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)

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)

Daily-Quiz (Wed) 9/11

1280, 5120, 20480

Multiply the previous number by 4

Daily-Quiz (Thurs.) 9/12

3, 9, 27

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.

Conjecture – is an unproven statement that is based on observation.

Example: If yesterday was Monday and today is Tuesday tomorrow is ________.

KEY TERMS:

Inductive Reasoning – process of recognizing or observing a pattern and drawing conclusion.

Example #1:

KEY TERMS:

Describe the pattern in the numbers-1, -4, -16, -64, …Write the next 3 numbers in the pattern.

Example#2:

-256, -1024, -4096

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

Counterexample – Is a specific case for which the conjecture is false.

KEY TERMS:

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.

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?

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

>

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

= +

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

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:

Assignment 2.1

Worksheet pg. 15Front & back