Q1 · hard · AI-verified
A Class 5 student claims: 'Dividing a number always makes it smaller.' A teacher wants to create a SINGLE counter-example that most effectively challenges this overgeneralization. Which example should the teacher choose?
- 8 ÷ (1/2) = 16
- 0 ÷ 5 = 0
- 15 ÷ 3 = 5
- 12 ÷ 1 = 12
Q2 · hard · AI-verified
A Class 4 teacher observes that when asked to find the perimeter of a rectangle with length 12 cm and breadth 7 cm, a student writes: 12 × 7 = 84 cm. Which of the following BEST describes the conceptual error the student is making?
- The student is applying the correct formula but has used the wrong numbers, indicating a reading comprehension error rather than a mathematical misconception.
- The student is confusing the formula for area (l × b) with the formula for perimeter (2 × (l + b)), showing a lack of conceptual distinction between the two measurements.
- The student has made a procedural error in multiplication and would solve the problem correctly if reminded to add before multiplying.
- The student lacks knowledge of what a rectangle is and needs to be retaught basic shapes before attempting perimeter.
Q3 · hard · AI-verified
In a Class 5 problem-solving lesson, a student correctly computes 3/4 + 1/3 = 4/7 by adding numerators and denominators separately. Which of the following instructional approaches would MOST effectively remediate this error?
- Use a fraction strip or number line to show that 3/4 is already close to 1, so the answer cannot be 4/7, which is less than 3/4, thereby creating cognitive conflict.
- Immediately re-teach the LCM method and ask the student to redo the problem using LCM = 12.
- Tell the student that the rule is to find a common denominator first, and provide five similar practice problems.
- Ask the student to convert both fractions to decimals and add them to verify.
Q4 · hard · AI-verified
A teacher in Class 3 introduces multiplication by skip counting: 'Count by 6s: 6, 12, 18, 24, 30.' This teaching strategy is BEST described as helping students see multiplication as:
- Repeated addition of equal groups
- The inverse operation of division
- A shortcut to avoid counting individual objects
- A way to find the area of rectangular arrays
Q5 · hard · AI-verified
A teacher writes the problem: 'Renu has 3 bags with 8 marbles each. She gives away 2 marbles from each bag. How many marbles does she have in total?' A student writes: 3 × 8 − 2 = 22. Which error has the student made?
- The student's answer is correct; 3 × 8 − 2 = 22 marbles is the right answer.
- The student used multiplication incorrectly; the correct operation is 3 + 8 − 2 = 9.
- The student subtracted only 2 marbles instead of 2 marbles from each bag (2 × 3 = 6), giving 24 − 6 = 18 as the correct answer.
- The student subtracted from the wrong value; the correct calculation is 3 × (8 + 2) = 30.