___ cups." -> 16

Ready to practise?

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