Question

Mr. Sharma was assessing the students' work on exponents. One of the response sheet was as follows :

(a) 23 × 25 = 2⁸

(b) 32 × 42 = (12)⁴

(c) 3³ ÷ 3⁵ = 3^-2

(d) 7²⁰ ÷ 7¹⁴ = 7⁶

(e) \(9^3 \div 18^6 = \left(\dfrac{1}{2}\right)^3\)

On the basis of this response sheet Mr. Sharma can make the following observations

1. Child has understood the laws of exponents and can apply them well
2. Child has understood the laws of exponents but has made clerical errors.
3. Child has understood the laws of exponents but has not practised the questions involving division of two numbers.
4. Child has understood the law of exponents for the cases where the base is same and has missed the concept for the case where the base is different

Answer 1

Correct Answer - Option 4 : Child has understood the law of exponents for the cases where the base is same and has missed the concept for the case where the base is different

Mathematics is the study of patterns, numbers, geometrical objects, data, and information. It deals with data analysis, integration of various fields of knowledge, deductive and inductive reasoning, and generalizations.

• Assessment in mathematics refers to the process of collecting, receiving, and using data for the purpose of improvement of the mathematical learning process.
• ​It is expected that every teacher while teaching mathematics in the classroom, should explore the nature of their student's development of the concepts and procedures.

The laws of Exponents provide a set of rules that can be used to simplify complex expressions that contain exponents. There are different Exponent Rule to solve problems. In the given problem, while assessing the sheet Mr Sharma observed that child has understood the law of exponents for the cases where the base is the same and has missed the concept for the case where the base is different.

• It is observed that Options (a),(c),(d) are correct responses but others responses are incorrect. Other responses i.e Option (b),(e) are based on concepts where the base is different. It is obvious that student is facing problem when the base is different but have proper understanding and clarity when the base is same.​

​Hence, it is clear from the above observation that the child has understood the law of exponents for the cases where the base is the same and has missed the concept for the case where the base is different.