There are 170 blocks in a container. Of these blocks, 10% are green. How many blocks in the container are...

1. TRANSLATE the problem information

• Given information:
  • Total blocks: 170
  • Percentage that are green: \(10\%\)
• What we need to find: Number of green blocks

2. TRANSLATE percentage to mathematical operation

• "10% are green" means we need 10% of 170
• Convert percentage to decimal: \(10\% = \frac{10}{100} = 0.1\)
• This gives us: \(0.1 \times 170\)

3. SIMPLIFY the calculation

• \(0.1 \times 170 = 17\)

Answer: 17

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skill: Students may not know how to convert \(10\%\) to a usable mathematical form, or they might try to work directly with "10%" without converting it to \(0.1\). Some students might set up incorrect operations like \(170 \div 10\) or \(170 - 10\).

This leads to confusion and incorrect calculations, causing them to abandon systematic solution and guess.

Second Most Common Error:

Conceptual confusion about percentages: Students might know that 10% means "10 out of 100" but struggle to apply this to a different total (170). They might incorrectly think 10% of any number is just 10.

This may lead them to incorrectly answer \(10\) instead of the correct \(17\).

The Bottom Line:

This problem tests the fundamental skill of converting percentages to decimals and applying them to find parts of quantities. The key insight is recognizing that "10% of 170" requires the mathematical operation \(0.1 \times 170\).