Praxis 5001 Mathematics Instruction 1 — Questions and Answers
Question 1: A student solves 47 + 38 by adding 40 + 30 = 70, then 7 + 8 = 15, then 70 + 15 = 85. Which mathematical strategy is the student using?
- Standard algorithm
- Decomposition and partial sums (Correct answer)
- Counting on
- Compensation
Correct answer: Decomposition and partial sums
The student is decomposing numbers by place value and adding the partial sums separately, which is a decomposition/partial sums strategy.
Question 2: Which manipulative is most appropriate for helping first graders understand place value concepts?
- Fraction tiles
- Base-ten blocks (Correct answer)
- Pattern blocks
- Geoboards
Correct answer: Base-ten blocks
Base-ten blocks physically represent ones, tens, and hundreds, making the structure of place value concrete and visible for young learners.
Question 3: According to the Common Core State Standards progression, which multiplication concept should students understand before learning the standard algorithm?
- Long division
- Fraction multiplication
- Area model and partial products (Correct answer)
- Integer operations
Correct answer: Area model and partial products
The area model and partial products strategy builds conceptual understanding of multiplication before students transition to the more abstract standard algorithm.
Question 4: A teacher presents a problem and asks students to solve it in multiple ways and share their strategies. Which instructional approach does this reflect?
- Direct instruction only
- Rote memorization practice
- Cognitively demanding mathematical discourse (Correct answer)
- Timed fluency drills
Correct answer: Cognitively demanding mathematical discourse
Inviting multiple solution strategies and student discourse reflects a cognitively demanding, student-centered approach that builds mathematical reasoning and communication.
Question 5: Which type of problem is most effective for developing students' number sense and flexible thinking in elementary math?
- Problems with a single prescribed method
- Open-ended or low-floor/high-ceiling tasks (Correct answer)
- Timed computation worksheets
- Identical practice problems in sequence
Correct answer: Open-ended or low-floor/high-ceiling tasks
Low-floor/high-ceiling tasks are accessible to all learners yet extendable for advanced students, promoting flexible and creative mathematical thinking.
Question 6: A third grader understands that 3 × 4 = 12 but struggles with 4 × 3. Which fundamental property should the teacher address?
- Distributive property
- Associative property
- Commutative property (Correct answer)
- Identity property
Correct answer: Commutative property
The commutative property of multiplication states that the order of factors does not change the product (a × b = b × a), which the student has not yet generalized.
Praxis 5001 Mathematics Instruction 1
A student solves 47 + 38 by adding 40 + 30 = 70, then 7 + 8 = 15, then 70 + 15 = 85.
Which mathematical strategy is the student using?