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Beginning to understand PROOF. TBAT  prove something is not true by counter-example  prove something you know.... PLTS To get stuck and be ok with it!

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Presentation on theme: "Beginning to understand PROOF. TBAT  prove something is not true by counter-example  prove something you know.... PLTS To get stuck and be ok with it!"— Presentation transcript:

1 Beginning to understand PROOF

2 TBAT  prove something is not true by counter-example  prove something you know.... PLTS To get stuck and be ok with it!

3 All prime numbers are odd 3, 5, 7, 11, 13, 17, 19..... they are all odd....... so I have proved it! Have you proved it??

4 A counter example show something can’t be true All prime numbers are odd 3, 5, 7, 11, 13, 17, 19..... they are all odd....... so I have proved it! What about 2?

5 Find a counter example if you can 1.If you subtract 7 from a number the answer is always odd 2.When you square a number the answer is always even 3.When you treble a prime number, the answer is always odd 4.When you find the product of two consecutive numbers, the answer is always odd

6 Prove to me that the area of a rectangle is base x height

7  What is area?  What is the area of this rectangle?  What can we say about any rectangle?

8 Angles in a triangle add up 180  Do they? How do you know? Always? Show me!!!!

9 Angles in a triangle add up 180  Will this work for any triangle? Is this a proof? Are you convinced?

10 http://www.mathsrevision.net/gcse/pages.php?page=17 Is this proof better???? http://www.youtube.com/watch?v=f3mf5s3_mvQ

11 TBAT  prove something is always true using algebra PLTS To get stuck and be ok with it!

12 Prove to me that the sum of two consecutive even numbers is always even

13 Let n be any number What can we ‘do to’ n to make sure it’s always even

14 Prove to me that the sum of two consecutive even numbers is always even What if the numbers were even but not consecutive ????

15 Now try without me Prove  Squaring an even number gives an number that is in the four times table  The sum of an odd number and an even number is always odd  The answer to each equation in the pattern is 4 5 x 8 – 4 x 9 = 4 6 x 9 – 5 x 10 = 4 7 x 10 – 6 x 11 = 4


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