Subject Matter:Patterns and Inductive Reasoning ObjectivePacing To use inductive reasoning to make conjectures 1 period Standards G-1.2 Communicate knowledge.

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Presentation transcript:

Subject Matter:Patterns and Inductive Reasoning ObjectivePacing To use inductive reasoning to make conjectures 1 period Standards G-1.2 Communicate knowledge of geometric relationships by using mathematical terminology appropriately. G-2.1 Infer missing elements of visual or numerical geometric patterns (including triangular and rectangular numbers and the number of diagonals in polygons). G-1.4 Formulate and test conjectures by using a variety of tools such as concrete models, graphing calculators, spreadsheets, and dynamic geometry software. G-1.5 Use inductive reasoning to formulate conjectures. G-1.7 Understand the historical development of geometry.

Guided Instruction and Targeted Resources Problem 1: Finding and Using Pattern A. What are the next two terms in the sequence? 3, 9, 27, 81, … B. What are the next two terms in the sequence? 45, 40, 35, 30, …

C. Look at the pattern. What are next two terms in the sequence?

Problem 2: Using Inductive Reasoning A.Look at the circles. What conjecture can you make about the number of regions 20 diameters form?

B. What conjecture can you make about the twenty- first term in R, W, B, R, W, B, …?

Problem 3: Collecting Information to Make a Conjecture A.What conjecture can make about the sum of the first 10 even numbers?

B.What conjecture can make about the sum of the first 100 even numbers?

C.What conjecture can make about the sum of the first 15 odd numbers?

D.What conjecture can make about the sum of the first 90 odd numbers?

Problem 4: Making a Prediction A. S ALES Sales of backpacks at a nationwide company decreased over a period of six consecutive months. What conjecture can you make about the number of backpacks the company will sell in May?

B. S ALES What conjecture can you make about backpack sales in June?

Problem 5: Finding a Counterexample What is the counterexample for each conjecture? A.If the name of the month starts with a letter J, it is a summer month. B.You can connect any three points to form a triangle.

What is the counterexample for each conjecture? C. When you multiply a number by 2, the product is greater than the original number.

What is the counterexample for each conjecture? D. If a flower is red, then it is a rose.

Close the instruction by asking: Q: How do you use inductive reasoning to make a conjecture? [Analyze a limited number of cases to find a pattern, then use the pattern to make a conjecture about other cases.] Practice: Do # 6 – 30 on page 85. Homework: Do # 33 – 46 on page 86.