Sensim Math · Depth 한국어

2-2 · Measuring Length

Convert to one unit, then compare lengths

2.MD.A.14.MD.A.1 · adapt · grade 4

Archetype: Length as Sum of Parts with Unit Matching · step in a 7-type progression

▶ Practice — 12 problems

The post office is 24 ft 1 in24\ \text{ft}\ 1\ \text{in} tall, the school is 320 in320\ \text{in} tall, and the fire station is 267 in267\ \text{in} tall. List the buildings in order from shortest to tallest.

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Understand

Three buildings have heights given in mixed units: the post office is 24 ft 1 in, the school is 320 in, and the fire station is 267 in. Put the buildings in order from shortest to tallest.

Givens
  • Post office height: 24 ft 1 in.
  • School height: 320 in.
  • Fire station height: 267 in.
  • 1 foot = 12 inches.
Unknowns
  • The ordering of the three buildings from shortest to tallest.
Constraints
  • Heights must be compared in a single common unit (inches).

Plan

#8 Analyze the Units · also uses: #2 Make a Systematic List

The heights are in different units (feet-and-inches versus inches), so they can't be compared directly. First convert everything to one unit (inches), then list the three numbers and order them.

Execute

#8 Analyze the Units 4.MD.A.1
Change 24 ft 1 in into inches. Each foot is 12 inches, so 24 feet is 24 times 12, then add the extra 1 inch.
24×12=288,288+1=28924 \times 12 = 288,\quad 288 + 1 = 289
Knowing 1 ft = 12 in lets us turn a larger unit into the smaller unit so all three heights share one unit.
#2 Make a Systematic List 2.MD.A.1
Now every height is in inches: post office 289 in, school 320 in, fire station 267 in.
267, 289, 320267,\ 289,\ 320
Writing them in one common unit makes a straight number comparison possible.
#2 Make a Systematic List 2.MD.A.1
Compare the three inch values: 267 is least, then 289, then 320 is greatest. So fire station is shortest, post office is next, school is tallest.
267<289<320267 < 289 < 320
Once numbers share a unit, ordering them is just comparing whole numbers.
Answer: From shortest to tallest: fire station (267 in), post office (24 ft 1 in = 289 in), school (320 in).

Review

All three are a few hundred inches (about 22-27 feet), reasonable building heights, and the order 267 < 289 < 320 inches is correct. Converting back, 289 in = 24 ft 1 in matches the post office.

Convert everything to feet-and-inches instead: school 320 in = 26 ft 8 in, fire station 267 in = 22 ft 3 in, post office 24 ft 1 in. Comparing feet first gives 22 ft < 24 ft < 26 ft, the same order.

Standards · min grade 4

  • 4.MD.A.1 Know relative sizes of measurement units and convert larger to smaller units — Converting 24 ft 1 in into inches using 1 ft = 12 in.
  • 2.MD.A.1 Measure the length of an object by selecting and using appropriate tools — Comparing and ordering the three heights once expressed in the same unit (inches).
💡 Make every height use the same unit first, then it's just Grade 2 'which number is bigger' comparing!