A kangaroo has a mass of 28 kilograms. What is the kangaroo's mass, in grams? (1text{ kilogram} = 1{,}000text{ grams})

1. TRANSLATE the problem information

• Given information:
  • Kangaroo's mass: \(\mathrm{28\text{ kilograms}}\)
  • Conversion factor: \(\mathrm{1\text{ kilogram} = 1{,}000\text{ grams}}\)
• What we need to find: mass in grams

2. INFER the approach

• This is a unit conversion problem - we're changing from one unit (kg) to another (g)
• Since we're converting from a larger unit (kg) to a smaller unit (g), we need to multiply
• The conversion factor tells us: \(\mathrm{1\text{ kg} = 1{,}000\text{ g}}\)

3. Set up the conversion

• Use the conversion factor as a ratio: \(\mathrm{\frac{1{,}000\text{ grams}}{1\text{ kilogram}}}\)
• Multiply the given mass by this ratio: \(\mathrm{28\text{ kg} \times \frac{1{,}000\text{ g}}{1\text{ kg}}}\)

4. Calculate the result

• \(\mathrm{28 \times 1{,}000 = 28{,}000\text{ grams}}\)
• Notice the kg units cancel out, leaving just grams

Answer: A. 28,000

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak INFER reasoning: Students don't recognize that unit conversion requires multiplication by the conversion factor. Instead, they might think "I have 28 and 1,000, so I need to combine them somehow" and choose addition: \(\mathrm{28 + 1{,}000 = 1{,}028}\).

This may lead them to select Choice B (1,028).

Second Most Common Error:

Poor INFER execution: Students recognize they need to do something with 28 and 1,000, but choose subtraction instead of multiplication, thinking "grams are smaller than kilograms, so the number should be smaller": \(\mathrm{1{,}000 - 28 = 972}\).

This may lead them to select Choice C (972).

The Bottom Line:

Unit conversion problems require understanding that the conversion factor should be used as a multiplier, not as a number to add or subtract. The key insight is that when converting to smaller units, the numerical value gets larger through multiplication.