TExES EC-6 Mathematics Instruction & Problem Solving 2 — Questions and Answers
Question 1: A teacher wants students to discover the relationship between repeated addition and multiplication. Which instructional approach best supports this conceptual understanding?
- Drill multiplication facts using flashcards
- Have students model 4 groups of 3 objects then write the corresponding multiplication sentence (Correct answer)
- Assign a worksheet of multiplication problems to practice
- Show students the commutative property using examples
Correct answer: Have students model 4 groups of 3 objects then write the corresponding multiplication sentence
Using manipulatives to model equal groups connects concrete experience to the abstract multiplication symbol, building conceptual understanding.
Question 2: When teaching place value, a second-grade teacher uses base-ten blocks. A student correctly identifies that 3 tens and 7 ones equals 37. What is the MOST appropriate next instructional step?
- Move immediately to three-digit numbers
- Ask the student to explain why the 3 is in the tens place and the 7 is in the ones place (Correct answer)
- Have the student memorize all two-digit numbers
- Introduce addition of two-digit numbers without regrouping
Correct answer: Ask the student to explain why the 3 is in the tens place and the 7 is in the ones place
Asking for explanation assesses depth of understanding and promotes mathematical reasoning before advancing to more complex content.
Question 3: Which problem-solving strategy is MOST appropriate when helping kindergarteners determine how many students are in the class if 5 are absent and 18 are present?
- Write an algebraic equation
- Use a number line to count on from 18 to find the total (Correct answer)
- Apply the standard algorithm for addition
- Memorize number bonds to 23
Correct answer: Use a number line to count on from 18 to find the total
A number line provides a concrete, visual tool for counting on that is developmentally appropriate for kindergarteners.
Question 4: A student consistently makes errors when adding fractions by adding both numerators and denominators (e.g., 1/2 + 1/3 = 2/5). What is the BEST instructional response?
- Provide more practice problems of the same type
- Use fraction strips to demonstrate why denominators must be equal before adding (Correct answer)
- Re-teach the standard algorithm with step-by-step instructions
- Mark the answers wrong and ask the student to try again
Correct answer: Use fraction strips to demonstrate why denominators must be equal before adding
Fraction strips provide a visual, conceptual explanation for why common denominators are required, addressing the root misconception.
Question 5: According to the TEKS, which of the following is an appropriate expectation for first-grade students regarding measurement?
- Calculate area using square units
- Measure length using non-standard units and compare lengths of objects (Correct answer)
- Convert between inches and centimeters
- Use a ruler to measure to the nearest half-inch
Correct answer: Measure length using non-standard units and compare lengths of objects
First-grade TEKS focus on measuring with non-standard units and comparing lengths, which builds foundational measurement concepts.
Question 6: A teacher poses this problem: 'Maria has some apples. She gives 4 away and has 9 left. How many did she start with?' What type of problem structure is this?
- Join result unknown
- Separate change unknown
- Start unknown (separate) (Correct answer)
- Compare difference unknown
Correct answer: Start unknown (separate)
The initial quantity is missing after a removal action, making this a 'start unknown' problem in the separate problem type.
Question 7: Which formative assessment technique is MOST effective for quickly gauging all students' understanding of a math concept mid-lesson?
- End-of-unit test
- Individual student interviews conducted one at a time
- Exit tickets or hand signals where all students respond simultaneously (Correct answer)
- Calling on students who raise their hands
Correct answer: Exit tickets or hand signals where all students respond simultaneously
Simultaneous response techniques like exit tickets or hand signals provide immediate data from every student, not just those who volunteer.
TExES EC-6 Mathematics Instruction & Problem Solving 2
A teacher wants students to discover the relationship between repeated addition and multiplication.
Which instructional approach best supports this conceptual understanding?