2. 2.1 Describe patterns and use inductive reasoning August 31, 2011
2-1 Inductive Reasoning
Objectives:
1. Describe patterns
2. Use inductive reasoning to find the next term in a number or picture pattern.
Draw the next 2 figures in the sequence below:
HW pg. 75 #317 2
4. 2.1 Describe patterns and use inductive reasoning August 31, 2011
What is inductive reasoning?
reaching a conclusion based on a pattern discovered through observation
Conjecture: an unproven statement that is based on observation
Make a conjecture about the rule for the sequence below & find the next 2 terms:
5, 10, 15, 20, __, __ You can add 5 to the last number to
get the next number in the sequence;
25, 30
Make a conjecture about the rule for the sequence below & find the next 2 terms:
1, 1 , 1, 1 , __, __ Multiply by -1/3 to get the
3 9 27 next number in the sequence;
1/81, -1/243
HW pg. 75 #317 4
6. 2.1 Describe patterns and use inductive reasoning August 31, 2011
Counterexample: a specific case when the conjecture is false
The past 5 times that you have walked across your carpet barefoot and then touch the
door knob on the front door you were shocked.
a) What conclusion might you make about the next time you walk across
the floor barefoot and touch the door knob?
b) What counterexample would you need to find to disprove this
conclusion?
HW pg. 75 #317 6
