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Folding Paper How many rectangles?

Can you find a pattern that you can describe and then predict how many rectangles on the next fold?. Folding Paper How many rectangles?. 1 st fold. 2. 4. 2 nd fold. 8. 3 rd fold. 4 th fold. 16. 5 th fold. 32. 25 th fold. 50. 2.1 Inductive Reasoning Chapter 2 Pg 82-84.

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Folding Paper How many rectangles?

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  1. Can you find a pattern that you can describe and then predict how many rectangles on the next fold? Folding PaperHow many rectangles? 1st fold 2 4 2nd fold 8 3rd fold 4th fold 16 5th fold 32 25th fold 50

  2. 2.1 Inductive ReasoningChapter 2 Pg 82-84 DoDEA Standards Addressed in this lesson: G.6: Proof and ReasoningStudents apply geometric skills to making conjectures, using axioms and theorems, understanding the converse and contrapositive of a statement, constructing logical arguments, and writing geometric proofs.  G.1.1: Demonstrate understanding by identifying and giving examples of undefined terms, axioms, theorems, and inductive and deductive reasoning Objectives: I CAN use patterns to make conjectures. I CAN disprove geometric conjectures using counterexamples.

  3. Patterns and Inductive Reasoning What You'll Learn You will learn to identify patterns and use inductive reasoning. If you were to see dark, towering cloudsapproaching, you might want to take cover. What would cause you to think bad weather is on its way ? Your past experience tells you that athunderstorm is likely to happen. When you make a conclusion based on a pattern of examples or past events, you are using inductive reasoning.

  4. What teams will go to the next Super Bowl? How do you know? What evidence did you use to make your prediction? Inductive Reasoning is used to predict a future event based on observed patterns.

  5. X 2 X 2 X 2 + 1 X 2 + 3 + 5 + 7 + 9 X 2 Patterns and Inductive Reasoning You can use inductive reasoning to find the next terms in a sequence. Find the next three terms of the sequence: 24, 48, 96, 3, 6, 12, Find the next three terms of the sequence: 16, 23, 32 7, 8, 11,

  6. Patterns and Inductive Reasoning Draw the next figure in the pattern. Lesson 2-1 Patterns and Inductive Reasoning

  7. Example #1Describe how to sketch the 4th figure. Then sketch it. Each circle is divided into twice as many equal regions as the figure number. The fourth figure should be divided into eighths and the section just above the horizontal segment on the left should be shaded.

  8. Example #2Describe the pattern. Write the next three numbers. Multiply by 3 to get the next number in the sequence.

  9. The next figure is . Example 1C: Identifying a Pattern Find the next item in the pattern. In this pattern, the figure rotates 90° counter-clockwise each time.

  10. Vocabulary conjecture inductive reasoning counterexample

  11. What is a conjecture? Inductive Reasoning: conjecture based on patterns What is inductive reasoning? Proving conjectures TRUE is very hard. Proving conjectures FALSE is much easier. Conjecture: conclusion made based on observation Counterexample: example that shows a conjecture is false What is a counterexample? How do you disprove a conjecture? What are the steps for inductive reasoning? How do you use inductive reasoning? Steps for Inductive Reasoning Find pattern. Make a conjecture. Test your conjecture or find a counterexample.

  12. To show that a conjecture is always true, you must prove it. To show that a conjecture is false, you have to find only one example in which the conjecture is NOT true. This case is called acounterexample. A counterexample can be a drawing, a statement, or a number.

  13. Steps for Inductive Reasoning

  14. 23° 157° Check It Out! Show that the conjecture is false by finding a counterexample. Supplementary angles are always adjacent. True or false? If false provide a counterexample. This drawing is a counterexample to the statement, making it false. The supplementary angles are not adjacent, so the conjecture is false.

  15. Example #3Make and test a conjecture about the sum of any 3 consecutive numbers.(Consecutive numbers are numbers that follow one after another like 3, 4, and 5.) Conjecture: The sum of any 3 consecutive numbers is 3 times the middle number.

  16. sum > larger number Example #4Conjecture:The sum of two numbers is always greater than the larger number.True or false? A counterexample was found, so the conjecture is false.

  17. Hannah sells snow cones during soccer tournaments. She records data for snow cone sales and temperature. a. Predict the amount of snow cone sales when the temperature is 100°F. b. Is it reasonable to use the graph to predict sales for when the temperature is 15ºF? Explain. One Possible Answer: Sales decrease as temperature drops. Sales at 100°F is predicted to be in this range. $4500 to $5000

  18. Objective Practice: Go to flippedmath.com Select courses tab MyGeometry Semester 1 Unit 2 Section 2.1 Watch the Inductive Reasoning video – This video is accessible from any internet connection. USE IT IF YOU ARE STUCK AT HOME Complete Packet 2.1 while listening to the video. After video complete the Practice 2.1 exercises. HW Complete the entire Packet 2.1 DUE FRIDAYOct 12

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