conjectures patterns counter- examples linesplanes 10 20 30 40 50
TRANSCRIPT
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