A principal used a total of 25 flags that were either blue or yellow for field day. The principal used...

1. TRANSLATE the problem information

• Given information:
  • Total flags = 25
  • Blue flags = 20
  • All flags are either blue or yellow
• What we need to find: Number of yellow flags

2. INFER the mathematical relationship

• Since the flags are only blue or yellow: \(\mathrm{Total\ flags = Blue\ flags + Yellow\ flags}\)
• To find yellow flags: \(\mathrm{Yellow\ flags = Total\ flags - Blue\ flags}\)
• This is a classic part-whole problem where we know the whole and one part

3. Calculate the answer

• \(\mathrm{Yellow\ flags = 25 - 20 = 5}\)

Answer: A. 5

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak INFER skill: Students don't recognize what the question is actually asking for and instead select information already given in the problem.

They might think: "The problem mentions 20 blue flags, so that must be the answer" or "The problem mentions 25 total flags, so that must be the answer."

This may lead them to select Choice B (20) or Choice C (25).

Second Most Common Error:

Poor TRANSLATE reasoning: Students misunderstand the relationship between the parts and might think they need to add numbers instead of subtract.

They might think: "I have 25 and 20, so I need to combine them somehow" leading to incorrect arithmetic operations.

This causes them to get stuck and guess, or potentially select Choice D (30).

The Bottom Line:

This problem tests whether students can identify part-whole relationships and understand that finding a missing part requires subtraction. The key insight is recognizing that "either blue or yellow" means these are the only two types, so blue + yellow = total.