Perry High School. Algebra 3: S2W2

Transcription

1 Monday: Real Numbers Algebra 3: S2W2 appendix 1 pre reading due Tuesday: Quadratic Equations redux 4.1 pre reading due Wednesday: Present worksheets on the board Thursday: 5.2 Complex Numbers 5.2 pre reading due Friday: 5.2 Work Day Next Week: MLK Day; 5.2 on Board; Review; Exam; Debrief 1

2 Monday Pre reading appendix 1 due Body Scan Meditation Talk about worksheets 1. Rules to Chess 2. Mate in One Worksheet Real Numbers 2

3 Negative Numbers Are Weird Negative numbers, darken the very whole doctrines of the equations and make dark of things which are in their nature excessively obvious and simple. Frances Maseres, s before fully worked out in the west. 3

4 Earlier Accounting 200 BCE Chinese rod system for commercial and tax systems. 200 CE Greeks geometry renders negative results as absurd 620 CE India fortunes and debts 4

5 Earlier Negatives 800 s CE -- Persians -- geometric models giving negative results are meaningless 900 s Persians arrive at idea of debt 1100 s -- Persians develop some rules of negative numbers 1400 Europeans get negative numbers 5

6 Earlier Acceptance 1500 s Italy Mixed feelings wrt negative numbers fictitious but working with these and some new imaginary numbers help with proofs involving negative roots s and 1700 s negative numbers and imaginary needed to develop calculus; number line developed 6

7 Zero is also weird Independently invented by several civilizations 400 to 300 BCE Babylon, as placeholder 130 CE Greek astronomers, as placeholder CE in India, as placeholder 7

8 Zero Numbers represent collections of objects. What is a zero collection? Analogy, My hobby is not collecting stamps. 630 CE start seeing zero as a number in India Confusion as to how to handle division 8

9 Zero 1200 s Chinese seem to have zero 1600 s Europeans have zero, but not happy about it. Descartes used it as the origin of coordinates. Newton and Leibiniz needed it for calculus. 9

10 Number System Development Worksheet The myth of developing the real number system counting, whole, integers, rational, irrational, real, imaginary 10

11 To Do 1. Real Number worksheet. Will have you all answer in class on Wednesday Pre-reading is due tomorrow: definitions, postulates or axioms, theorems, miscellaneous (formulas, algorithms, etc.) 11

12 4.1 Quadratics, Redux Pre-reading due Body Sound Meditation Questions on real numbers? 12

13 polynomial of degree 2 graph is a parabola 13

14 Changing the a value 14

15 Standard Form goodies Graph y = x 2 4x +3 y = 2 x y = (x + 2)(x 4) 15

16 y = 2 x

17 y = (x-2)(x+4) 17

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19 To Do 1. Quadratic worksheet. Will have you all answer in class on Tomorrow Pre-reading is due thursday: definitions, postulates or axioms, theorems, miscellaneous (formulas, algorithms, etc.) 19

20 Breathing Meditation White Board Day Students at the white board presenting their work from previous two worksheets. Tomorrow: 5.2 Pre-reading due 20

21 5.2 Complex Numbers Pre-reading due Working with Difficulties Meditation Questions on previous work? The Useless Number 21

22 Recall What We Need with Numbers Count Things Add a zero Add negative numbers Add being able to divide Add measuring across squares Solve weird things like x = 0 22

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24 The i of the tiger Powers of i? 24

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27 5.2 p , 11, 19, 33, 45, 51 Examples 27

28 Fundamental Theorem of Algebra By Monday 5.2 p Evens Students to Board on Monday 28