Daily-Quiz (Monday) 9/9
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Daily-Quiz (Monday) 9/9
M is the midpoint of . L has coordinates (7, -4) and M has coordinates (1, -8). Find the coordinates of N.
(−𝟓 ,−𝟏𝟐)
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Daily-Quiz (Tuesday) 9/10
Find the coordinates of the midpoint of the segment.
with A(-2,3) and B(4,1).
𝑴 (𝟏 ,𝟐)
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Daily-Quiz (Wed) 9/11
1280, 5120, 20480
Multiply the previous number by 4
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Daily-Quiz (Thurs.) 9/12
3, 9, 27
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2.1 Using Inductive Reasoning to make conjectures
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Learning Objective: SWBAT
1. Use inductive reasoning to identify patterns and make conjectures.
2. Find counterexamples to disprove conjectures.
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Conjecture – is an unproven statement that is based on observation.
Example: If yesterday was Monday and today is Tuesday tomorrow is ________.
KEY TERMS:
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Inductive Reasoning – process of recognizing or observing a pattern and drawing conclusion.
Example #1:
KEY TERMS:
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Describe the pattern in the numbers-1, -4, -16, -64, …Write the next 3 numbers in the pattern.
Example#2:
-256, -1024, -4096
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Example#3:Given 5 noncollinear points, make a conjecture about the # of ways to connect different pairs of the points.
Make a table and look for a pattern.
Make a Conjecture
0 1 3 6 10
1 2 3 4
6+4 10
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Counterexample – Is a specific case for which the conjecture is false.
KEY TERMS:
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A student makes the following conjecture about the sum of two #’s. Find a counterexample to disprove the students conjecture.
Example #4:
Conjecture: The sum of two #’s is always greater than the larger number.
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Example #4:Conjecture: The sum of two #’s is always greater than the larger number.
1 + 2 = 33 > 2 True -3 + -4 = -7
-7 -4 False
So, because a counterexample exist the conjecture is false.
Is this true for all positive integers?
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Example #5: (you try)
Conjecture: The value of is always greater than the value of x.
So, because a counterexample exist the conjecture is false.
Find a counterexample to show that the followingconjecture is false.
>
4 > 2 True .25 .50 False
>
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Example #6:
Conjecture: The product is equal to , for
So, because a counterexample exist the conjecture is false.
Find a counterexample to show that the followingconjecture is false.
Counterexample:
(𝟏+𝟐)𝟐=𝟗 = 5 False
= +
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Example #7:
Conjecture: The difference of 2 positive #’s is always a positive #.
So, because a counterexample exist the conjecture is false.
Find a counterexample to show that the followingconjecture is false.
Counterexample:
False10 – 4 = 6 True
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Example #8:
Given: AB + BC = ACConjecture: AB = BC
So, because a counterexample exist the conjecture is false.
Find a counterexample to show that the followingconjecture is false.
Counterexample:
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Assignment 2.1
Worksheet pg. 15Front & back