Conjectures Patterns Counter- examples LinesPlanes 10 20 30 40 50.

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Presentation transcript:

Conjectures Patterns Counter- examples LinesPlanes

+ Question conjectures - 10 The sum of any two odd numbers is? (LIST SIX EXAMPLES)

+ Answer conjectures – = = 6 ETC. THE SUM OF ANY TWO ODD NUMBERS IS EVEN!!!

+ Question conjectures - 20 The product of any two odd numbers is (LIST SIX EXAMPLES)

+ Answer conjectures – 20 1 X 3 = 3 7 X 9 = 63 ETC. THE PRODUCT OF ANY TWO ODD NUMBERS IS ODD!!!

+ Question conjectures - 30 The difference of any two odd numbers is _____? Show six examples!!!

+ Answer conjectures – 30 ODD! 9/3 = 3 21/ 7 = 3 Etc.

+ Question conjectures - 40 The sum of an odd number and an even number is? (list six examples!)

+ Answer conjectures – 40 ODD! = = 9 Etc.

+ Question conjectures - 50 Explain what a conjecture is!

+ Answer conjectures – 50 An unproven statement that is based upon a pattern or observation

+ Question patterns- 10 4, 8, 12, 16… find the next three numbers!

+ Answer patterns – 10 20, 24, 28

+ Question patterns , 30, 25, 20, find the next three!

+ Answer patterns – 20 15, 10, 5

+ Question patterns- 30 3, 0, -3, 0, 3, 0…find the next two!

+ Answer patterns – 30 The numbers in the odd numbered positions alternate between 3 and -3; the numbers in the even number positions are 0; -3, 0

+ Question patterns , 7, 1, -5…find the next two numbers!

+ Answer patterns – 40 Each number is 6 less than the previous number; -11, -17

+ Question patterns , 7, 11, 17, 25…find the next number!

+ Answer patterns – 50 Begin with 5 and add two, then 4, then 6, then 8 and so on…35!

+ Question counterexamples - 10 The sum of two numbers is always greater than the larger of the two numbers.

+ Answer counterexamples – 10 Not if you add 0 or –s!

+ Question counterexamples - 20 What is a counterexample?

+ Answer counterexamples – 20 An example that shows a conjecture if false.

+ Question counterexamples - 30 If a four sided shape has two sides the same length then it must be a rectangle.

+ Answer counterexamples – 30 ***draw on board

+ Question counterexamples - 40 All shapes with four sides are the same length are squares…

+ Answer counterexamples – 40

+ Question counterexamples - 50 If the product of two numbers is even then the numbers must be even.

+ Answer counterexamples – 50 Let the numbers be 2 and 3. The product 6, is even, but one of the numbers is not even. The conjecture is false.

+ Question lines - 10 THROUGH ANY ___ POINTS THERE IS EXACTLY ONE _____.

+ Answer lines – 10 TWO LINE

+ Question lines - 20 GIVE THREE NAMES FOR THE LINE k G F A

+ Answer lines – 20 AFG GFA k

+ Question lines - 30 Coplanar lines are…

+ Answer lines – 30 Lines that lie on the same plane!

+ Question lines - 40 Two points create a _______ even though you can’t see it!

+ Answer lines – 40 line

+ Question lines - 50 NAME THE LINE THAT IS INTERSECTING THE PLANE l n y

+ Answer lines – 50 l

+ Question planes - 10 What are coplanar points?

+ Answer planes – 10 Points that lie on the same plane

+ Question planes - 20 Draw and label a plane!!!

+ Answer planes – 20 This will vary!

+ Question planes - 30 A plane has how many dimensions?

+ Answer planes – 30 Two!

+ Question planes - 40 Name three points that are coplanar A B C V

+ Answer planes – 40 A B and C

+ Question planes - 50 The reason that two points can’t form a plane is because with only two points there would be a _____________ number of planes.

+ Answer planes – 50 infinite