1. Entry Task P. 82 – Blue Box LT: I can observe patterns and reach a conclusion based on those patterns

2. Using Patterns and Inductive Reasoning Learning Target: I can observe patterns and reach a conclusion based on those patterns Success Criteria: I can recognize patterns both geometrically and algebraically

3. Patterns 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,… LT: I can observe patterns and reach a conclusion based on those patterns

4. Patterns 1,1,2,3,5,8,13… What are the next 3? Can you create one for your partner? LT: I can observe patterns and reach a conclusion based on those patterns

5. 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 LT: I can observe patterns and reach a conclusion based on those patterns

6. 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. LT: I can observe patterns and reach a conclusion based on those patterns Important!!!

7. LT: I can observe patterns and reach a conclusion based on those patterns

9. Counter Example If a flower is red, it is a rose. –Is this true? Always? If you can give me an example of when it isn’t true then it is a false statement. It only takes one time to prove something false. That example of when a statement is false is called a counterexample. LT: I can observe patterns and reach a conclusion based on those patterns

10. 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) LT: I can observe patterns and reach a conclusion based on those patterns

11. Homework Homework: p. 85 #7-55 odds Challenge - 56 LT: I can observe patterns and reach a conclusion based on those patterns