Mathematics Instruction & Problem Solving Flashcards

A student solving 63 − 28 writes: 60 − 20 = 40, then 3 − 8, says 'I can't do that,' and stops. Which instructional strategy addresses this error most directly?

Answer: Use base-ten blocks to show trading a ten for ten ones so the ones place has enough to subtract

Base-ten blocks make regrouping concrete by physically trading a ten rod for ten unit cubes, connecting the procedure to its meaning.

Which representation best supports the transition from concrete to abstract understanding of multiplication for early elementary students?

Answer: Drawing an array to represent 3 × 5 before writing the number sentence

Arrays provide a pictorial/representational bridge between physical objects and the abstract multiplication symbol.

A teacher asks students to sort shapes into groups and explain their sorting rule. Which mathematical practice does this activity MOST directly promote?

Answer: Constructing viable arguments and critiquing the reasoning of others

Sorting and explaining a rule requires students to construct and communicate mathematical arguments, a key mathematical practice.

What does research identify as the MOST critical factor in helping young children develop number sense?

Answer: Providing rich experiences with counting, comparing, and composing/decomposing numbers

Number sense develops through varied hands-on experiences that build flexible understanding of quantity and number relationships.

A teacher uses a balance scale to introduce the concept of equality. A student adds 3 cubes to one side. What question BEST deepens algebraic thinking at this point?

Answer: What could you put on the right side to make the scale balance?

Asking what restores balance develops the concept that both sides of an equation must be equal, a foundation for algebraic reasoning.

Which situation BEST illustrates the use of the 'think-aloud' strategy in mathematics instruction?

Answer: The teacher verbalizes every step and decision while working through a problem

Think-aloud makes the teacher's reasoning visible by narrating thought processes, which models metacognitive problem-solving strategies.

A student can count to 20 but cannot tell that 15 is greater than 12 without recounting. Which concept is the student MOST likely lacking?

Answer: Number magnitude and comparison

The ability to compare numbers without recounting requires understanding number magnitude, which goes beyond rote counting.