Conjectures Patterns

Counter-example

sLines Planes

10 10 10 10 10

20 20 20 20 20

30 30 30 30 30

40 40 40 40 40

50 50 50 50 50

+Question conjectures - 10

The sum of any two odd numbers is? (LIST SIX EXAMPLES)

+Answer conjectures – 10

1 + 1 = 2

5 + 1 = 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!

2 + 3 = 5

4 + 5 = 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 - 20

35, 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 - 40

13, 7, 1, -5…find the next two numbers!

+Answer patterns – 40

Each number is 6 less than the previous number; -11, -17

+Question patterns - 50

5, 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

kG

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

ny

+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

CV

+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