← Smaller error means a better weight estimate · Get Closest to a Target Value

Smaller error means a better weight estimate · 12 practice problems

3.MD.A.2

Generated variants — 12

Freshly produced from the archetype’s parameters — problem, figure, and solution derived together.

Variant 1 easy answer: Sophia

Caleb's weight is 15 lb 14 oz15\ \text{lb}\ 14\ \text{oz}. When his weight was estimated as below, who made the estimate closest to his actual weight?

  • Sophia: I think it's about 16 lb16\ \text{lb}.
  • Lucas: That much? I think it's about 15 lb 0 oz15\ \text{lb}\ 0\ \text{oz}.
  • Mia: I'll estimate it as 250 oz250\ \text{oz}!
Show solution
1 · Understandwhat's really being asked

Caleb actually weighs 15 lb 14 oz. Three people guess his weight: Sophia about 16 lb, Lucas about 15 lb 0 oz, and Mia 250 oz. Find whose estimate is closest to the real weight.

Givens
  • Caleb's actual weight is 15 lb 14 oz.
  • Sophia estimates 16 lb.
  • Lucas estimates 15 lb 0 oz.
  • Mia estimates 250 oz.
  • 1 lb = 16 oz.
Unknowns
  • Which person's estimate is closest to the actual weight.
Constraints
  • Closeness is measured by how small the difference from the actual weight is.
2 · Planchoose the strategy

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

Convert every weight into a single unit (ounces) so they can be compared fairly, then list each person's error from the actual weight and pick the smallest error.

3 · Execute3 carry out the plan

1Put the actual weight in ounces

#8 Analyze the Units 3.MD.A.2
Since 1 lb = 16 oz, change 15 lb 14 oz to ounces: 15 x 16 = 240, plus 14 gives 254 oz.
15×16+14=240+14=254 oz15 \times 16 + 14 = 240 + 14 = 254\ \text{oz}
Using one unit (ounces) lets us compare all the guesses on the same scale.

2Put each estimate in ounces

#8 Analyze the Units 3.MD.A.2
Sophia: 16 lb = 16 x 16 = 256 oz. Lucas: 15 lb 0 oz = 15 x 16 + 0 = 240 + 0 = 240 oz. Mia is already 250 oz.
16×16=256,15×16+0=240,25016 \times 16 = 256,\quad 15 \times 16 + 0 = 240,\quad 250
Once every guess is in ounces, comparing is just subtraction.

3Find each person's error and compare

#2 Make a Systematic List 3.MD.A.2
Compare each estimate to the actual 254 oz. Sophia: 2 oz off. Lucas: 14 oz off. Mia: 4 oz off. The smallest error (2) belongs to Sophia.
∣256−254∣=2,∣240−254∣=14,∣250−254∣=4|256-254|=2,\quad |240-254|=14,\quad |250-254|=4
The best estimate is the one with the smallest gap from the true weight, and Sophia got the smallest gap.
Answer: Sophia
4 · Reviewdoes it hold up?

Caleb's true weight is 254 oz; Sophia has the smallest error (2 oz), smaller than the other two (Sophia 2 oz, Lucas 14 oz, Mia 4 oz). Sophia being closest makes sense.

Another way: Work in pounds and ounces directly (tool 1, picture a number line): place each estimate next to the actual 15 lb 14 oz and read off which one sits nearest.

Standardsmin grade 3
  • 3.MD.A.2 Measure and estimate liquid volumes and masses of objects — Converting and comparing weights in pounds and ounces to judge estimate accuracy.
💡Takeaway. This only needs Grade 3 measurement sense: change everything to ounces, then the smallest gap wins!
Variant 2 easy answer: Mia

Caleb's weight is 22 lb 9 oz22\ \text{lb}\ 9\ \text{oz}. When his weight was estimated as below, who made the estimate closest to his actual weight?

  • Sophia: I think it's about 23 lb23\ \text{lb}.
  • Lucas: That much? I think it's about 22 lb 0 oz22\ \text{lb}\ 0\ \text{oz}.
  • Mia: I'll estimate it as 360 oz360\ \text{oz}!
Show solution
1 · Understandwhat's really being asked

Caleb actually weighs 22 lb 9 oz. Three people guess his weight: Sophia about 23 lb, Lucas about 22 lb 0 oz, and Mia 360 oz. Find whose estimate is closest to the real weight.

Givens
  • Caleb's actual weight is 22 lb 9 oz.
  • Sophia estimates 23 lb.
  • Lucas estimates 22 lb 0 oz.
  • Mia estimates 360 oz.
  • 1 lb = 16 oz.
Unknowns
  • Which person's estimate is closest to the actual weight.
Constraints
  • Closeness is measured by how small the difference from the actual weight is.
2 · Planchoose the strategy

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

Convert every weight into a single unit (ounces) so they can be compared fairly, then list each person's error from the actual weight and pick the smallest error.

3 · Execute3 carry out the plan

1Put the actual weight in ounces

#8 Analyze the Units 3.MD.A.2
Since 1 lb = 16 oz, change 22 lb 9 oz to ounces: 22 x 16 = 352, plus 9 gives 361 oz.
22×16+9=352+9=361 oz22 \times 16 + 9 = 352 + 9 = 361\ \text{oz}
Using one unit (ounces) lets us compare all the guesses on the same scale.

2Put each estimate in ounces

#8 Analyze the Units 3.MD.A.2
Sophia: 23 lb = 23 x 16 = 368 oz. Lucas: 22 lb 0 oz = 22 x 16 + 0 = 352 + 0 = 352 oz. Mia is already 360 oz.
23×16=368,22×16+0=352,36023 \times 16 = 368,\quad 22 \times 16 + 0 = 352,\quad 360
Once every guess is in ounces, comparing is just subtraction.

3Find each person's error and compare

#2 Make a Systematic List 3.MD.A.2
Compare each estimate to the actual 361 oz. Sophia: 7 oz off. Lucas: 9 oz off. Mia: 1 oz off. The smallest error (1) belongs to Mia.
∣368−361∣=7,∣352−361∣=9,∣360−361∣=1|368-361|=7,\quad |352-361|=9,\quad |360-361|=1
The best estimate is the one with the smallest gap from the true weight, and Mia got the smallest gap.
Answer: Mia
4 · Reviewdoes it hold up?

Caleb's true weight is 361 oz; Mia has the smallest error (1 oz), smaller than the other two (Sophia 7 oz, Lucas 9 oz, Mia 1 oz). Mia being closest makes sense.

Another way: Work in pounds and ounces directly (tool 1, picture a number line): place each estimate next to the actual 22 lb 9 oz and read off which one sits nearest.

Standardsmin grade 3
  • 3.MD.A.2 Measure and estimate liquid volumes and masses of objects — Converting and comparing weights in pounds and ounces to judge estimate accuracy.
💡Takeaway. This only needs Grade 3 measurement sense: change everything to ounces, then the smallest gap wins!
Variant 3 easy answer: Mia

Caleb's weight is 28 lb 6 oz28\ \text{lb}\ 6\ \text{oz}. When his weight was estimated as below, who made the estimate closest to his actual weight?

  • Sophia: I think it's about 27 lb27\ \text{lb}.
  • Lucas: That much? I think it's about 29 lb 2 oz29\ \text{lb}\ 2\ \text{oz}.
  • Mia: I'll estimate it as 460 oz460\ \text{oz}!
Show solution
1 · Understandwhat's really being asked

Caleb actually weighs 28 lb 6 oz. Three people guess his weight: Sophia about 27 lb, Lucas about 29 lb 2 oz, and Mia 460 oz. Find whose estimate is closest to the real weight.

Givens
  • Caleb's actual weight is 28 lb 6 oz.
  • Sophia estimates 27 lb.
  • Lucas estimates 29 lb 2 oz.
  • Mia estimates 460 oz.
  • 1 lb = 16 oz.
Unknowns
  • Which person's estimate is closest to the actual weight.
Constraints
  • Closeness is measured by how small the difference from the actual weight is.
2 · Planchoose the strategy

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

Convert every weight into a single unit (ounces) so they can be compared fairly, then list each person's error from the actual weight and pick the smallest error.

3 · Execute3 carry out the plan

1Put the actual weight in ounces

#8 Analyze the Units 3.MD.A.2
Since 1 lb = 16 oz, change 28 lb 6 oz to ounces: 28 x 16 = 448, plus 6 gives 454 oz.
28×16+6=448+6=454 oz28 \times 16 + 6 = 448 + 6 = 454\ \text{oz}
Using one unit (ounces) lets us compare all the guesses on the same scale.

2Put each estimate in ounces

#8 Analyze the Units 3.MD.A.2
Sophia: 27 lb = 27 x 16 = 432 oz. Lucas: 29 lb 2 oz = 29 x 16 + 2 = 464 + 2 = 466 oz. Mia is already 460 oz.
27×16=432,29×16+2=466,46027 \times 16 = 432,\quad 29 \times 16 + 2 = 466,\quad 460
Once every guess is in ounces, comparing is just subtraction.

3Find each person's error and compare

#2 Make a Systematic List 3.MD.A.2
Compare each estimate to the actual 454 oz. Sophia: 22 oz off. Lucas: 12 oz off. Mia: 6 oz off. The smallest error (6) belongs to Mia.
∣432−454∣=22,∣466−454∣=12,∣460−454∣=6|432-454|=22,\quad |466-454|=12,\quad |460-454|=6
The best estimate is the one with the smallest gap from the true weight, and Mia got the smallest gap.
Answer: Mia
4 · Reviewdoes it hold up?

Caleb's true weight is 454 oz; Mia has the smallest error (6 oz), smaller than the other two (Sophia 22 oz, Lucas 12 oz, Mia 6 oz). Mia being closest makes sense.

Another way: Work in pounds and ounces directly (tool 1, picture a number line): place each estimate next to the actual 28 lb 6 oz and read off which one sits nearest.

Standardsmin grade 3
  • 3.MD.A.2 Measure and estimate liquid volumes and masses of objects — Converting and comparing weights in pounds and ounces to judge estimate accuracy.
💡Takeaway. This only needs Grade 3 measurement sense: change everything to ounces, then the smallest gap wins!
Variant 4 easy answer: Mia

Caleb's weight is 33 lb 11 oz33\ \text{lb}\ 11\ \text{oz}. When his weight was estimated as below, who made the estimate closest to his actual weight?

  • Sophia: I think it's about 34 lb34\ \text{lb}.
  • Lucas: That much? I think it's about 33 lb 0 oz33\ \text{lb}\ 0\ \text{oz}.
  • Mia: I'll estimate it as 535 oz535\ \text{oz}!
Show solution
1 · Understandwhat's really being asked

Caleb actually weighs 33 lb 11 oz. Three people guess his weight: Sophia about 34 lb, Lucas about 33 lb 0 oz, and Mia 535 oz. Find whose estimate is closest to the real weight.

Givens
  • Caleb's actual weight is 33 lb 11 oz.
  • Sophia estimates 34 lb.
  • Lucas estimates 33 lb 0 oz.
  • Mia estimates 535 oz.
  • 1 lb = 16 oz.
Unknowns
  • Which person's estimate is closest to the actual weight.
Constraints
  • Closeness is measured by how small the difference from the actual weight is.
2 · Planchoose the strategy

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

Convert every weight into a single unit (ounces) so they can be compared fairly, then list each person's error from the actual weight and pick the smallest error.

3 · Execute3 carry out the plan

1Put the actual weight in ounces

#8 Analyze the Units 3.MD.A.2
Since 1 lb = 16 oz, change 33 lb 11 oz to ounces: 33 x 16 = 528, plus 11 gives 539 oz.
33×16+11=528+11=539 oz33 \times 16 + 11 = 528 + 11 = 539\ \text{oz}
Using one unit (ounces) lets us compare all the guesses on the same scale.

2Put each estimate in ounces

#8 Analyze the Units 3.MD.A.2
Sophia: 34 lb = 34 x 16 = 544 oz. Lucas: 33 lb 0 oz = 33 x 16 + 0 = 528 + 0 = 528 oz. Mia is already 535 oz.
34×16=544,33×16+0=528,53534 \times 16 = 544,\quad 33 \times 16 + 0 = 528,\quad 535
Once every guess is in ounces, comparing is just subtraction.

3Find each person's error and compare

#2 Make a Systematic List 3.MD.A.2
Compare each estimate to the actual 539 oz. Sophia: 5 oz off. Lucas: 11 oz off. Mia: 4 oz off. The smallest error (4) belongs to Mia.
∣544−539∣=5,∣528−539∣=11,∣535−539∣=4|544-539|=5,\quad |528-539|=11,\quad |535-539|=4
The best estimate is the one with the smallest gap from the true weight, and Mia got the smallest gap.
Answer: Mia
4 · Reviewdoes it hold up?

Caleb's true weight is 539 oz; Mia has the smallest error (4 oz), smaller than the other two (Sophia 5 oz, Lucas 11 oz, Mia 4 oz). Mia being closest makes sense.

Another way: Work in pounds and ounces directly (tool 1, picture a number line): place each estimate next to the actual 33 lb 11 oz and read off which one sits nearest.

Standardsmin grade 3
  • 3.MD.A.2 Measure and estimate liquid volumes and masses of objects — Converting and comparing weights in pounds and ounces to judge estimate accuracy.
💡Takeaway. This only needs Grade 3 measurement sense: change everything to ounces, then the smallest gap wins!
Variant 5 medium answer: Sophia

Caleb's weight is 35 lb 4 oz35\ \text{lb}\ 4\ \text{oz}. When his weight was estimated as below, who made the estimate closest to his actual weight?

  • Sophia: I think it's about 36 lb36\ \text{lb}.
  • Lucas: That much? I think it's about 34 lb 0 oz34\ \text{lb}\ 0\ \text{oz}.
  • Mia: I'll estimate it as 580 oz580\ \text{oz}!
Show solution
1 · Understandwhat's really being asked

Caleb actually weighs 35 lb 4 oz. Three people guess his weight: Sophia about 36 lb, Lucas about 34 lb 0 oz, and Mia 580 oz. Find whose estimate is closest to the real weight.

Givens
  • Caleb's actual weight is 35 lb 4 oz.
  • Sophia estimates 36 lb.
  • Lucas estimates 34 lb 0 oz.
  • Mia estimates 580 oz.
  • 1 lb = 16 oz.
Unknowns
  • Which person's estimate is closest to the actual weight.
Constraints
  • Closeness is measured by how small the difference from the actual weight is.
2 · Planchoose the strategy

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

Convert every weight into a single unit (ounces) so they can be compared fairly, then list each person's error from the actual weight and pick the smallest error.

3 · Execute3 carry out the plan

1Put the actual weight in ounces

#8 Analyze the Units 3.MD.A.2
Since 1 lb = 16 oz, change 35 lb 4 oz to ounces: 35 x 16 = 560, plus 4 gives 564 oz.
35×16+4=560+4=564 oz35 \times 16 + 4 = 560 + 4 = 564\ \text{oz}
Using one unit (ounces) lets us compare all the guesses on the same scale.

2Put each estimate in ounces

#8 Analyze the Units 3.MD.A.2
Sophia: 36 lb = 36 x 16 = 576 oz. Lucas: 34 lb 0 oz = 34 x 16 + 0 = 544 + 0 = 544 oz. Mia is already 580 oz.
36×16=576,34×16+0=544,58036 \times 16 = 576,\quad 34 \times 16 + 0 = 544,\quad 580
Once every guess is in ounces, comparing is just subtraction.

3Find each person's error and compare

#2 Make a Systematic List 3.MD.A.2
Compare each estimate to the actual 564 oz. Sophia: 12 oz off. Lucas: 20 oz off. Mia: 16 oz off. The smallest error (12) belongs to Sophia.
∣576−564∣=12,∣544−564∣=20,∣580−564∣=16|576-564|=12,\quad |544-564|=20,\quad |580-564|=16
The best estimate is the one with the smallest gap from the true weight, and Sophia got the smallest gap.
Answer: Sophia
4 · Reviewdoes it hold up?

Caleb's true weight is 564 oz; Sophia has the smallest error (12 oz), smaller than the other two (Sophia 12 oz, Lucas 20 oz, Mia 16 oz). Sophia being closest makes sense.

Another way: Work in pounds and ounces directly (tool 1, picture a number line): place each estimate next to the actual 35 lb 4 oz and read off which one sits nearest.

Standardsmin grade 3
  • 3.MD.A.2 Measure and estimate liquid volumes and masses of objects — Converting and comparing weights in pounds and ounces to judge estimate accuracy.
💡Takeaway. This only needs Grade 3 measurement sense: change everything to ounces, then the smallest gap wins!
Variant 6 medium answer: Mia

Caleb's weight is 40 lb 8 oz40\ \text{lb}\ 8\ \text{oz}. When his weight was estimated as below, who made the estimate closest to his actual weight?

  • Sophia: I think it's about 41 lb41\ \text{lb}.
  • Lucas: That much? I think it's about 39 lb 10 oz39\ \text{lb}\ 10\ \text{oz}.
  • Mia: I'll estimate it as 650 oz650\ \text{oz}!
Show solution
1 · Understandwhat's really being asked

Caleb actually weighs 40 lb 8 oz. Three people guess his weight: Sophia about 41 lb, Lucas about 39 lb 10 oz, and Mia 650 oz. Find whose estimate is closest to the real weight.

Givens
  • Caleb's actual weight is 40 lb 8 oz.
  • Sophia estimates 41 lb.
  • Lucas estimates 39 lb 10 oz.
  • Mia estimates 650 oz.
  • 1 lb = 16 oz.
Unknowns
  • Which person's estimate is closest to the actual weight.
Constraints
  • Closeness is measured by how small the difference from the actual weight is.
2 · Planchoose the strategy

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

Convert every weight into a single unit (ounces) so they can be compared fairly, then list each person's error from the actual weight and pick the smallest error.

3 · Execute3 carry out the plan

1Put the actual weight in ounces

#8 Analyze the Units 3.MD.A.2
Since 1 lb = 16 oz, change 40 lb 8 oz to ounces: 40 x 16 = 640, plus 8 gives 648 oz.
40×16+8=640+8=648 oz40 \times 16 + 8 = 640 + 8 = 648\ \text{oz}
Using one unit (ounces) lets us compare all the guesses on the same scale.

2Put each estimate in ounces

#8 Analyze the Units 3.MD.A.2
Sophia: 41 lb = 41 x 16 = 656 oz. Lucas: 39 lb 10 oz = 39 x 16 + 10 = 624 + 10 = 634 oz. Mia is already 650 oz.
41×16=656,39×16+10=634,65041 \times 16 = 656,\quad 39 \times 16 + 10 = 634,\quad 650
Once every guess is in ounces, comparing is just subtraction.

3Find each person's error and compare

#2 Make a Systematic List 3.MD.A.2
Compare each estimate to the actual 648 oz. Sophia: 8 oz off. Lucas: 14 oz off. Mia: 2 oz off. The smallest error (2) belongs to Mia.
∣656−648∣=8,∣634−648∣=14,∣650−648∣=2|656-648|=8,\quad |634-648|=14,\quad |650-648|=2
The best estimate is the one with the smallest gap from the true weight, and Mia got the smallest gap.
Answer: Mia
4 · Reviewdoes it hold up?

Caleb's true weight is 648 oz; Mia has the smallest error (2 oz), smaller than the other two (Sophia 8 oz, Lucas 14 oz, Mia 2 oz). Mia being closest makes sense.

Another way: Work in pounds and ounces directly (tool 1, picture a number line): place each estimate next to the actual 40 lb 8 oz and read off which one sits nearest.

Standardsmin grade 3
  • 3.MD.A.2 Measure and estimate liquid volumes and masses of objects — Converting and comparing weights in pounds and ounces to judge estimate accuracy.
💡Takeaway. This only needs Grade 3 measurement sense: change everything to ounces, then the smallest gap wins!
Variant 7 medium answer: Sophia

Caleb's weight is 47 lb 10 oz47\ \text{lb}\ 10\ \text{oz}. When his weight was estimated as below, who made the estimate closest to his actual weight?

  • Sophia: I think it's about 48 lb48\ \text{lb}.
  • Lucas: That much? I think it's about 46 lb 12 oz46\ \text{lb}\ 12\ \text{oz}.
  • Mia: I'll estimate it as 770 oz770\ \text{oz}!
Show solution
1 · Understandwhat's really being asked

Caleb actually weighs 47 lb 10 oz. Three people guess his weight: Sophia about 48 lb, Lucas about 46 lb 12 oz, and Mia 770 oz. Find whose estimate is closest to the real weight.

Givens
  • Caleb's actual weight is 47 lb 10 oz.
  • Sophia estimates 48 lb.
  • Lucas estimates 46 lb 12 oz.
  • Mia estimates 770 oz.
  • 1 lb = 16 oz.
Unknowns
  • Which person's estimate is closest to the actual weight.
Constraints
  • Closeness is measured by how small the difference from the actual weight is.
2 · Planchoose the strategy

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

Convert every weight into a single unit (ounces) so they can be compared fairly, then list each person's error from the actual weight and pick the smallest error.

3 · Execute3 carry out the plan

1Put the actual weight in ounces

#8 Analyze the Units 3.MD.A.2
Since 1 lb = 16 oz, change 47 lb 10 oz to ounces: 47 x 16 = 752, plus 10 gives 762 oz.
47×16+10=752+10=762 oz47 \times 16 + 10 = 752 + 10 = 762\ \text{oz}
Using one unit (ounces) lets us compare all the guesses on the same scale.

2Put each estimate in ounces

#8 Analyze the Units 3.MD.A.2
Sophia: 48 lb = 48 x 16 = 768 oz. Lucas: 46 lb 12 oz = 46 x 16 + 12 = 736 + 12 = 748 oz. Mia is already 770 oz.
48×16=768,46×16+12=748,77048 \times 16 = 768,\quad 46 \times 16 + 12 = 748,\quad 770
Once every guess is in ounces, comparing is just subtraction.

3Find each person's error and compare

#2 Make a Systematic List 3.MD.A.2
Compare each estimate to the actual 762 oz. Sophia: 6 oz off. Lucas: 14 oz off. Mia: 8 oz off. The smallest error (6) belongs to Sophia.
∣768−762∣=6,∣748−762∣=14,∣770−762∣=8|768-762|=6,\quad |748-762|=14,\quad |770-762|=8
The best estimate is the one with the smallest gap from the true weight, and Sophia got the smallest gap.
Answer: Sophia
4 · Reviewdoes it hold up?

Caleb's true weight is 762 oz; Sophia has the smallest error (6 oz), smaller than the other two (Sophia 6 oz, Lucas 14 oz, Mia 8 oz). Sophia being closest makes sense.

Another way: Work in pounds and ounces directly (tool 1, picture a number line): place each estimate next to the actual 47 lb 10 oz and read off which one sits nearest.

Standardsmin grade 3
  • 3.MD.A.2 Measure and estimate liquid volumes and masses of objects — Converting and comparing weights in pounds and ounces to judge estimate accuracy.
💡Takeaway. This only needs Grade 3 measurement sense: change everything to ounces, then the smallest gap wins!
Variant 8 medium answer: Mia

Caleb's weight is 50 lb 0 oz50\ \text{lb}\ 0\ \text{oz}. When his weight was estimated as below, who made the estimate closest to his actual weight?

  • Sophia: I think it's about 49 lb49\ \text{lb}.
  • Lucas: That much? I think it's about 51 lb 8 oz51\ \text{lb}\ 8\ \text{oz}.
  • Mia: I'll estimate it as 810 oz810\ \text{oz}!
Show solution
1 · Understandwhat's really being asked

Caleb actually weighs 50 lb 0 oz. Three people guess his weight: Sophia about 49 lb, Lucas about 51 lb 8 oz, and Mia 810 oz. Find whose estimate is closest to the real weight.

Givens
  • Caleb's actual weight is 50 lb 0 oz.
  • Sophia estimates 49 lb.
  • Lucas estimates 51 lb 8 oz.
  • Mia estimates 810 oz.
  • 1 lb = 16 oz.
Unknowns
  • Which person's estimate is closest to the actual weight.
Constraints
  • Closeness is measured by how small the difference from the actual weight is.
2 · Planchoose the strategy

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

Convert every weight into a single unit (ounces) so they can be compared fairly, then list each person's error from the actual weight and pick the smallest error.

3 · Execute3 carry out the plan

1Put the actual weight in ounces

#8 Analyze the Units 3.MD.A.2
Since 1 lb = 16 oz, change 50 lb 0 oz to ounces: 50 x 16 = 800, plus 0 gives 800 oz.
50×16+0=800+0=800 oz50 \times 16 + 0 = 800 + 0 = 800\ \text{oz}
Using one unit (ounces) lets us compare all the guesses on the same scale.

2Put each estimate in ounces

#8 Analyze the Units 3.MD.A.2
Sophia: 49 lb = 49 x 16 = 784 oz. Lucas: 51 lb 8 oz = 51 x 16 + 8 = 816 + 8 = 824 oz. Mia is already 810 oz.
49×16=784,51×16+8=824,81049 \times 16 = 784,\quad 51 \times 16 + 8 = 824,\quad 810
Once every guess is in ounces, comparing is just subtraction.

3Find each person's error and compare

#2 Make a Systematic List 3.MD.A.2
Compare each estimate to the actual 800 oz. Sophia: 16 oz off. Lucas: 24 oz off. Mia: 10 oz off. The smallest error (10) belongs to Mia.
∣784−800∣=16,∣824−800∣=24,∣810−800∣=10|784-800|=16,\quad |824-800|=24,\quad |810-800|=10
The best estimate is the one with the smallest gap from the true weight, and Mia got the smallest gap.
Answer: Mia
4 · Reviewdoes it hold up?

Caleb's true weight is 800 oz; Mia has the smallest error (10 oz), smaller than the other two (Sophia 16 oz, Lucas 24 oz, Mia 10 oz). Mia being closest makes sense.

Another way: Work in pounds and ounces directly (tool 1, picture a number line): place each estimate next to the actual 50 lb 0 oz and read off which one sits nearest.

Standardsmin grade 3
  • 3.MD.A.2 Measure and estimate liquid volumes and masses of objects — Converting and comparing weights in pounds and ounces to judge estimate accuracy.
💡Takeaway. This only needs Grade 3 measurement sense: change everything to ounces, then the smallest gap wins!
Variant 9 hard answer: Mia

Caleb's weight is 53 lb 12 oz53\ \text{lb}\ 12\ \text{oz}. When his weight was estimated as below, who made the estimate closest to his actual weight?

  • Sophia: I think it's about 55 lb55\ \text{lb}.
  • Lucas: That much? I think it's about 52 lb 5 oz52\ \text{lb}\ 5\ \text{oz}.
  • Mia: I'll estimate it as 860 oz860\ \text{oz}!
Show solution
1 · Understandwhat's really being asked

Caleb actually weighs 53 lb 12 oz. Three people guess his weight: Sophia about 55 lb, Lucas about 52 lb 5 oz, and Mia 860 oz. Find whose estimate is closest to the real weight.

Givens
  • Caleb's actual weight is 53 lb 12 oz.
  • Sophia estimates 55 lb.
  • Lucas estimates 52 lb 5 oz.
  • Mia estimates 860 oz.
  • 1 lb = 16 oz.
Unknowns
  • Which person's estimate is closest to the actual weight.
Constraints
  • Closeness is measured by how small the difference from the actual weight is.
2 · Planchoose the strategy

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

Convert every weight into a single unit (ounces) so they can be compared fairly, then list each person's error from the actual weight and pick the smallest error.

3 · Execute3 carry out the plan

1Put the actual weight in ounces

#8 Analyze the Units 3.MD.A.2
Since 1 lb = 16 oz, change 53 lb 12 oz to ounces: 53 x 16 = 848, plus 12 gives 860 oz.
53×16+12=848+12=860 oz53 \times 16 + 12 = 848 + 12 = 860\ \text{oz}
Using one unit (ounces) lets us compare all the guesses on the same scale.

2Put each estimate in ounces

#8 Analyze the Units 3.MD.A.2
Sophia: 55 lb = 55 x 16 = 880 oz. Lucas: 52 lb 5 oz = 52 x 16 + 5 = 832 + 5 = 837 oz. Mia is already 860 oz.
55×16=880,52×16+5=837,86055 \times 16 = 880,\quad 52 \times 16 + 5 = 837,\quad 860
Once every guess is in ounces, comparing is just subtraction.

3Find each person's error and compare

#2 Make a Systematic List 3.MD.A.2
Compare each estimate to the actual 860 oz. Sophia: 20 oz off. Lucas: 23 oz off. Mia: 0 oz off. The smallest error (0) belongs to Mia.
∣880−860∣=20,∣837−860∣=23,∣860−860∣=0|880-860|=20,\quad |837-860|=23,\quad |860-860|=0
The best estimate is the one with the smallest gap from the true weight, and Mia got the smallest gap.
Answer: Mia
4 · Reviewdoes it hold up?

Caleb's true weight is 860 oz; Mia has the smallest error (0 oz), smaller than the other two (Sophia 20 oz, Lucas 23 oz, Mia 0 oz). Mia being closest makes sense.

Another way: Work in pounds and ounces directly (tool 1, picture a number line): place each estimate next to the actual 53 lb 12 oz and read off which one sits nearest.

Standardsmin grade 3
  • 3.MD.A.2 Measure and estimate liquid volumes and masses of objects — Converting and comparing weights in pounds and ounces to judge estimate accuracy.
💡Takeaway. This only needs Grade 3 measurement sense: change everything to ounces, then the smallest gap wins!
Variant 10 hard answer: Sophia

Caleb's weight is 60 lb 0 oz60\ \text{lb}\ 0\ \text{oz}. When his weight was estimated as below, who made the estimate closest to his actual weight?

  • Sophia: I think it's about 60 lb60\ \text{lb}.
  • Lucas: That much? I think it's about 58 lb 8 oz58\ \text{lb}\ 8\ \text{oz}.
  • Mia: I'll estimate it as 970 oz970\ \text{oz}!
Show solution
1 · Understandwhat's really being asked

Caleb actually weighs 60 lb 0 oz. Three people guess his weight: Sophia about 60 lb, Lucas about 58 lb 8 oz, and Mia 970 oz. Find whose estimate is closest to the real weight.

Givens
  • Caleb's actual weight is 60 lb 0 oz.
  • Sophia estimates 60 lb.
  • Lucas estimates 58 lb 8 oz.
  • Mia estimates 970 oz.
  • 1 lb = 16 oz.
Unknowns
  • Which person's estimate is closest to the actual weight.
Constraints
  • Closeness is measured by how small the difference from the actual weight is.
2 · Planchoose the strategy

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

Convert every weight into a single unit (ounces) so they can be compared fairly, then list each person's error from the actual weight and pick the smallest error.

3 · Execute3 carry out the plan

1Put the actual weight in ounces

#8 Analyze the Units 3.MD.A.2
Since 1 lb = 16 oz, change 60 lb 0 oz to ounces: 60 x 16 = 960, plus 0 gives 960 oz.
60×16+0=960+0=960 oz60 \times 16 + 0 = 960 + 0 = 960\ \text{oz}
Using one unit (ounces) lets us compare all the guesses on the same scale.

2Put each estimate in ounces

#8 Analyze the Units 3.MD.A.2
Sophia: 60 lb = 60 x 16 = 960 oz. Lucas: 58 lb 8 oz = 58 x 16 + 8 = 928 + 8 = 936 oz. Mia is already 970 oz.
60×16=960,58×16+8=936,97060 \times 16 = 960,\quad 58 \times 16 + 8 = 936,\quad 970
Once every guess is in ounces, comparing is just subtraction.

3Find each person's error and compare

#2 Make a Systematic List 3.MD.A.2
Compare each estimate to the actual 960 oz. Sophia: 0 oz off. Lucas: 24 oz off. Mia: 10 oz off. The smallest error (0) belongs to Sophia.
∣960−960∣=0,∣936−960∣=24,∣970−960∣=10|960-960|=0,\quad |936-960|=24,\quad |970-960|=10
The best estimate is the one with the smallest gap from the true weight, and Sophia got the smallest gap.
Answer: Sophia
4 · Reviewdoes it hold up?

Caleb's true weight is 960 oz; Sophia has the smallest error (0 oz), smaller than the other two (Sophia 0 oz, Lucas 24 oz, Mia 10 oz). Sophia being closest makes sense.

Another way: Work in pounds and ounces directly (tool 1, picture a number line): place each estimate next to the actual 60 lb 0 oz and read off which one sits nearest.

Standardsmin grade 3
  • 3.MD.A.2 Measure and estimate liquid volumes and masses of objects — Converting and comparing weights in pounds and ounces to judge estimate accuracy.
💡Takeaway. This only needs Grade 3 measurement sense: change everything to ounces, then the smallest gap wins!
Variant 11 hard answer: Mia

Caleb's weight is 70 lb 2 oz70\ \text{lb}\ 2\ \text{oz}. When his weight was estimated as below, who made the estimate closest to his actual weight?

  • Sophia: I think it's about 69 lb69\ \text{lb}.
  • Lucas: That much? I think it's about 71 lb 4 oz71\ \text{lb}\ 4\ \text{oz}.
  • Mia: I'll estimate it as 1130 oz1130\ \text{oz}!
Show solution
1 · Understandwhat's really being asked

Caleb actually weighs 70 lb 2 oz. Three people guess his weight: Sophia about 69 lb, Lucas about 71 lb 4 oz, and Mia 1130 oz. Find whose estimate is closest to the real weight.

Givens
  • Caleb's actual weight is 70 lb 2 oz.
  • Sophia estimates 69 lb.
  • Lucas estimates 71 lb 4 oz.
  • Mia estimates 1130 oz.
  • 1 lb = 16 oz.
Unknowns
  • Which person's estimate is closest to the actual weight.
Constraints
  • Closeness is measured by how small the difference from the actual weight is.
2 · Planchoose the strategy

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

Convert every weight into a single unit (ounces) so they can be compared fairly, then list each person's error from the actual weight and pick the smallest error.

3 · Execute3 carry out the plan

1Put the actual weight in ounces

#8 Analyze the Units 3.MD.A.2
Since 1 lb = 16 oz, change 70 lb 2 oz to ounces: 70 x 16 = 1120, plus 2 gives 1122 oz.
70×16+2=1120+2=1122 oz70 \times 16 + 2 = 1120 + 2 = 1122\ \text{oz}
Using one unit (ounces) lets us compare all the guesses on the same scale.

2Put each estimate in ounces

#8 Analyze the Units 3.MD.A.2
Sophia: 69 lb = 69 x 16 = 1104 oz. Lucas: 71 lb 4 oz = 71 x 16 + 4 = 1136 + 4 = 1140 oz. Mia is already 1130 oz.
69×16=1104,71×16+4=1140,113069 \times 16 = 1104,\quad 71 \times 16 + 4 = 1140,\quad 1130
Once every guess is in ounces, comparing is just subtraction.

3Find each person's error and compare

#2 Make a Systematic List 3.MD.A.2
Compare each estimate to the actual 1122 oz. Sophia: 18 oz off. Lucas: 18 oz off. Mia: 8 oz off. The smallest error (8) belongs to Mia.
∣1104−1122∣=18,∣1140−1122∣=18,∣1130−1122∣=8|1104-1122|=18,\quad |1140-1122|=18,\quad |1130-1122|=8
The best estimate is the one with the smallest gap from the true weight, and Mia got the smallest gap.
Answer: Mia
4 · Reviewdoes it hold up?

Caleb's true weight is 1122 oz; Mia has the smallest error (8 oz), smaller than the other two (Sophia 18 oz, Lucas 18 oz, Mia 8 oz). Mia being closest makes sense.

Another way: Work in pounds and ounces directly (tool 1, picture a number line): place each estimate next to the actual 70 lb 2 oz and read off which one sits nearest.

Standardsmin grade 3
  • 3.MD.A.2 Measure and estimate liquid volumes and masses of objects — Converting and comparing weights in pounds and ounces to judge estimate accuracy.
💡Takeaway. This only needs Grade 3 measurement sense: change everything to ounces, then the smallest gap wins!
Variant 12 hard answer: Mia

Caleb's weight is 88 lb 5 oz88\ \text{lb}\ 5\ \text{oz}. When his weight was estimated as below, who made the estimate closest to his actual weight?

  • Sophia: I think it's about 90 lb90\ \text{lb}.
  • Lucas: That much? I think it's about 87 lb 8 oz87\ \text{lb}\ 8\ \text{oz}.
  • Mia: I'll estimate it as 1410 oz1410\ \text{oz}!
Show solution
1 · Understandwhat's really being asked

Caleb actually weighs 88 lb 5 oz. Three people guess his weight: Sophia about 90 lb, Lucas about 87 lb 8 oz, and Mia 1410 oz. Find whose estimate is closest to the real weight.

Givens
  • Caleb's actual weight is 88 lb 5 oz.
  • Sophia estimates 90 lb.
  • Lucas estimates 87 lb 8 oz.
  • Mia estimates 1410 oz.
  • 1 lb = 16 oz.
Unknowns
  • Which person's estimate is closest to the actual weight.
Constraints
  • Closeness is measured by how small the difference from the actual weight is.
2 · Planchoose the strategy

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

Convert every weight into a single unit (ounces) so they can be compared fairly, then list each person's error from the actual weight and pick the smallest error.

3 · Execute3 carry out the plan

1Put the actual weight in ounces

#8 Analyze the Units 3.MD.A.2
Since 1 lb = 16 oz, change 88 lb 5 oz to ounces: 88 x 16 = 1408, plus 5 gives 1413 oz.
88×16+5=1408+5=1413 oz88 \times 16 + 5 = 1408 + 5 = 1413\ \text{oz}
Using one unit (ounces) lets us compare all the guesses on the same scale.

2Put each estimate in ounces

#8 Analyze the Units 3.MD.A.2
Sophia: 90 lb = 90 x 16 = 1440 oz. Lucas: 87 lb 8 oz = 87 x 16 + 8 = 1392 + 8 = 1400 oz. Mia is already 1410 oz.
90×16=1440,87×16+8=1400,141090 \times 16 = 1440,\quad 87 \times 16 + 8 = 1400,\quad 1410
Once every guess is in ounces, comparing is just subtraction.

3Find each person's error and compare

#2 Make a Systematic List 3.MD.A.2
Compare each estimate to the actual 1413 oz. Sophia: 27 oz off. Lucas: 13 oz off. Mia: 3 oz off. The smallest error (3) belongs to Mia.
∣1440−1413∣=27,∣1400−1413∣=13,∣1410−1413∣=3|1440-1413|=27,\quad |1400-1413|=13,\quad |1410-1413|=3
The best estimate is the one with the smallest gap from the true weight, and Mia got the smallest gap.
Answer: Mia
4 · Reviewdoes it hold up?

Caleb's true weight is 1413 oz; Mia has the smallest error (3 oz), smaller than the other two (Sophia 27 oz, Lucas 13 oz, Mia 3 oz). Mia being closest makes sense.

Another way: Work in pounds and ounces directly (tool 1, picture a number line): place each estimate next to the actual 88 lb 5 oz and read off which one sits nearest.

Standardsmin grade 3
  • 3.MD.A.2 Measure and estimate liquid volumes and masses of objects — Converting and comparing weights in pounds and ounces to judge estimate accuracy.
💡Takeaway. This only needs Grade 3 measurement sense: change everything to ounces, then the smallest gap wins!