Smaller error means a better weight estimate

3.MD.A.2 · adapt · grade 3

Archetype: Get Closest to a Target Value · step in a 4-type progression

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 $860\ \text{oz}$ !

Show solution

Understand

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.

Plan

#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.

Execute

#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.

#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.

#2 Make a Systematic List 3.MD.A.2

Compare each estimate to the actual 860 oz. Sophia: 880 - 860 = 20 oz off. Lucas: 860 - 837 = 23 oz off. Mia: 860 - 860 = 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 matched it exactly.

Answer: Mia

Review

Caleb's true weight is 860 oz; Mia guessed exactly 860 oz, so her error of 0 oz is smaller than Sophia's 20 oz and Lucas's 23 oz. Mia being closest makes sense.

Work in pounds and ounces directly (tool 1, picture a number line): the actual weight 53 lb 12 oz sits between Lucas (52 lb 5 oz, below) and Sophia (55 lb, above), while Mia's 860 oz lands right on it.

Standards · min 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.

💡 This only needs Grade 3 measurement sense: change everything to ounces, then the smallest gap wins!