Download 5.1- Patterns and Conjectures

Integrated Math 1 Extended - Unit 5
Name: __________________________
Date: _____________ Period: ______
5.1- Patterns and Conjectures
Objective: To determine the next item in a pattern and draw logical conclusions based on the
pattern, write conjectures and provide counterexamples
Warm-up:
Vocabulary:
Inductive reasoning – The process of arriving at a conclusion based on a set of
observations.
Conjecture – An unproven statement that is based on a pattern or observations.
Counterexample – An example that disproves a statement or a conjecture.
Example #1:
Sketch the next picture in the pattern
A.)
C.)
B.)
Example #2:
Identify the next two numbers in the pattern and describe the pattern (rule)
A.) 1, 2, 4, 7, 11, ___________
Pattern:
B.) 25, 23, 21, 19, 17, 15, __________
Pattern:
C.) 2, 4, 8, 16, 32, 64, ___________
Pattern:
D.) 0, 1, 1, 2, 3, 5, 8, 13, 21, __________
Pattern:
E.) 1, 1, 2, 1, 1, 3, 1, ______________
Pattern:
Example #3:
Is the conjecture true or false? If it is false give a counterexample.
1.
Conjecture: We all live in Antioch, Illinois.
2.
Conjecture: Sunny days make us happy.
3.
Conjecture: All three sided shapes are triangles
4.
Conjecture: Two angles that are both right angles are congruent.
5.
Conjecture: Anything on the wall is a whiteboard.
6.
Conjecture: All shapes with four right angles are squares
We need to complete the conjecture below.
CONJECTURE: The sum of any two odd numbers is _____
First, double-check that you understand what you need to test.
Do you know what “sum” means and what an “odd number” is?
Finish the examples below, then look for a pattern in the solutions.
1+1=
5+7=
7 + 11 =
3 + 13 =
21 + 13 =
73 + 19 =
Based on the pattern in the examples, complete the conjecture.
___
Example #4:
Complete the conjecture.
CONJECTURE A: The product of any two odd numbers is
________.
CONJECTURE: If the sum of two numbers is positive, then the numbers must be is
CONJECTURE: The sum of two numbers is always
________.
_______________ than both numbers.
Example #5:
Write a conjecture based on the given information.
A.
Given: Point C lies between points A and B
Conjecture: ____________________________________________________________
B
Given: <1 and <2 form a right angle
Conjecture: ____________________________________________________________
C.
Given: Points A, B, and C are non-collinear
Conjecture: ____________________________________________________________
D.
Given:
AB
and
CD
intersect at point E
Conjecture: ____________________________________________________________