AECTP Mathematics Instruction 3 — Questions and Answers
Question 1: Which instructional sequence best follows the Concrete-Representational-Abstract (CRA) framework for teaching subtraction with regrouping?
- Worksheets → base-ten blocks → number lines
- Base-ten blocks → drawings of blocks → standard algorithm (Correct answer)
- Algorithm → manipulatives → mental math
- Flashcards → timed tests → word problems
Correct answer: Base-ten blocks → drawings of blocks → standard algorithm
CRA moves from hands-on manipulatives to pictorial representations and finally to abstract symbolic notation.
Question 2: A teacher uses think-alouds while solving a word problem. What is the primary instructional purpose?
- To model metacognitive problem-solving strategies explicitly (Correct answer)
- To reduce the time students spend on independent practice
- To demonstrate that teachers always get correct answers
- To replace written explanations in math class
Correct answer: To model metacognitive problem-solving strategies explicitly
Think-alouds make the teacher's reasoning process visible, modeling metacognition and problem-solving strategies for students.
Question 3: When differentiating mathematics instruction, which approach best addresses the needs of advanced learners without simply assigning more of the same work?
- Giving extra practice problems from the same lesson
- Providing enrichment tasks with greater depth and complexity (Correct answer)
- Allowing early finishers to help struggling peers only
- Skipping ahead to the next grade-level textbook chapter
Correct answer: Providing enrichment tasks with greater depth and complexity
Enrichment tasks with depth and complexity extend thinking rather than just increasing quantity of the same-level work.
Question 4: A student solves 7 × 8 by thinking '7 × 8 = 7 × 4 × 2 = 28 × 2 = 56.' This strategy demonstrates:
- A procedural error requiring correction
- The distributive property applied to decomposition
- The associative property of multiplication (Correct answer)
- Lack of basic fact memorization
Correct answer: The associative property of multiplication
Rewriting 8 as 4 × 2 and regrouping factors applies the associative property of multiplication.
Question 5: What is the primary benefit of using open-ended mathematical tasks in instruction?
- They are easier to grade than closed tasks
- They allow multiple solution paths and promote deeper reasoning (Correct answer)
- They eliminate the need for manipulatives
- They focus instruction on procedural speed
Correct answer: They allow multiple solution paths and promote deeper reasoning
Open-ended tasks invite multiple approaches, encouraging flexible thinking and deeper mathematical understanding.
Question 6: Which practice best supports English Language Learners in mathematics class?
- Excusing them from word problems until fluent
- Using visual representations and math-specific vocabulary instruction alongside content (Correct answer)
- Providing only computational tasks to reduce language demands
- Separating them from grade-level content until language improves
Correct answer: Using visual representations and math-specific vocabulary instruction alongside content
Visual supports and explicit math vocabulary instruction allow ELLs to access grade-level content while building language skills simultaneously.
Question 7: A formative assessment strategy where students write the most important concept they learned and one lingering question is known as:
- Exit ticket
- Muddiest point
- Think-pair-share
- The 3-2-1 strategy (Correct answer)
Correct answer: The 3-2-1 strategy
The 3-2-1 strategy (or a variant) captures key learning and remaining questions to inform next instruction.
AECTP Mathematics Instruction 3
Which instructional sequence best follows the Concrete-Representational-Abstract (CRA) framework for teaching subtraction with regrouping?