Practice · Smaller error means a better weight estimate · Sensim Math

Variant 1 easy

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

Sophia: I think it's about $16\ \text{lb}$ .
Lucas: That much? I think it's about $15\ \text{lb}\ 0\ \text{oz}$ .
Mia: I'll estimate it as $250\ \text{oz}$ !

Your answer (check it yourself)

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 \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 \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,\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

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

Sophia: I think it's about $23\ \text{lb}$ .
Lucas: That much? I think it's about $22\ \text{lb}\ 0\ \text{oz}$ .
Mia: I'll estimate it as $360\ \text{oz}$ !

Your answer (check it yourself)

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 \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 \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,\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

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

Sophia: I think it's about $27\ \text{lb}$ .
Lucas: That much? I think it's about $29\ \text{lb}\ 2\ \text{oz}$ .
Mia: I'll estimate it as $460\ \text{oz}$ !

Your answer (check it yourself)

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 \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 \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,\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

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

Sophia: I think it's about $34\ \text{lb}$ .
Lucas: That much? I think it's about $33\ \text{lb}\ 0\ \text{oz}$ .
Mia: I'll estimate it as $535\ \text{oz}$ !

Your answer (check it yourself)

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 \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 \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,\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

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

Sophia: I think it's about $36\ \text{lb}$ .
Lucas: That much? I think it's about $34\ \text{lb}\ 0\ \text{oz}$ .
Mia: I'll estimate it as $580\ \text{oz}$ !

Your answer (check it yourself)

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 \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 \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,\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

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

Sophia: I think it's about $41\ \text{lb}$ .
Lucas: That much? I think it's about $39\ \text{lb}\ 10\ \text{oz}$ .
Mia: I'll estimate it as $650\ \text{oz}$ !

Your answer (check it yourself)

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 \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 \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,\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

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

Sophia: I think it's about $48\ \text{lb}$ .
Lucas: That much? I think it's about $46\ \text{lb}\ 12\ \text{oz}$ .
Mia: I'll estimate it as $770\ \text{oz}$ !

Your answer (check it yourself)

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 \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 \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,\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

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

Sophia: I think it's about $49\ \text{lb}$ .
Lucas: That much? I think it's about $51\ \text{lb}\ 8\ \text{oz}$ .
Mia: I'll estimate it as $810\ \text{oz}$ !

Your answer (check it yourself)

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 \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 \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,\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

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

Sophia: I think it's about $55\ \text{lb}$ .
Lucas: That much? I think it's about $52\ \text{lb}\ 5\ \text{oz}$ .
Mia: I'll estimate it as $860\ \text{oz}$ !

Your answer (check it yourself)

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 \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 \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,\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

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

Sophia: I think it's about $60\ \text{lb}$ .
Lucas: That much? I think it's about $58\ \text{lb}\ 8\ \text{oz}$ .
Mia: I'll estimate it as $970\ \text{oz}$ !

Your answer (check it yourself)

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 \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 \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,\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

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

Sophia: I think it's about $69\ \text{lb}$ .
Lucas: That much? I think it's about $71\ \text{lb}\ 4\ \text{oz}$ .
Mia: I'll estimate it as $1130\ \text{oz}$ !

Your answer (check it yourself)

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 \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 \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,\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

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

Sophia: I think it's about $90\ \text{lb}$ .
Lucas: That much? I think it's about $87\ \text{lb}\ 8\ \text{oz}$ .
Mia: I'll estimate it as $1410\ \text{oz}$ !

Your answer (check it yourself)

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 \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 \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,\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!

Smaller error means a better weight estimate · 12 practice problems

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