Rational Numbers and Powers

# Instructional Objectives

The students should be able to know the following concepts after the lesson

• Rational numbers are closed under the operations of addition, subtraction and multiplication.
• The operations addition and multiplication are (i) commutative for rational numbers. (ii) associative for rational numbers.
• The rational number 0 is the additive identity for rational numbers.
• The rational number 1 is the multiplicative identity for rational numbers.
• The additive inverse of the rational number a/b is -a/b and vice-versa.
• The reciprocal or multiplicative inverse of the rational number a/b is c/d if a/b*c/d=1 * Distributivity of rational numbers: For all rational numbers a, band c, a(b+ c) = ab+ ac and a(b– c) = ab– ac
• Rational numbers can be represented on a number line.
• Between any two given rational numbers there are countless rational numbers. The idea of mean helps us to find rational numbers between two rational numbers.
• Numbers with negative exponents obey the following laws of exponents. (a) am× an = am+n (b) am÷ an = am–n (c) (am)n = amn (d) am × bm = (ab)m (e) a0 = 1 (f) am/bm = (a/b)m
• Very small numbers can be expressed in standard form using negative exponents.

## Teaching process

• Properties of rational numbers (including identities). Using general form of expression to describe properties
• Consolidation of operations on rational numbers.
• Representation of rational numbers on the number line
• Between any two rational numbers there lies another rational number (Making children see that if we take two rational numbers then unlike for whole numbers, in this case you can keep finding more and more numbers that lie between them.)
• Word problem (higher logic, two operations, including ideas like area)
• Integers as exponents.
• Laws of exponents with integral powers.

## Special needs

• Need to identify gray areas among students
• Provide necessary support though IEP and additional worksheets

## Evaluation tools

• Constant evaluation through interactions in classroom.
• Seminar by students on a self chosen topic
• Exercise questions and worksheets on respective sub topic covered.

## Self Reflection

• Very responsive children and eager to learn
• Covered most of the topics