Inductive Reasoning and Conjecture Section 2.1

Sarah is making a tile pattern with identical regular hexagons Sarah is making a tile pattern with identical regular hexagons. She wants to outline the pattern with ribbon and needs to know its outer perimeter. What is the outer perimeter if she uses 4 hexagons? What is the outer perimeter if she uses 8 hexagons? What is the outer perimeter if she uses 30 hexagons?

Shawna liked to jog in the late afternoon Shawna liked to jog in the late afternoon. As she passed her neighbors’ house, their dog would hear her and start barking. After the dog had barked for 15 seconds, two other dogs would join in and bark. In another 15 seconds, each barking dog would inspire two more dogs to start barking. At the end of 1 minute, how many dogs were barking? At the end of 2 minutes, how many dogs were barking? Looking For Patterns

Find the distance around each figure. Organize your results in a table. Use your table to describe a pattern in the distances. Predict the distance around the twentieth figure in this pattern. Looking for Patterns

Melanie is having an allergic reaction when she eats certain foods Melanie is having an allergic reaction when she eats certain foods. Here is a list of foods that Melanie ate last month with their ingredients listed. Hypothesize what Melanie is allergic to. Reaction Macaroni Salad Macaroni, Mayo, Mini Shrimp, Green Onions Fish Tacos Tortilla, Shrimp, Cheese, Lettuce, Pico No Reaction Salmon Grilled Cheese Sandwich Beef Tacos Tortilla, hamburger, cheese, lettuce, pico Looking for Patterns

Conjectures and Counterexamples What county do students at Madison High School live in? What age are the students in our class? Conjectures and Counterexamples

Conjectures Make a conjecture given the following examples: A number sequence: 2, 5, 8, 11, … A number sequence: 16, 8, 4, 2, … The product of any 2 even numbers is ______________. The difference of any 2 odd numbers is ____________. Conjectures

#30 Carrie collected canned food for a homeless shelter in her area each day for a week. On day one, she collected 7 cans of food. On day two, she collected 8 cans. On day three, she collected 10 cans. On day four, she collected 13 cans. If Carrie wanted to give at least 100 cans of food to the shelter and this pattern of can collecting continued, did she meet her goal?

I have made several conjectures. See if you can find a counterexample. Everyone in this room is younger than 19. If you like chocolate, then you will love 3 Musketeer bars! When you add 2 numbers, the sum is always greater than either of the 2 numbers. If the quotient of 2 numbers is positive, both numbers must be positive. If 𝑚 and 𝑛 are nonzero real numbers, than 𝑚 𝑛 <𝑚. Counterexamples