Practice · Convert to one unit, then compare lengths · Sensim Math

Variant 1 easy

The post office is $16\ \text{ft}\ 5\ \text{in}$ tall, the school is $180\ \text{in}$ tall, and the fire station is $220\ \text{in}$ tall. List the buildings in order from shortest to tallest.

Your answer (check it yourself)

Show solution

1 · Understandwhat's really being asked

Three buildings have heights given in mixed units: the post office is 16 ft 5 in, the school is 180 in, and the fire station is 220 in. Put the buildings in order from shortest to tallest.

Givens

Post office height: 16 ft 5 in.
School height: 180 in.
Fire station height: 220 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).

2 · Planchoose the strategy

#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.

3 · Execute3 carry out the plan

1Convert the post office to inches

#8 Analyze the Units 4.MD.A.1

Change 16 ft 5 in into inches. Each foot is 12 inches, so 16 feet is 16 times 12, then add the extra 5 inch.

16 \times 12 = 192,\quad 192 + 5 = 197

Knowing 1 ft = 12 in lets us turn a larger unit into the smaller unit so all three heights share one unit.

2List all three heights in inches

#2 Make a Systematic List 2.MD.A.1

Now every height is in inches: post office 197 in, school 180 in, fire station 220 in.

197,\ 180,\ 220

Writing them in one common unit makes a straight number comparison possible.

3Order from shortest to tallest

#2 Make a Systematic List 2.MD.A.1

Compare the three inch values: 180 is least, then 197, then 220 is greatest. So school is shortest, post office is next, fire station is tallest.

180 < 197 < 220

Once numbers share a unit, ordering them is just comparing whole numbers.

Answer: From shortest to tallest: school (180 in), post office (16 ft 5 in), fire station (220 in).

4 · Reviewdoes it hold up?

All three are a few hundred inches (around 20-30 feet), reasonable building heights, and the order 180 < 197 < 220 inches is correct. Converting back, 197 in = 16 ft 5 in matches the post office.

Another way: Convert everything to feet-and-inches instead and compare the feet first, then the leftover inches; the order comes out the same.

Standardsmin grade 4

4.MD.A.1 Know relative sizes of measurement units and convert larger to smaller units — Converting 16 ft 5 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).

💡Takeaway. Make every height use the same unit first, then it's just Grade 2 'which number is bigger' comparing!

Variant 2 easy

The post office is $18\ \text{ft}\ 3\ \text{in}$ tall, the school is $250\ \text{in}$ tall, and the fire station is $190\ \text{in}$ tall. List the buildings in order from shortest to tallest.

Your answer (check it yourself)

Show solution

1 · Understandwhat's really being asked

Three buildings have heights given in mixed units: the post office is 18 ft 3 in, the school is 250 in, and the fire station is 190 in. Put the buildings in order from shortest to tallest.

Givens

Post office height: 18 ft 3 in.
School height: 250 in.
Fire station height: 190 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).

2 · Planchoose the strategy

#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.

3 · Execute3 carry out the plan

1Convert the post office to inches

#8 Analyze the Units 4.MD.A.1

Change 18 ft 3 in into inches. Each foot is 12 inches, so 18 feet is 18 times 12, then add the extra 3 inch.

18 \times 12 = 216,\quad 216 + 3 = 219

Knowing 1 ft = 12 in lets us turn a larger unit into the smaller unit so all three heights share one unit.

2List all three heights in inches

#2 Make a Systematic List 2.MD.A.1

Now every height is in inches: post office 219 in, school 250 in, fire station 190 in.

219,\ 250,\ 190

Writing them in one common unit makes a straight number comparison possible.

3Order from shortest to tallest

#2 Make a Systematic List 2.MD.A.1

Compare the three inch values: 190 is least, then 219, then 250 is greatest. So fire station is shortest, post office is next, school is tallest.

190 < 219 < 250

Once numbers share a unit, ordering them is just comparing whole numbers.

Answer: From shortest to tallest: fire station (190 in), post office (18 ft 3 in), school (250 in).

4 · Reviewdoes it hold up?

All three are a few hundred inches (around 20-30 feet), reasonable building heights, and the order 190 < 219 < 250 inches is correct. Converting back, 219 in = 18 ft 3 in matches the post office.

Another way: Convert everything to feet-and-inches instead and compare the feet first, then the leftover inches; the order comes out the same.

Standardsmin grade 4

4.MD.A.1 Know relative sizes of measurement units and convert larger to smaller units — Converting 18 ft 3 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).

💡Takeaway. Make every height use the same unit first, then it's just Grade 2 'which number is bigger' comparing!

Variant 3 easy

The post office is $19\ \text{ft}\ 11\ \text{in}$ tall, the school is $260\ \text{in}$ tall, and the fire station is $230\ \text{in}$ tall. List the buildings in order from shortest to tallest.

Your answer (check it yourself)

Show solution

1 · Understandwhat's really being asked

Three buildings have heights given in mixed units: the post office is 19 ft 11 in, the school is 260 in, and the fire station is 230 in. Put the buildings in order from shortest to tallest.

Givens

Post office height: 19 ft 11 in.
School height: 260 in.
Fire station height: 230 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).

2 · Planchoose the strategy

#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.

3 · Execute3 carry out the plan

1Convert the post office to inches

#8 Analyze the Units 4.MD.A.1

Change 19 ft 11 in into inches. Each foot is 12 inches, so 19 feet is 19 times 12, then add the extra 11 inch.

19 \times 12 = 228,\quad 228 + 11 = 239

Knowing 1 ft = 12 in lets us turn a larger unit into the smaller unit so all three heights share one unit.

2List all three heights in inches

#2 Make a Systematic List 2.MD.A.1

Now every height is in inches: post office 239 in, school 260 in, fire station 230 in.

239,\ 260,\ 230

Writing them in one common unit makes a straight number comparison possible.

3Order from shortest to tallest

#2 Make a Systematic List 2.MD.A.1

Compare the three inch values: 230 is least, then 239, then 260 is greatest. So fire station is shortest, post office is next, school is tallest.

230 < 239 < 260

Once numbers share a unit, ordering them is just comparing whole numbers.

Answer: From shortest to tallest: fire station (230 in), post office (19 ft 11 in), school (260 in).

4 · Reviewdoes it hold up?

All three are a few hundred inches (around 20-30 feet), reasonable building heights, and the order 230 < 239 < 260 inches is correct. Converting back, 239 in = 19 ft 11 in matches the post office.

Another way: Convert everything to feet-and-inches instead and compare the feet first, then the leftover inches; the order comes out the same.

Standardsmin grade 4

4.MD.A.1 Know relative sizes of measurement units and convert larger to smaller units — Converting 19 ft 11 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).

💡Takeaway. Make every height use the same unit first, then it's just Grade 2 'which number is bigger' comparing!

Variant 4 easy

The post office is $20\ \text{ft}\ 5\ \text{in}$ tall, the school is $280\ \text{in}$ tall, and the fire station is $199\ \text{in}$ tall. List the buildings in order from shortest to tallest.

Your answer (check it yourself)

Show solution

1 · Understandwhat's really being asked

Three buildings have heights given in mixed units: the post office is 20 ft 5 in, the school is 280 in, and the fire station is 199 in. Put the buildings in order from shortest to tallest.

Givens

Post office height: 20 ft 5 in.
School height: 280 in.
Fire station height: 199 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).

2 · Planchoose the strategy

#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.

3 · Execute3 carry out the plan

1Convert the post office to inches

#8 Analyze the Units 4.MD.A.1

Change 20 ft 5 in into inches. Each foot is 12 inches, so 20 feet is 20 times 12, then add the extra 5 inch.

20 \times 12 = 240,\quad 240 + 5 = 245

Knowing 1 ft = 12 in lets us turn a larger unit into the smaller unit so all three heights share one unit.

2List all three heights in inches

#2 Make a Systematic List 2.MD.A.1

Now every height is in inches: post office 245 in, school 280 in, fire station 199 in.

245,\ 280,\ 199

Writing them in one common unit makes a straight number comparison possible.

3Order from shortest to tallest

#2 Make a Systematic List 2.MD.A.1

Compare the three inch values: 199 is least, then 245, then 280 is greatest. So fire station is shortest, post office is next, school is tallest.

199 < 245 < 280

Once numbers share a unit, ordering them is just comparing whole numbers.

Answer: From shortest to tallest: fire station (199 in), post office (20 ft 5 in), school (280 in).

4 · Reviewdoes it hold up?

All three are a few hundred inches (around 20-30 feet), reasonable building heights, and the order 199 < 245 < 280 inches is correct. Converting back, 245 in = 20 ft 5 in matches the post office.

Another way: Convert everything to feet-and-inches instead and compare the feet first, then the leftover inches; the order comes out the same.

Standardsmin grade 4

4.MD.A.1 Know relative sizes of measurement units and convert larger to smaller units — Converting 20 ft 5 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).

💡Takeaway. Make every height use the same unit first, then it's just Grade 2 'which number is bigger' comparing!

Variant 5 medium

The post office is $22\ \text{ft}\ 7\ \text{in}$ tall, the school is $300\ \text{in}$ tall, and the fire station is $250\ \text{in}$ tall. List the buildings in order from shortest to tallest.

Your answer (check it yourself)

Show solution

1 · Understandwhat's really being asked

Three buildings have heights given in mixed units: the post office is 22 ft 7 in, the school is 300 in, and the fire station is 250 in. Put the buildings in order from shortest to tallest.

Givens

Post office height: 22 ft 7 in.
School height: 300 in.
Fire station height: 250 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).

2 · Planchoose the strategy

#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.

3 · Execute3 carry out the plan

1Convert the post office to inches

#8 Analyze the Units 4.MD.A.1

Change 22 ft 7 in into inches. Each foot is 12 inches, so 22 feet is 22 times 12, then add the extra 7 inch.

22 \times 12 = 264,\quad 264 + 7 = 271

Knowing 1 ft = 12 in lets us turn a larger unit into the smaller unit so all three heights share one unit.

2List all three heights in inches

#2 Make a Systematic List 2.MD.A.1

Now every height is in inches: post office 271 in, school 300 in, fire station 250 in.

271,\ 300,\ 250

Writing them in one common unit makes a straight number comparison possible.

3Order from shortest to tallest

#2 Make a Systematic List 2.MD.A.1

Compare the three inch values: 250 is least, then 271, then 300 is greatest. So fire station is shortest, post office is next, school is tallest.

250 < 271 < 300

Once numbers share a unit, ordering them is just comparing whole numbers.

Answer: From shortest to tallest: fire station (250 in), post office (22 ft 7 in), school (300 in).

4 · Reviewdoes it hold up?

All three are a few hundred inches (around 20-30 feet), reasonable building heights, and the order 250 < 271 < 300 inches is correct. Converting back, 271 in = 22 ft 7 in matches the post office.

Another way: Convert everything to feet-and-inches instead and compare the feet first, then the leftover inches; the order comes out the same.

Standardsmin grade 4

4.MD.A.1 Know relative sizes of measurement units and convert larger to smaller units — Converting 22 ft 7 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).

💡Takeaway. Make every height use the same unit first, then it's just Grade 2 'which number is bigger' comparing!

Variant 6 medium

The post office is $23\ \text{ft}\ 6\ \text{in}$ tall, the school is $310\ \text{in}$ tall, and the fire station is $240\ \text{in}$ tall. List the buildings in order from shortest to tallest.

Your answer (check it yourself)

Show solution

1 · Understandwhat's really being asked

Three buildings have heights given in mixed units: the post office is 23 ft 6 in, the school is 310 in, and the fire station is 240 in. Put the buildings in order from shortest to tallest.

Givens

Post office height: 23 ft 6 in.
School height: 310 in.
Fire station height: 240 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).

2 · Planchoose the strategy

#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.

3 · Execute3 carry out the plan

1Convert the post office to inches

#8 Analyze the Units 4.MD.A.1

Change 23 ft 6 in into inches. Each foot is 12 inches, so 23 feet is 23 times 12, then add the extra 6 inch.

23 \times 12 = 276,\quad 276 + 6 = 282

Knowing 1 ft = 12 in lets us turn a larger unit into the smaller unit so all three heights share one unit.

2List all three heights in inches

#2 Make a Systematic List 2.MD.A.1

Now every height is in inches: post office 282 in, school 310 in, fire station 240 in.

282,\ 310,\ 240

Writing them in one common unit makes a straight number comparison possible.

3Order from shortest to tallest

#2 Make a Systematic List 2.MD.A.1

Compare the three inch values: 240 is least, then 282, then 310 is greatest. So fire station is shortest, post office is next, school is tallest.

240 < 282 < 310

Once numbers share a unit, ordering them is just comparing whole numbers.

Answer: From shortest to tallest: fire station (240 in), post office (23 ft 6 in), school (310 in).

4 · Reviewdoes it hold up?

All three are a few hundred inches (around 20-30 feet), reasonable building heights, and the order 240 < 282 < 310 inches is correct. Converting back, 282 in = 23 ft 6 in matches the post office.

Another way: Convert everything to feet-and-inches instead and compare the feet first, then the leftover inches; the order comes out the same.

Standardsmin grade 4

4.MD.A.1 Know relative sizes of measurement units and convert larger to smaller units — Converting 23 ft 6 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).

💡Takeaway. Make every height use the same unit first, then it's just Grade 2 'which number is bigger' comparing!

Variant 7 medium

The post office is $21\ \text{ft}\ 9\ \text{in}$ tall, the school is $275\ \text{in}$ tall, and the fire station is $310\ \text{in}$ tall. List the buildings in order from shortest to tallest.

Your answer (check it yourself)

Show solution

1 · Understandwhat's really being asked

Three buildings have heights given in mixed units: the post office is 21 ft 9 in, the school is 275 in, and the fire station is 310 in. Put the buildings in order from shortest to tallest.

Givens

Post office height: 21 ft 9 in.
School height: 275 in.
Fire station height: 310 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).

2 · Planchoose the strategy

#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.

3 · Execute3 carry out the plan

1Convert the post office to inches

#8 Analyze the Units 4.MD.A.1

Change 21 ft 9 in into inches. Each foot is 12 inches, so 21 feet is 21 times 12, then add the extra 9 inch.

21 \times 12 = 252,\quad 252 + 9 = 261

Knowing 1 ft = 12 in lets us turn a larger unit into the smaller unit so all three heights share one unit.

2List all three heights in inches

#2 Make a Systematic List 2.MD.A.1

Now every height is in inches: post office 261 in, school 275 in, fire station 310 in.

261,\ 275,\ 310

Writing them in one common unit makes a straight number comparison possible.

3Order from shortest to tallest

#2 Make a Systematic List 2.MD.A.1

Compare the three inch values: 261 is least, then 275, then 310 is greatest. So post office is shortest, school is next, fire station is tallest.

261 < 275 < 310

Once numbers share a unit, ordering them is just comparing whole numbers.

Answer: From shortest to tallest: post office (21 ft 9 in), school (275 in), fire station (310 in).

4 · Reviewdoes it hold up?

All three are a few hundred inches (around 20-30 feet), reasonable building heights, and the order 261 < 275 < 310 inches is correct. Converting back, 261 in = 21 ft 9 in matches the post office.

Another way: Convert everything to feet-and-inches instead and compare the feet first, then the leftover inches; the order comes out the same.

Standardsmin grade 4

4.MD.A.1 Know relative sizes of measurement units and convert larger to smaller units — Converting 21 ft 9 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).

💡Takeaway. Make every height use the same unit first, then it's just Grade 2 'which number is bigger' comparing!

Variant 8 medium

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

Your answer (check it yourself)

Show solution

1 · Understandwhat's really being asked

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).

2 · Planchoose the strategy

#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.

3 · Execute3 carry out the plan

1Convert the post office to inches

#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 \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.

2List all three heights in inches

#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.

289,\ 320,\ 267

Writing them in one common unit makes a straight number comparison possible.

3Order from shortest to tallest

#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 < 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), school (320 in).

4 · Reviewdoes it hold up?

All three are a few hundred inches (around 20-30 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.

Another way: Convert everything to feet-and-inches instead and compare the feet first, then the leftover inches; the order comes out the same.

Standardsmin 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).

💡Takeaway. Make every height use the same unit first, then it's just Grade 2 'which number is bigger' comparing!

Variant 9 hard

The post office is $26\ \text{ft}\ 2\ \text{in}$ tall, the school is $290\ \text{in}$ tall, and the fire station is $340\ \text{in}$ tall. List the buildings in order from shortest to tallest.

Your answer (check it yourself)

Show solution

1 · Understandwhat's really being asked

Three buildings have heights given in mixed units: the post office is 26 ft 2 in, the school is 290 in, and the fire station is 340 in. Put the buildings in order from shortest to tallest.

Givens

Post office height: 26 ft 2 in.
School height: 290 in.
Fire station height: 340 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).

2 · Planchoose the strategy

#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.

3 · Execute3 carry out the plan

1Convert the post office to inches

#8 Analyze the Units 4.MD.A.1

Change 26 ft 2 in into inches. Each foot is 12 inches, so 26 feet is 26 times 12, then add the extra 2 inch.

26 \times 12 = 312,\quad 312 + 2 = 314

Knowing 1 ft = 12 in lets us turn a larger unit into the smaller unit so all three heights share one unit.

2List all three heights in inches

#2 Make a Systematic List 2.MD.A.1

Now every height is in inches: post office 314 in, school 290 in, fire station 340 in.

314,\ 290,\ 340

Writing them in one common unit makes a straight number comparison possible.

3Order from shortest to tallest

#2 Make a Systematic List 2.MD.A.1

Compare the three inch values: 290 is least, then 314, then 340 is greatest. So school is shortest, post office is next, fire station is tallest.

290 < 314 < 340

Once numbers share a unit, ordering them is just comparing whole numbers.

Answer: From shortest to tallest: school (290 in), post office (26 ft 2 in), fire station (340 in).

4 · Reviewdoes it hold up?

All three are a few hundred inches (around 20-30 feet), reasonable building heights, and the order 290 < 314 < 340 inches is correct. Converting back, 314 in = 26 ft 2 in matches the post office.

Another way: Convert everything to feet-and-inches instead and compare the feet first, then the leftover inches; the order comes out the same.

Standardsmin grade 4

4.MD.A.1 Know relative sizes of measurement units and convert larger to smaller units — Converting 26 ft 2 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).

💡Takeaway. Make every height use the same unit first, then it's just Grade 2 'which number is bigger' comparing!

Variant 10 hard

The post office is $27\ \text{ft}\ 8\ \text{in}$ tall, the school is $350\ \text{in}$ tall, and the fire station is $290\ \text{in}$ tall. List the buildings in order from shortest to tallest.

Your answer (check it yourself)

Show solution

1 · Understandwhat's really being asked

Three buildings have heights given in mixed units: the post office is 27 ft 8 in, the school is 350 in, and the fire station is 290 in. Put the buildings in order from shortest to tallest.

Givens

Post office height: 27 ft 8 in.
School height: 350 in.
Fire station height: 290 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).

2 · Planchoose the strategy

#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.

3 · Execute3 carry out the plan

1Convert the post office to inches

#8 Analyze the Units 4.MD.A.1

Change 27 ft 8 in into inches. Each foot is 12 inches, so 27 feet is 27 times 12, then add the extra 8 inch.

27 \times 12 = 324,\quad 324 + 8 = 332

Knowing 1 ft = 12 in lets us turn a larger unit into the smaller unit so all three heights share one unit.

2List all three heights in inches

#2 Make a Systematic List 2.MD.A.1

Now every height is in inches: post office 332 in, school 350 in, fire station 290 in.

332,\ 350,\ 290

Writing them in one common unit makes a straight number comparison possible.

3Order from shortest to tallest

#2 Make a Systematic List 2.MD.A.1

Compare the three inch values: 290 is least, then 332, then 350 is greatest. So fire station is shortest, post office is next, school is tallest.

290 < 332 < 350

Once numbers share a unit, ordering them is just comparing whole numbers.

Answer: From shortest to tallest: fire station (290 in), post office (27 ft 8 in), school (350 in).

4 · Reviewdoes it hold up?

All three are a few hundred inches (around 20-30 feet), reasonable building heights, and the order 290 < 332 < 350 inches is correct. Converting back, 332 in = 27 ft 8 in matches the post office.

Another way: Convert everything to feet-and-inches instead and compare the feet first, then the leftover inches; the order comes out the same.

Standardsmin grade 4

4.MD.A.1 Know relative sizes of measurement units and convert larger to smaller units — Converting 27 ft 8 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).

💡Takeaway. Make every height use the same unit first, then it's just Grade 2 'which number is bigger' comparing!

Variant 11 hard

The post office is $25\ \text{ft}\ 4\ \text{in}$ tall, the school is $200\ \text{in}$ tall, and the fire station is $360\ \text{in}$ tall. List the buildings in order from shortest to tallest.

Your answer (check it yourself)

Show solution

1 · Understandwhat's really being asked

Three buildings have heights given in mixed units: the post office is 25 ft 4 in, the school is 200 in, and the fire station is 360 in. Put the buildings in order from shortest to tallest.

Givens

Post office height: 25 ft 4 in.
School height: 200 in.
Fire station height: 360 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).

2 · Planchoose the strategy

#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.

3 · Execute3 carry out the plan

1Convert the post office to inches

#8 Analyze the Units 4.MD.A.1

Change 25 ft 4 in into inches. Each foot is 12 inches, so 25 feet is 25 times 12, then add the extra 4 inch.

25 \times 12 = 300,\quad 300 + 4 = 304

Knowing 1 ft = 12 in lets us turn a larger unit into the smaller unit so all three heights share one unit.

2List all three heights in inches

#2 Make a Systematic List 2.MD.A.1

Now every height is in inches: post office 304 in, school 200 in, fire station 360 in.

304,\ 200,\ 360

Writing them in one common unit makes a straight number comparison possible.

3Order from shortest to tallest

#2 Make a Systematic List 2.MD.A.1

Compare the three inch values: 200 is least, then 304, then 360 is greatest. So school is shortest, post office is next, fire station is tallest.

200 < 304 < 360

Once numbers share a unit, ordering them is just comparing whole numbers.

Answer: From shortest to tallest: school (200 in), post office (25 ft 4 in), fire station (360 in).

4 · Reviewdoes it hold up?

All three are a few hundred inches (around 20-30 feet), reasonable building heights, and the order 200 < 304 < 360 inches is correct. Converting back, 304 in = 25 ft 4 in matches the post office.

Another way: Convert everything to feet-and-inches instead and compare the feet first, then the leftover inches; the order comes out the same.

Standardsmin grade 4

4.MD.A.1 Know relative sizes of measurement units and convert larger to smaller units — Converting 25 ft 4 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).

💡Takeaway. Make every height use the same unit first, then it's just Grade 2 'which number is bigger' comparing!

Variant 12 hard

The post office is $30\ \text{ft}\ 0\ \text{in}$ tall, the school is $400\ \text{in}$ tall, and the fire station is $333\ \text{in}$ tall. List the buildings in order from shortest to tallest.

Your answer (check it yourself)

Show solution

1 · Understandwhat's really being asked

Three buildings have heights given in mixed units: the post office is 30 ft 0 in, the school is 400 in, and the fire station is 333 in. Put the buildings in order from shortest to tallest.

Givens

Post office height: 30 ft 0 in.
School height: 400 in.
Fire station height: 333 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).

2 · Planchoose the strategy

#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.

3 · Execute3 carry out the plan

1Convert the post office to inches

#8 Analyze the Units 4.MD.A.1

Change 30 ft 0 in into inches. Each foot is 12 inches, so 30 feet is 30 times 12, then add the extra 0 inch.

30 \times 12 = 360,\quad 360 + 0 = 360

Knowing 1 ft = 12 in lets us turn a larger unit into the smaller unit so all three heights share one unit.

2List all three heights in inches

#2 Make a Systematic List 2.MD.A.1

Now every height is in inches: post office 360 in, school 400 in, fire station 333 in.

360,\ 400,\ 333

Writing them in one common unit makes a straight number comparison possible.

3Order from shortest to tallest

#2 Make a Systematic List 2.MD.A.1

Compare the three inch values: 333 is least, then 360, then 400 is greatest. So fire station is shortest, post office is next, school is tallest.

333 < 360 < 400

Once numbers share a unit, ordering them is just comparing whole numbers.

Answer: From shortest to tallest: fire station (333 in), post office (30 ft 0 in), school (400 in).

4 · Reviewdoes it hold up?

All three are a few hundred inches (around 20-30 feet), reasonable building heights, and the order 333 < 360 < 400 inches is correct. Converting back, 360 in = 30 ft 0 in matches the post office.

Another way: Convert everything to feet-and-inches instead and compare the feet first, then the leftover inches; the order comes out the same.

Standardsmin grade 4

4.MD.A.1 Know relative sizes of measurement units and convert larger to smaller units — Converting 30 ft 0 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).

💡Takeaway. Make every height use the same unit first, then it's just Grade 2 'which number is bigger' comparing!

Convert to one unit, then compare lengths · 12 practice problems

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