Download - 2-1 Patterns and Inductive Reasoning Objective: Use inductive reasoning to make conjectures
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2-12-1Patterns and Inductive Patterns and Inductive
ReasoningReasoning
Objective:Objective:
Use inductive reasoning to Use inductive reasoning to make conjecturesmake conjectures
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• Inductive ReasoningReasoning based on patterns you observe.
• ConjectureA conclusion you reach using inductive reasoning.
ExampleA scientist dips a platinum wire into a solution containing salt (sodium chloride), passes the wire over a flame, and observes that it produces an orange-yellow flame.
She does this with many other solutions that contain salt, finding that they all produce an orange-yellow flame.
Conjecture
If a solution contains sodium chloride, then in a flame test it produces an orange-yellow flame.
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Example 2:Consider the sequence
2, 4, 7, 11, . . .
Make a conjecture about the rule for generating the sequence.Then find the next three terms.
Conjecture:
You always add the next counting number to get the next term.
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• Patterns about 1st, 3rd, and 5th shape.– Half shaded circles, with the circle rotating a quarter turn
counter clockwise from previous circle.• Patterns about 2nd, 4th, and 6th shape.
– Polygons with consecutive odd numbered sides and a triangular pattern of dots, solid dot on top two hollow dots on bottom.
• Draw next two shapes.
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Find one counterexample to prove a conjecture is false.
CounterexampleAn example that shows that a conjecture is incorrect.
If the name of a month starts with the letter J, it is a summer month.
Counterexample: January starts with the letter J and it is a winter month.
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What is a counterexample for each conjecture?
• If a flower is red, it is a rose.
• When you multiply a number by 3, the product is divisible by 6.
p. 85: 7-23 odd, 31-39 odd