Entry task• 1) What can be concluded from the following pattern?

• 1 + 2 + 3 + 4 + 5 = 15 = 3 × 5• 2 + 3 + 4 + 5 + 6 = 20 = 4 × 5• 3 + 4 + 5 + 6 + 7 = 25 = 5 × 5• 4 + 5 + 6 + 7 + 8 = 30 = 6 × 5• 5 + 6 + 7 + 8 + 9 = 35 = 7 × 5

• 6 + 7 + 8 + 9 + 10 = 40 = 8 × 5

• 2) Can you find the pattern? J,F,M,A,…

Using Patterns and Inductive

Reasoning

Learning Target:I can observe patterns and

reach a conclusion based on those patterns

Definitions

• Inductive Reasoning – type of reasoning that allows you to reach

conclusions based on a pattern of specific examples

• Conjecture – conclusion reached by using inductive

reasoning

• Counterexample– An example that shows a conjecture is incorrect

• We can all see the pattern here, but what is important is the ideas we can take away from this to help us see other patterns.

Extra credit

• Find the sum of all numbers from 1 to 100– Hint : Look for a pattern– (you will not get credit if you simply use a

calculator, you must find the pattern)

Homework

• Homework: p. 85 #7,12,13,14,21,23,33,35,37,39,41,46,53,55

• Challenge - 56