Mathematics Instruction Flashcards

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?

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.

Which manipulative is most appropriate for helping first graders understand place value concepts?

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.

According to the Common Core State Standards progression, which multiplication concept should students understand before learning the standard algorithm?

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.

A teacher presents a problem and asks students to solve it in multiple ways and share their strategies. Which instructional approach does this reflect?

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.

Which type of problem is most effective for developing students' number sense and flexible thinking in elementary math?

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.

A third grader understands that 3 × 4 = 12 but struggles with 4 × 3. Which fundamental property should the teacher address?

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.