Difference between revisions of "Activities-Real numbers"
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#Pupil must have a sound understanding of Euclid's lemma | #Pupil must have a sound understanding of Euclid's lemma | ||
#The difference between mathematical proofs and Verification/Justification-the scope of mathematical proofs is beyond verification-Higher order skill in problem solving | #The difference between mathematical proofs and Verification/Justification-the scope of mathematical proofs is beyond verification-Higher order skill in problem solving | ||
| + | ==Method -1: Solution by cases== | ||
| + | Proposition: x is an integer. i.e., x=m, where m is an integer<br> | ||
| + | Conclusion : x(x+1) is an even integer. i.e., x(x+1) =2K<br> | ||
| + | |||
| + | Pupil can solve this in several ways viz., proofs by cases. | ||
| + | ===Case -1: x is an even integer === | ||
Revision as of 05:18, 10 July 2014
Problem 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
- What is an integer?
- What is an even integer?
- What is an odd integer?
- X and ( x+1) are consecutive integers and x(x+1) is the representation of the product
- Pupil should have the concept of distributive property of integers
- The pupil must have an opportunity for an arguement that the proof is true even of negative integers
- Pupil must have a sound understanding of Euclid's lemma
- The difference between mathematical proofs and Verification/Justification-the scope of mathematical proofs is beyond verification-Higher order skill in problem solving
Method -1: Solution by cases
Proposition: x is an integer. i.e., x=m, where m is an integer
Conclusion : x(x+1) is an even integer. i.e., x(x+1) =2K
Pupil can solve this in several ways viz., proofs by cases.