According to a model, the head width, in millimeters, of a worker bumblebee can be estimated by adding 0.6 to...

1. TRANSLATE the problem information

• Given information:
  • Model: head width = 0.6 + four times the body weight
  • Specific bee has body weight of 0.5 grams
  • Need to find: head width in millimeters

• Mathematical expression: \(\mathrm{head\ width = 0.6 + 4 \times (body\ weight)}\)

2. INFER what we need to do

• We have the model and a specific body weight value
• To find this bee's head width, substitute 0.5 grams into our expression

3. SIMPLIFY by substituting and calculating

• \(\mathrm{head\ width = 0.6 + 4 \times 0.5}\)
• Following order of operations, multiply first: \(\mathrm{4 \times 0.5 = 2}\)
• Then add: \(\mathrm{0.6 + 2 = 2.6}\)

Answer: 2.6 millimeters

Note: Acceptable answer forms include \(\mathrm{2.6}\), \(\mathrm{2.60}\), \(\mathrm{13/5}\), or \(\mathrm{26/10}\)

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skill: Students misinterpret 'adding 0.6 to four times the body weight' and create incorrect expressions like:

• \(\mathrm{0.6 \times 4 + body\ weight}\), or
• \(\mathrm{(0.6 + 4) \times body\ weight}\)

This leads to wrong calculations like:

\(\mathrm{0.6 \times 4 + 0.5 = 2.4 + 0.5 = 2.9}\)

causing them to select an incorrect answer or get confused.

Second Most Common Error:

Poor SIMPLIFY execution: Students correctly translate to \(\mathrm{0.6 + 4 \times body\ weight}\) but violate order of operations by adding first:

\(\mathrm{(0.6 + 4) \times 0.5 = 4.6 \times 0.5 = 2.3}\)

This leads them to an answer of \(\mathrm{2.3}\), which doesn't match any reasonable expectation and causes confusion.

The Bottom Line:

This problem tests whether students can accurately convert everyday language into mathematical expressions and then apply proper order of operations. The verbal description contains multiple operations that must be sequenced correctly.