2011 boolean project with due dates

8/3/2019 2011 Boolean Project With Due Dates

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Algebra II Boolean Project2011Due Dates: Tuesday, May 17, 2011 Odd Da

Wednesday, May 18, 2011 Even Da

Instructions:

1. _____ Read the introduction to Boolean Project:In his bookAn Investigation into the Laws of Thought(1854), the English mathematician George Boole

(1815-1864) approached logic in a system that reduced it to simple algebra. In his system, later called Boole

algebra or symbolic logic, expressions are combined using "and" (multiplication), "or" (addition), and "not"(negative), and then interpreted as "true" (1) or "false" (0). Today, Boolean algebraplays a fundamental rolin the design, construction, and programming of computers.

An example of a Boolean expression isx 5. In this case, ifx is 10, the expression is false and assigned a valuof 0. Ifx is 3, then the expression is true and it is assigned a value of 1. You can use Boolean expressions to

limit the domain of a function when graphing on your calculator. For example, the graph of Y1 = (x + 4)/(x 5

does not exist for values ofx greater than 5, because your calculator would be dividing by 0.

You are going to write your own program that will generate a logo or drawing that is reflective of you.

2.

_____ Explore Boolean Expressions and Drawing Segments with your Graphing Calculator and theCalculator Notes 4G and 4H. (See attached)

3. _____ Create a drawing/design on graph paper (cartoon character, sports object or mascot, design or sceneBE CREATIVE remember it should reflect something about you). Your program needs to

contain these design elements; 8 graphs (or pieces of graphs in your creation with the 6

transformations):

Graphs:

a. 2 linear lines with slopeb. 1 quadraticc.

1 square rootd. 1 semi-circle

e. 1 absolute valuef. any 2 more functions of your choice

Transformation:a. vertical translation (up/down)b. horizontal translation (left/right)c. vertical stretch or shrinkd. horizontal stretch or shrinke. reflection over the x-axisf. reflection over the y-axis

4. _____ Show me your completed picturesketch on graph paper by Tuesday, January 18th Even daand, Wednesday, January 19

thOdd day. I will initial it indicating it is OK to proceed with your

program. Once I have seen it, you must keep the design you chose.

5. _____ Write down and explore what you think the functions are for your drawing.


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Algebra II Boolean Project2011

6. _____ Create a table with four vertical columns titled as indicated and fill in the information for eachnumbered graph of your sketch. This will be need to be shown to me to get my initials by Thursday

February 18th

Even day and Friday, February 19th

Odd day. (you may use the chart on the back

of this handout!)

write the individual Line of Code example: DrawF (2 (x-4)) / (x>4) / (x


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Algebra II Boolean Project20117. _____ Enter the program in your calculator. The steps will be as follows.

a. Press the Program [PRGM] key on your calculator; select [NEW] to create a new program.b. Name: Use the first three letters from your first name and the first three letters from your last

name.c. 1st line of program: ClrDraw (Use [2nd] [PRGM] 1:) This will clear any pictures currently on

your graphing window.

d.

2

nd

line of program: AxesOff(Use [2

nd

] [Zoom]=Format, and select AxesOff).e. 3rd line of program: FcnOff(Use [VARS], [Y-VARS], 4: On/Off, and then select FcnOff).f. 4th line of program: PlotsOff(Use [2nd] [Y=]=Stat Plot, and select 4: PlotsOff).g. Next set the window (the minimum and maximum x and y values that will display on your

screen). Your commands should appear like the following (where is the STO or store keyon your calculator):

: -23.5 xmin (xmin, xmax, etc. are found: 23.5 xmax [VARS] 1: WINDOW)

: -15.5 ymin

:15.5 ymax

h. You may now enter the equations of your graphs. (Use [2nd] [PRGM] 6: DrawF).i. To restrict domain and only use pieces of graphs, follow this example:

: DrawF (your equation)/((x2) and (x4))This command will only draw the graph between x=2 and x=4.

***Note: To get the and symbols use [2nd] [MATH] [TEST]To get the and/or words, use [2

nd] [MATH] [LOGIC]

The / is the division sign

j. Use [CLEAR] to delete a linek.

Use [2

nd

] [INS] to insert a blank linel. If you wish to shade in a part of your graph, you may use the Shade command ([2nd] [PRGM7: Shade) as follows:

:Shade (_______,________,______)

Shade (bottom function where shading begins, top function where shading ends, # from 1 to 8where 1 is the darkest shade)

m. To graph vertical lines: use [2nd] [DRAW] [LINE]. The format of the command is thefollowing:

:Line (___,___,___,___)Line (1st point x value, 1st point y value, 2nd point x value, 2nd point y value)

e.g. :Line (2,4,3,11)

n. Execute your program!!8. _____ Showing Mrs. Cajudoy 50% of your program has been entered into your calculator. Write

down your program as you go on a separate piece of paper (typed) and title this PROGRAM.Due: Tuesday, April 12

thEven

Wednesday, April 13th

Odd


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9. _____ Cut out your design, cut a piece of construction paper/colored paper, and glue your design tothe construction paper. Color your design with crayons or colored pencils, and decorate any way you

wish!--glitter, etc.!

Your Project outcomes should include (turn these into me on the presentation day):

Your drawing on graph paper with my initials A neatcopy of your table showing all of the specified information (and an initialed copy whichcould be the same one if it was neat when I initialed it)

A copy of your program (just the program in your calculator) refer to step 8. Personal Reflection - Share how this design is a reflection of you. Consider why you chose this,

why it is significant to you personally typed (use this when presenting project)

Your colored design glued to construction paper backingHere is how your grade will be determined:

Project Component Points

Drawing on graph paper(must be initialed) 15Equations (Table) (must be initialed) 40

Program (line of codes from calculator) 20Personal Reflection 10

Final Design (colored and glued to construction paper) 10

Presentation 20Creativity and Neatness 5__

TOTAL 120

This project will be presented on these dates: Tuesday, May 17, 2011 Odd day in class

Wednesday, May 18, 2011 Even day in class

PROGRAM TABLE PRESENTATION OFPROGRAM & DRAWING

USED ALL 5FUNCTIONS

PARENTFUNCTIONS

UNIQUE, ASTHETIC

USED ALL 6TRANSFORMATIONS

THUMBNAILSKETCH

PRESENTATION EXPLAINED WELL

SET DOMAINS TRANSFORMATIONSAND DWG PIECE

SHARED PERSONALREFLECTION

LINE OF CODEEQUATIONS IN Y=FORMDOMAINSPERSONALREFLECTION (youcan place at thebottom of Table)

Projects submitted LATE will be penalizedone letter grade for each day that they are late. If you arenot present at school that day, see that your project is submitted early or that someone else brings it in

for you or it will be counted late!


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Good Luck, Enjoy, and Be Creative!!!

Also, as always, I will be glad to help anyone with their program, finding their equations, converting

equations into calculator form, etcANY TIME. Just COME ASK!! Dont wait until the last minute!it cget a bit crazy!

Boolean Project Presentation{When you present this is what I am looking for}

1) Clear your equation editor2) Operate from a clean home screen3) Walk us through your program (PRGM, EDIT),

Identify the 8 parent functions:

a. 2 linear equationb. quadratic equationc.

square root equationd. semi-circle function

e. absolute value functionf. any 2 more functions of your choice

Identify all six transformations:

a. vertical translationb. horizontal translationc. vertical stretch/shrinkd. horizontal stretch/shrinke. reflect over the x-axisf. reflect over the y-axis

4) Execute your program; explain what functions give the different components of your design.5) Share a personal reflection about your design.Prompts: What was doing this project like for you? In what poignant way, does this design reflect you?

What did you learn from this project?

6) Answer any questions about your project.


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Boolean Project Rubric

Program - submitted typed 20

Drawing - artistic and accurate (first one and final) 25Personal Reflection 10

(55)

Write up:Used all functions -

linear, square root, quadratic absolute value semi-circle

8

Used all transformations - vertical translation horizontal translation vertical stretch/shrink horizontal stretch/shrink reflection over the x-axis reflection over the y-axis

6

Set Domains 4Defined individual line of codes 4Identified corresponding equations 4Identified parent functions and transformations 6Gave thumbnail sketches 4Connected functions to drawing pieces 4

(40)

Presentation and Creativeness:Unique, aesthetic 5Explained well 10Shared personal reflection 10

(25)

TOTAL 120


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Algebra II Boolean Project2011Name ________________________________

Block: _______________________

Boolean Project Table

Graph

Number

Parent Function Equations in Calculator

Form (y= )

Restrictions (Domain)

Line of Code

Transformations Thumbnail Drawing with Label

Graph

Number


Form (y= )


Line of Code



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Graph

Number


Form (y= )


Line of Code


GraphNumber

Parent Function Equations in CalculatorForm (y= )


Line of Code


Graph

Number


Form (y= )


Line of Code



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Graph

Number


Form (y= )


Line of Code


GraphNumber



Line of Code


Graph

Number


Form (y= )


Line of Code



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Graph

Number


Form (y= )


Line of Code


GraphNumber



Line of Code


Graph

Number


Form (y= )


Line of Code



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Graph

Number


Form (y= )


Line of Code


Graph

Number


Form (y= )


Line of Code



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26 CHAPTER 4 Discovering Advanced Algebra Calculator Notes for the Texas Instruments TI-83 and TI-83/84 Plus

2004 Key Curriculum Press

Note 4A Function Notation

The calculator treats an equation entered into the Y screen as a function.A function can be evaluated for different x-values using standard functionnotation. For example, Y1(5) will give the value of the function when x is 5.On the Home screen press Y-VARS 1:Function followed by the number

of the equation you want, and the x-value.

Note 4B Movin Around

With bits of tape, label two CBRs A and B. Label two calculators A and B,and connect each to the respective CBR. Use the RANGER program to collectdata for 10 seconds. See Note 3C for help with the RANGER program.

For both calculators, the time data will be in list L1 and the distance data willbe in list L2. On the Home screen of calculator B, enter L1L3, press ,enter L2L4, and press . This moves calculator Bs time and distancedata to lists L3 and L4.

Finally, each group member should link to calculator A and copy lists L1 andL2, and link to calculator B and copy lists L3 and L4. See Note 1J for helpwith linking lists.

Note 4C Friendly Windows

A friendly window scales the x-axis to correspond to the Graph screens

width in pixels (94). As a result, when you trace a curve on a friendlywindow, the spider always falls on points whose x-coordinates are nicedecimal numbers. The y-coordinates are computed values and depend onthe function being traced; they may or may not be nice decimal values.

If the y-axis is scaled so its units are the same as the units on the x-axis,then the window will be a square window. On a square window there is nodistortion of the graph.

One friendly square window whose trace point has x-coordinates that areexact tenths can be found by pressing 4:Decimal.

[4, 4, 1, 4, 4, 1]

This window is a little small for much of the work in this course. However,if you double the minimum and maximum values in the window screen, youcan get a larger friendly square window that is often useful.

ZOOM

ENTER

ENTER

VARS

CHAPTE R 4 Calculator Notes for the TI-83 and TI-83/84 Plus

(continued)


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You can save the settings for this larger window and recall it at any time.After setting the window values, press MEMORY 2:ZoomSto. Now when

you want to use it again, press MEMORY 3:ZoomRcl. This particularwindow is often referred to as the friendly window with a factor of 2.

It is sometimes helpful to see a grid in the background of the screendisplay. To turn the grid on (or off), press [FORMAT] and select GridOn(or GridOff).

[9.4, 9.4, 1,6.2, 6.2, 1]

Note 4D Transformations and Compositions

You can use functions entered into the Y screen in other functions to showtransformations and to construct compositions.

Transformations of Functions

You can enter an equation into the Y screen and then define a secondequation as a transformation of the first. For example, enter 4X2 into Y1and define Y2 as Y23*Y1(X4)2. (To get Y1, press Y-Vars 1:Function 1:Y1.)Y2 is the image of Y1 after being stretched vertically by a factor of 3,translated right 4 units and up 2 units.

[9.4, 9.4, 1,6.2, 18.6, 1]

Compositions of FunctionsIf you enter two (or more) equations into the Y screen, you can defineanother equation as the composition of the equations you have entered. For

VARS

2nd

ZOOM

ZOOM

Note 4C Friendly Windows (continued) TI-83 and TI-83/84 Plus

Discovering Advanced Algebra Calculator Notes for the Texas Instruments TI-83 and TI-83/84 Plus CHAPTER 4 27


(continued


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Note 4D Transformations and Compositions (continued) TI-83 and TI-83/84 Plus

example, enter 4X2 into Y1 and X5 into Y3. Define Y4 as the composition ofY1 and Y3 by entering Y4Y1(Y3(X)).

[9.4, 9.4, 1,6.2, 6.2, 1]

You can use the Home screen recursive loop Y1(X)X (or simplyY1X) toevaluate the repeated composition of a function with itself. Store a startingvalue in X and then press Y-VARS 1:Function 1:Y1

. . . . (See Note 1B for more on Home screen recursion.)

Note 4E TRANSFRM Program

The program TRANSFRM gives you practice finding equations for given

graphs. From the first menu, choose the type of function you want topractice. In the second menu, you can turn the different transformationson or off by pressing the number key. Press when youre ready. Thecalculator will display a graph and stop. Study the graph and determineits equation. Press if you want to see the coordinates of points. When

you have decided on an equation, press , enter your equation intoY1, andpress . If your equation is correct, youll have a match and nothingnew will appear on the screen. You can press and toggle back andforth between the graph of your function in Y1 and the programs functionto confirm that they really do match. If your equation is not correct, thegraphs will not match. In that case, press and try again.

When you are finished with one graph, on the Graph screen press

to run the program again.

The option 5:GENERIC will draw the graph of a generic function using a thickline and the graph of its image after a transformation using the regular style.Enter the equation of the image into Y1. Use Y8(X) to represent the originalfunction.

[9.4, 9.4, 1,6.2, 6.2, 1]

[9.4, 9.4, 1,6.2, 6.2, 1]

ENTERCLEAR

Y

TRACE

GRAPH

Y

TRACE

4

ENTER

ENTERENTERX,T,,nSTOVARS



(continued)


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Clean-Up

After you quit the program, you may want to go to the Y screen and clearthe functions so they dont interfere with future work.P R O G R A M : T R A N S F R M 9 . 4 X m i n : 9 . 4 X m a x 6 . 2 Y m i n : 6 . 2 Y m a x1 Y s c l : 1 X s c lG r i d O n : A x e s O nP l o t s O f f" K + B ( ( X - H ) / A ) " Y 3" K + B ( ( X - H ) / A ) " Y 4" K + B a b s ( ( X - H ) / A " Y 5" K + B ( ( 1 - ( ( X - H ) / A ) ) " Y 6" K + B Y 8 ( ( X - H ) / A ) " Y 7" 2 ( X < 1 ) / ( X 3 ) + ( 1 - X ) ( X 1 )( X < 2 ) + ( 5 + 2 X ) ( X 2 ) / ( X 3 ) Y 8G r a p h S t y l e ( 8 , 2 )L b l 0 : 3 F :I f T 0 a n d T 1 : 1 TI f R 0 a n d R 1 : 0 RI f D 0 a n d D 1 : 0 DM e n u ( " T R A N S F O R M A T I O N S " , " P A R A B O L A " , 1 ," R O O T S " , 2 , " A B S O L U T E " , 3 , " S E M IC I R C L E " , 4 , " G E N E R I C " , 5 , " Q U I T " , 9 )L b l 5 : F + 1 FL b l 4 : F + 1 FL b l 3 : F + 1 FL b l 2 : F + 1 FL b l 1 : 1 A : 1 BC l r H o m e : 0 G : 0 H : 0 KD i s p s u b ( " P A R A B O L A S Q U A R ER O O T S A B S O L U T E V A L S E M I C I R C L EG E N E R I C " , 1 2 F - 3 5 , 1 2 )

Note 4E TRANSFRM Program (continued) TI-83 and TI-83/84 Plus



R e p e a t G = 8 2O u t p u t ( 3 , 1 , " 1 . T R A N L A T E : " + s u b( " O F F O N " , 3 T + 1 , 3 ) )O u t p u t ( 4 , 1 , " 2 . R E F L E C T : " + s u b( " O F F O N " , 3 R + 1 , 3 ) )O u t p u t ( 5 , 1 , " 3 . S T R E T C H: " + s u b ( " O F F O N " , 3 D + 1 , 3 ) )O u t p u t ( 6 , 1 , " 4 . G O " )g e t K e y G :I f G = 9 2 : 1 - T TI f G = 9 3 : 1 - R RI f G = 9 4 : 1 - D DE n dI f T : T h e nr a n d I n t ( 7 , 7 ) Hr a n d I n t ( 4 , 4 ) KE n dI f R : T h e nI f r a n d < 0 . 5 : 1 AI f r a n d < 0 . 5 : 1 BE n dI f D : T h e nA * r a n d I n t ( 1 , 5 ) AB * r a n d I n t ( 1 , 4 ) BE n dF n O f fF n O n FI f F = 7 : F n O n 8D i s p G r a p hL b l 9Note 4F Graphing Absolute-Value Functions

To use the absolute-value function, press NUM 1:abs(. For example,to graph y x 3, enter Y1abs(X3) into the Y screen, set anappropriate window, and press .

[9.4, 9.4, 1,6.2, 6.2, 1]

GRAPH

MATH


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TI-83 and TI-83/84 Plus

Note 4G Boolean Expressions

You can limit the domain of a function by using Boolean expressions. Theseare statements using , ,, , , or that have a value of 1 when trueand 0 when false. To find these symbols, press [TEST].

For example, the equation Y1(2X2)*(X1) will equal zero for all values

ofx less than1 and equal 2 x2 for values ofxgreater than or equal to1. You can evaluate the function on the Home screen or view it on theGraph screen.

[4.7, 4.7, 1,1, 5, 1]

The calculator wont graph anything when its dividing by 0, so the equation

Y1(2X2)(X1) will result in no graph when x is less than1.

By adding functions that are each multiplied and divided by a Booleanexpression, you can create a piecewise function that is defined over a limiteddomain. The equation Y1(4X)*(X1)(X3)(2X2)*(X1)(X2) willcreate a function by connecting the line y 4 xto the parabola y 2 x2

at (1, 3) and limiting the domain to the interval from 3 to 2.

[4.7, 4.7, 1,1, 7, 1]

Note 4H Drawing Segments

On the Graph screen you can draw an overlay on top of the graph.

Follow these steps to draw a segment:

a. Press [DRAW] 2:Line(.

b. Arrow to one endpoint of the segment you want and press .

c. Arrow to the other endpoint and press again.

Pressing twice ends one segment and begins another at the samepoint, so you can make a closed figure.

[9.4, 9.4, 1,6.2, 6.2, 1] [9.4, 9.4, 1,6.2, 6.2, 1] [9.4, 9.4, 1,6.2, 6.2, 1]

ENTER

ENTER

ENTER

2nd

2nd



[4.7, 4.7, 1,1, 5, 1]

(continued)


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You can also draw segments by entering instructions into the Home screen.To draw a segment between (1, 3.64) and (7.4, 3.64), enter Line(1,3.64,7.4,3.64).

[10, 10, 1, 10, 10, 1]

To erase any drawing, press [Draw] 1:ClrDraw.2nd

Note 4H Drawing Segments (continued) TI-83 and TI-83/84 Plus


2011 boolean project with due dates

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