Problem
Convert to one unit, then compare lengths
The post office is 24 ft 1 in tall, the school is 320 in tall, and the fire station is 267 in tall. List the buildings in order from shortest to tallest.
Measurement & data
Your answer
Watch out You can't just compare digits like 24 and 320 when the units differ — convert to one unit first.
How to solve
Strategy Analyze the Units — 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.
1STEP 1
Convert the post office to inches
24 ft is 288 in, plus the extra 1 in makes 289 in.
24 × 12 = 288, 288 + 1 = 289
One foot is always the same fixed 12 inches, so each foot can be renamed as a group of 12 inches. 24 feet is 24 such groups — 24×12=288 inches — and adding the leftover 1 inch gives the whole height, 288+1=289 inches.
Analyze Units4.MD.A.1Measuring LengthThe post office's height of 24 ft 1 in is the same length as 289 inches.
Why?
The 24 feet alone is 288 inches, because 24 feet is 24 equal groups of 12 inches and 24 groups of 12 makes 288.
Why?
Taking 24 equal groups of 12 inches is exactly what 24 times 12 means.
🧱Multiplication as equal groupsa times b means a equal groups of b — it is just repeated adding of the same amount.
Why?
One foot always equals the same fixed 12 inches, so each foot can be renamed as a group of 12 inches.
🧱A bigger unit is a fixed count of smaller unitsA bigger unit always equals the same fixed number of smaller units (1 hour = 60 minutes, 1 km = 1000 m), so a measure can be renamed between them.
Why?
With the feet rewritten as 288 inches, the whole height is that 288 inches plus the leftover 1 inch, which is 289 inches.
Why?
The 288 inches and the 1 inch are the two parts of one height, and since both are now measured in inches they add back to the whole height.
🧱Whole is the sum of its partsBreak a thing into pieces with no gaps or overlaps and the pieces add back to the whole.
2STEP 2
List all three heights in inches
Post office 289 in, fire station 267 in, school 320 in — now all in the same unit.
267, 289, 320
Once every length is written with one shared unit, all that's left between them is plain whole-number size. Different units make the bare digits meaningless for comparison, but once the unit matches, the larger number always means the longer length.
Systematic List2.MD.A.1Measuring Length3STEP 3
Order from shortest to tallest
In increasing order — 267, 289, 320 — that's fire station, post office, school.
267 → 289 → 320
Numbers written in the same unit can be ordered just by comparing them as whole numbers — the larger the number, the longer the length. Here 267 is least, then 289, then 320 is greatest, so that same order is the order of the building heights.
Systematic List2.MD.A.1Answer
Fire station, post office, school
267 → 289 → 320
Check — the post office's 24 ft 1 in converts to 289 in, which sits between 267 in and 320 in, confirming the order fire station, post office, school.
Takeaway
Once every length shares the same unit, ordering them is just comparing numbers!
- 24 ft 1 in converts to 289 in
- Three heights: 267 in, 289 in, 320 in
- Order: fire station, post office, school
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