How many tablespoons are equivalent to 14 teaspoons? (3 text{ teaspoons} = 1 text{ tablespoon})

1. TRANSLATE the problem information

• Given information:
  • \(\mathrm{3\text{ teaspoons} = 1\text{ tablespoon}}\) (conversion factor)
  • We have 14 teaspoons
  • We want to find equivalent tablespoons

2. INFER the conversion approach

• Since we're going from smaller units (teaspoons) to larger units (tablespoons), we need to divide
• Set up the conversion: \(\mathrm{14\text{ teaspoons} \times \frac{1\text{ tablespoon}}{3\text{ teaspoons}}}\)
• The teaspoons units will cancel out, leaving tablespoons

3. SIMPLIFY the calculation

• \(\mathrm{14\text{ teaspoons} \times \frac{1\text{ tablespoon}}{3\text{ teaspoons}} = \frac{14}{3}\text{ tablespoons}}\)
• Converting to decimal: \(\mathrm{14 \div 3 = 4.666...}\)
• This can be written as 4.667 when rounded to three decimal places

Answer: \(\mathrm{\frac{14}{3}}\) tablespoons (or 4.666, or 4.667)

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak INFER skill: Students use the conversion factor in the wrong direction, thinking "\(\mathrm{3\text{ teaspoons} = 1\text{ tablespoon}}\)" means they should multiply \(\mathrm{14 \times 3}\).

They reason: "If 3 teaspoons equals 1 tablespoon, then 14 teaspoons must equal \(\mathrm{14 \times 3 = 42}\) tablespoons."

This leads to the incorrect answer of 42 tablespoons, which doesn't make logical sense (you can't get more of a larger unit than you started with of a smaller unit).

Second Most Common Error:

Poor TRANSLATE reasoning: Students set up the problem as a proportion but flip the ratios incorrectly.

They might write: \(\mathrm{\frac{3\text{ tablespoons}}{1\text{ teaspoon}} = \frac{x\text{ tablespoons}}{14\text{ teaspoons}}}\), leading to \(\mathrm{x = 42}\).

This stems from not carefully reading which unit equals which in the given conversion.

The Bottom Line:

The key insight is recognizing that when converting from smaller to larger units, the numerical answer should be smaller than what you started with. 14 teaspoons should yield fewer than 14 tablespoons because tablespoons are larger units.