AEPA Mathematics 2 — Questions and Answers
Question 1: Which measure of central tendency is most affected by extreme outliers in a data set?
- Mode
- Median
- Mean (Correct answer)
- Range
Correct answer: Mean
The mean incorporates all values in its calculation, so a single extreme value can significantly shift it.
Question 2: A student says '1/2 is bigger than 1/3 because 2 is bigger than 3.' How should the teacher respond?
- Agree, since the student's logic is correct
- Use fraction strips to show that larger denominators mean smaller equal parts (Correct answer)
- Correct the student without explanation
- Move on since the answer is coincidentally right
Correct answer: Use fraction strips to show that larger denominators mean smaller equal parts
Fraction strips provide a concrete visual that larger denominators create smaller parts, addressing the common misconception.
Question 3: Which formula correctly calculates the area of a trapezoid?
- A = b × h
- A = ½(b₁ + b₂) × h (Correct answer)
- A = π r²
- A = l × w × h
Correct answer: A = ½(b₁ + b₂) × h
The area of a trapezoid is the average of the two parallel bases multiplied by the height.
Question 4: Which Arizona state standard domain focuses on ratios and proportional relationships for Grade 6 mathematics?
- Operations and Algebraic Thinking
- Ratios and Proportional Relationships (Correct answer)
- Geometry
- Number and Operations in Base Ten
Correct answer: Ratios and Proportional Relationships
The Ratios and Proportional Relationships domain is introduced in Grade 6 per Arizona Mathematics Standards.
Question 5: What is the primary purpose of using manipulatives such as base-ten blocks in mathematics instruction?
- To replace abstract thinking permanently
- To provide kinesthetic and visual concrete models before moving to abstract concepts (Correct answer)
- To keep students entertained during transitions
- To assess memorization of facts
Correct answer: To provide kinesthetic and visual concrete models before moving to abstract concepts
Manipulatives support the concrete-representational-abstract progression, building conceptual understanding before symbolic notation.
Question 6: A student solves 3 × (4 + 5) as 3 × 4 + 5 = 17. Which mathematical property does the student misapply?
- Associative property
- Commutative property
- Distributive property (Correct answer)
- Identity property
Correct answer: Distributive property
The distributive property requires multiplying 3 by both addends: 3 × 4 + 3 × 5 = 27, not just the first.
AEPA Mathematics 2
Which measure of central tendency is most affected by extreme outliers in a data set?