TExES EC-6 Mathematics Instruction & Problem Solving 4 — Questions and Answers
Question 1: When selecting manipulatives for a lesson on fractions, which consideration is MOST important for instructional effectiveness?
- The manipulatives should be colorful and attractive to students
- The manipulatives should directly model the mathematical concept being taught (Correct answer)
- Students should be allowed to choose any manipulative they prefer
- Manipulatives should minimize the time needed to set up the lesson
Correct answer: The manipulatives should directly model the mathematical concept being taught
Manipulatives are most effective when they have a clear structural connection to the concept, such as fraction bars for comparing fractional parts.
Question 2: A student uses the strategy of breaking 8 + 6 into 8 + 2 + 4 to get 10 + 4 = 14. Which reasoning strategy is the student applying?
- Commutative property
- Making ten (bridging through ten) (Correct answer)
- Doubles plus one
- Counting all
Correct answer: Making ten (bridging through ten)
The student decomposes 6 to make a ten first, then adds the remainder—a strategy called 'making ten' or 'bridging through ten.'
Question 3: Which type of question promotes the HIGHEST level of mathematical thinking during classroom discussion?
- 'What is 6 × 7?'
- 'Is your answer even or odd?'
- 'Why does your strategy always work, and can you prove it?' (Correct answer)
- 'Did you use a calculator?'
Correct answer: 'Why does your strategy always work, and can you prove it?'
Asking students to justify and generalize their strategy promotes analysis and evaluation—higher-order thinking skills.
Question 4: A teacher notices that ELL students struggle with math word problems despite understanding the calculations. What instructional accommodation is MOST effective?
- Exempt ELL students from word problems
- Provide word problems with visual supports, simplified language, and key vocabulary pre-taught (Correct answer)
- Read the problems aloud once and move on
- Assign simpler problems with smaller numbers only
Correct answer: Provide word problems with visual supports, simplified language, and key vocabulary pre-taught
Visual supports and pre-taught vocabulary reduce language barriers while preserving the mathematical rigor of the task.
Question 5: In the context of early geometry instruction, which activity is MOST developmentally appropriate for kindergarten students?
- Calculating perimeter of rectangles
- Identifying and sorting two-dimensional shapes by their attributes (Correct answer)
- Learning the Pythagorean theorem with visual proof
- Plotting points on a coordinate plane
Correct answer: Identifying and sorting two-dimensional shapes by their attributes
Kindergarten TEKS focus on identifying, sorting, and describing two-dimensional shapes by their properties through hands-on exploration.
Question 6: A teacher presents a pattern: 2, 4, 6, 8, __ and asks, 'What comes next and why?' What mathematical concept does this question MOST directly develop?
- Place value
- Multiplication facts
- Algebraic thinking through identifying and extending patterns (Correct answer)
- Measurement estimation
Correct answer: Algebraic thinking through identifying and extending patterns
Identifying and extending repeating or growing patterns is a foundational algebraic thinking skill in early mathematics.
Question 7: Which instructional sequence BEST represents the concrete-to-abstract progression for teaching addition with regrouping?
- Algorithm → word problems → manipulatives
- Flashcards → timed tests → word problems
- Base-ten blocks → drawn place-value diagrams → standard algorithm (Correct answer)
- Memorize rules → practice problems → manipulatives
Correct answer: Base-ten blocks → drawn place-value diagrams → standard algorithm
Moving from physical blocks (concrete) to drawings (representational) to the algorithm (abstract) follows the CPA framework supported by research.
TExES EC-6 Mathematics Instruction & Problem Solving 4
When selecting manipulatives for a lesson on fractions, which consideration is MOST important for instructional effectiveness?