Activities-Real numbers

Problem 1

1. For every integer prove that x(x+1) is an even integer (Problem related to mathematical proofs in Chapter 1)

Approaches to solutions

The concepts that a pupil must know are

1. What is an integer?
2. What is an even integer?
3. What is an odd integer?
4. X and ( x+1) are consecutive integers and x(x+1) is the representation of the product
5. Pupil should have the concept of distributive property of integers
6. The pupil must have an opportunity for an arguement that the proof is true even of negative integers
7. Pupil must have a sound understanding of Euclid's lemma
8. The difference between mathematical proofs and Verification/Justification-the scope of mathematical proofs is beyond verification-Higher order skill in problem solving