module 3 lesson 13 intro to inequalities

Module 3 Lesson 13 Intro to Inequalities.notebook

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AIM: Properties of Inequalities

Do Now

11/15/16 Homework:Lesson 13 Problem Set Page 55 #1-4

Module 3 Lesson 12

Lesson 12 Sprint

Module 3 Lesson 13 Intro to Inequalities.notebook

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43210­1­2791113155420­1­2­3­6­18­6

3535353535444447531­1­3­1­1­15­1­5

Module 3 Lesson 12 Sprint Round 1

Module 3 Lesson 13 Intro to Inequalities.notebook

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November 15, 2016

234567810121416203210­1­3­4­8­12­4

505050505044444

­1/2­3/2

­7/2­4­9/21111

­5/2

2­1

Module 3 Lesson 12 Sprint Round 2

Module 3 Lesson 13 Intro to Inequalities.notebook

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November 15, 2016

1.) What numbers could you substitute for the variable in this mathematical sentence?

x > 3

2.) What numbers can not be substituted for x?

x > 3 is an INEQUALITY- a mathematical sentence that contains

Inequalities 51

Module 3 Lesson 13 Intro to Inequalities.notebook

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November 15, 2016

51

Module 3 Lesson 13 Intro to Inequalities.notebook

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November 15, 2016

means the inequality symbol stays the same

means the inequality symbol switches direction

51

Module 3 Lesson 13 Intro to Inequalities.notebook

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51

When adding and subtracting, the inequality symbol is preserved

Module 3 Lesson 13 Intro to Inequalities.notebook

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November 15, 2016

4 ­3>4 + ­3 > ­3 + ­3       1 > ­6 Preserved

3 > 23 ­ 2 > 2 ­ 2     1 > 0 Preserved

­3 ­4> ­3 ­ (­1) > ­4 ­ (­1)         ­2 > ­3

­2 5< ­2 + 1 < 5 + 1­1 < 6

Preserved

Preserved

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When adding and subtracting, the inequality symbol is preserved

Module 3 Lesson 13 Intro to Inequalities.notebook

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November 15, 2016

When multiplying by ­1, the inequality symbol is  reversed 

Module 3 Lesson 13 Intro to Inequalities.notebook

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November 15, 2016

-3 < 4-3(-1) < 4(-1)

Plot the points on the number line below based on multiplying both values by -1. What is the result to the inequality symbol?

Module 3 Lesson 13 Intro to Inequalities.notebook

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November 15, 2016

-3 < 4-3(-1) < 4(-1)

3 > -4The symbol is

reversed

Module 3 Lesson 13 Intro to Inequalities.notebook

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November 15, 2016

4 ­3>

3 > 2

­3 ­4>

­2 5<

4(­1) > (­3)(­1)   ­4 < 3 Reversed

Reversed

Reversed

3(­1) > 2(­1)   ­3 < ­2

­3(­1) > (­4)(­1)       3 < 4

­2(­1) < 5(­1)       2 > ­5 Reversed

When multiplying by ­1, the inequality symbol is  reversed 

Module 3 Lesson 13 Intro to Inequalities.notebook

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November 15, 2016

52

When multiplying or dividing by a positive value, the inequality symbol is preserved

Station 2

Module 3 Lesson 13 Intro to Inequalities.notebook

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November 15, 2016

4 ­3>

3 > 2

­3 ­4>

­2 5<

4(2) > (­3)(2)   8 > ­6

3 > 22    2

   1.5 > 1

­3 > (­4)      

 ­6 > ­8

­2(3) < 5(3)      ­6 < 15

Preserved

Preserved

Preserved

Preserved

52

When multiplying or dividing by a positive value, the inequality symbol is preserved

Station 2

Module 3 Lesson 13 Intro to Inequalities.notebook

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November 15, 2016

53

When multiplying and dividing by a negative, the inequality symbol is reversed.

Station 3

Module 3 Lesson 13 Intro to Inequalities.notebook

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November 15, 2016

4 ­3>

3 > 2

­3 ­4>

­2 5<

4(­3) > (­3)(­3)   ­12 < 9

­3 > (­4)

       6 < 8

­2(   ) < 5(   )

       1 > ­2.5

Reversed

Reversed

Reversed

Reversed

3 > 2­2   ­2

   ­1.5 < ­1

53

When multiplying and dividing by a negative, the inequality symbol is reversed.

Station 3

Module 3 Lesson 13 Intro to Inequalities.notebook

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November 15, 2016

DiscussionTo summarize, when did the inequality symbol change and when did it stay the same?

Preserved Reversed

1.) Add or subtract any number

2.) Multiply or divide by a positive

1.) Multiply or divide by a negative

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Module 3 Lesson 13 Intro to Inequalities.notebook

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November 15, 2016

4 < 74(-1) < 7(-1)

-4 > -7

Module 3 Lesson 13 Intro to Inequalities.notebook

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November 15, 2016

54

Preserved

Reversed

PreservedPreserved

PreservedReversed

PreservedPreserved

ReversedPreserved

Module 3 Lesson 13 Intro to Inequalities.notebook

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November 15, 2016

Closing:1.) What does it mean for an inequality to be preserved? What does it mean for the inequality to be reversed?

2.) When does a greater than become a less than?

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Module 3 Lesson 13 Intro to Inequalities.notebook

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November 15, 2016