L1 · The imperial system: units, relationships, and fractions
“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 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.
Imperial conversions are harder to do in your head than SI conversions because...
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
"Chain it: 1 gal = 4 qt, and 1 qt = 4 cups (from the paired problem), so 1 gal = ___ cups." -> 16
10 scored questions with a 3-rung hint ladder. Mastery needs 8/10 plus both gate questions.