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Ch. 1.notebook
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January 18, 2016
Chapter 1: Inductive and Deductive Reasoning
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Section 1.1: Making Conjectures: Inductive Reasoning
Conjecture a testable expression that is based on available evidence but is not yet proved.
** In this chapter, you will be asked to write many conjectures. Please write your conjectures in sentence form.
Inductive Reasoning drawing a general conclusion by observing patterns and identifying properties in specific examples.
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Example 1Write a conjecture to describe the pattern in each sequence. Use the conjecture to determine the next item.a) 2, 4, 6, 8, ...
b) 1, 2, 4, 8, ...
c) 10, 4, ...
d) 3, ...
Conjecture: Is an unproven conclusion based on evidence
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Example 2Make a conjecture about the product of two odd integers.
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Example 3Make a conjecture about the difference between consecutive perfect squares.
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Example 4Make a conjecture about the sum of the squares of two consecutive numbers.
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Example 5: Examine the pattern in the addition sentences and their sums. What conjecture can you make?
1+3 = 4 3+5 = 8 5+7 = 12 7+9 = 16
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Carol gathered the following evidence and noticed a pattern
10 + 01 = 11 24 + 42 = 66 78 + 87 = 165
13 + 31 = 44 39 + 93 = 132 89 + 98 = 187
Example 6
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Anita works at a coffee shop. Number of sales for regular, medium and large coffees were 3000, 3500, and 7000 in January. For February Anita ordered twice as many large coffee cups as regular or medium cups. What conjecture might she have made?
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Make a conjecture about the sum of two even integers. Develop evidence to test your conjecture.
Make a conjecture about the sum of one odd integer and one even integer. Test your conjecture with at least three examples.
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Make a conjecture based on the pattern in the table
Multiples of 3 12 15 18 21 24 27 30
Sum of digits 3 6 9 3 6 9 3
Make a conjecture based on the pattern in the table.
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Write a conjecture for:
11 x 42 = 462
11 x 71 = 781
11 x 45 = 495
When 11 is multiplied by a two digit number, the three digit answer begins with the first number of the two digit number and ends with the last digit of the two digit number. The middle number is the sum of the two digits of the original two digit number.
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Pages 12 – 13 #‛s 1 – 3, 5 – 9
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Section 1.3: Using Reasoning to Find a Counterexample to a Conjecture
Counterexample an example that proves a conjecture is wrong
**Only one counterexample is needed to show that a conjecture is invalid!
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