Algebra II Boolean Project—2012 - 13 - Kamehameha …blogs.ksbe.edu/brcajudo/files/2009/11/2012_13_-Boolean_Project... · Algebra II Boolean Project—2012 - 13 ... 6.2, 18.6, 1]

Algebra II Boolean Project—2012 - 13

Instructions: 1. Read the introduction to Boolean Project:

Last Due Date: Monday, May 6, 2013 Even Days Tuesday, May 7, 2013 Odd Days

In his book An 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 Boolean 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 algebra plays a fundamental role in the design, construction, and programming of computers. An example of a Boolean expression is x ≤ 5. In this case, if x is 10, the expression is false and assigned a value of 0. If x 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 of x greater than 5, because your calculator would be dividing by 0. You are going to write your own program that will generate a logo, tattoo or drawing that is reflective of you. I had this yearning, this desire, to be like my ancestors — to connect. But I wanted to kind of do it in the traditional style. Not one exactly as my ancestors but one that I thought was close enough because in truth I don't know. So I created. Frank Kawaikapuokalani Hewett speaking about his kakau

My name is Kyle Nakanelua, and I was born and raised on Oahu. And I now live in Haiku on Maui. First of all I think my most important thing that I do is I'm a dad. Second, I'm a husband. Third, I'm a fireman: I'm a captain at Kahului airport, and I run a shift of fire fighters and our basic duties and responsibilities are about caring for people in need of our services in the event that the airplane should have trouble or if they experience medical difficulties, we normally respond first to them. And I'm the alaka'i for the halemua. I've gone into the prison several times to just talk about Hawaiian things for the men who are in prison. The halemua, traditionally was the first formal institute of learning in which a Hawaiian male enters, when he enters into society… approximately five, six, seven, eight years old. He's cast in to this place called the halemua — the house of men. It's where men hold council for matters of spirit, for matters of intellect, for matters of things of the physical world. The group specializes in male activities within Hawaiian life, past, present, and future. [The halemua] does things of the earth such as planting, farming food products, farming products for material use in the culture, like koa trees, like 'ohi'a, like wauke, like 'awa. we do other physical things like dance, that people call hula. We do storytelling, we do singing or oli. We do pule. We do ceremonial welcoming of visitors to our places, to our islands, to our culture. 'Awa is another facet of specifically Hawaiian male society. Taro, which is turned into poi, nourishes the body. 'Awanourishes the spirit. So we grow 'awa, we care for 'awa, we prepare 'awa, and we inu'awa. And from beginning to end, it nourishes the spirit. It ties us into an older time, when men were more dominant within their society. So attaching ourselves to that gives us back that connection to that older masculinity. Kyle's Decision to Receive a Tattoo I was just doing genealogical research, finding out who you are, where you come from, et cetera, et cetera. That was in my twenties. When I turned thirty was when the idea of placing a tattoo or a tatau, became a little bit more prevalent. I was interested in putting something on that would mean something special to mark this particular time in my life, and to reach into those things that let us know who we are, therefore why we are the way we are now. But Was He Ready? Now, I was talking about getting a tattoo. I wanted a Hawaiian particular design. Nothing heavy, just you know a little patch. Just to show I am Hawaiian. And so my sister says, oh no, he's gonna embarrass the family again, I better get to him and make sure he doesn't put anything idiotic on. So my older sister introduces me to her friend named Keone. And so I get there, he introduces himself, and ... Keone is so different, you know. He's not like your typical person who would get tattooed. Keone was this soft-spoken, intelligent, humble, kind person. And I just never associated those traits with tattoos. But here was this guy, and he was just so full of knowledge and all of my perceptions about tattooing just got blown out of the water when I was talking to him. I was so pissed off at him, because he's telling me everything I'm doing is wrong. It's like you're talking to him, and he's going "Oh, that's interesting. Oh, hmm, where did you get that idea from?" The questions he asks, just makes you question yourself so deep. And basically, all my thoughts and perceptions, there was nothing there. It was so superficial, it was painful. He told me that I should go read certain books and look into certain things. And so I did. And that I should do my family research in who they were and learn the language, which is important. Because when you get your family names, and you know the language, then you can associate the names with the particular kuleanas that your families were associated with. And that's the treasures that I got out of talking with Keone. And when I did that, and I came back to him with it, he said okay, now you're on the right track. So about two or three years later, I was finally ready, in his eyes, to put one on. And from that point on, everything turned.

Source: http://www.pbs.org/skinstories/stories/nakanelua.html

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

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 numberof 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 L1→L3, press ,enter L2→L4, and press . This moves calculator B’s 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 screen’swidth in pixels (94). As a result, when you trace a curve on a friendlywindow, the spider always falls on points whose x-coordinates are “nice”decimal 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

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

(continued)

DAACN615_04_k1.qxd 8/2/05 3:09 PM Page 26

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 whenyou 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 FunctionsYou can enter an equation into the Y� screen and then define a secondequation as a transformation of the first. For example, enter 4�X2 into Y1

and define Y2 as Y2�3*Y1(X�4)�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©2004 Key Curriculum Press

(continued)


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

example, enter 4�X2 into Y1 and X�5 into Y3. Define Y4 as the composition ofY1 and Y3 by entering Y4�Y1(Y3(X)).

[�9.4, 9.4, 1, �6.2, 6.2, 1]

You can use the Home screen recursive loop Y1(X)→X (or simply Y1→X) 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 givengraphs. 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 you’re ready. Thecalculator will display a graph and stop. Study the graph and determineits equation. Press if you want to see the coordinates of points. Whenyou have decided on an equation, press , enter your equation into Y1, andpress . If your equation is correct, you’ll 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 program’s 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,�,nSTOÍVARS



(continued)


Clean-UpAfter you quit the program, you may want to go to the Y� screen and clearthe functions so they don’t interfere with future work.

PROGRAM:TRANSFRM

— 9 . 4áXmin :9 .4áXmax

— 6 . 2áYmin :6 .2áYmax

1áY s c l : 1áX s c l

GridOn :AxesOn

P l o t s O f f

"K+B ( ( X -H ) / A ) ¯ "áY3

"K+B√( (X-H )/A )"áY4

"K+Babs ( (X-H ) /A"áY5

"K+B√( ( 1 - ( ( X -H ) /A ) ¯ ) "áY6

"K+BY8( ( X - H ) / A ) "áY7

" 2 ( X < — 1 ) / ( X ≥ — 3 ) + ( 1 - X ) ( X ≥ — 1 )

( X < 2 ) + ( — 5 + 2 X ) ( X ≥ 2 ) / ( X ≤ 3 )áY8

G r aph S t y l e ( 8 , 2 )

L b l 0 : 3áF:

I f T ≠ 0 a n d T ≠ 1 : 1áT

I f R≠0 and R≠1 : 0áR

I f D≠0 and D≠1 : 0áD

Menu("TRANSFORMATIONS","PARABOLA",1,

"ROO T S " , 2 , "ABSOLU T E " , 3 , " S EMI

C I R C L E " , 4 , " G EN E R I C " , 5 , " Q U I T " , 9 )

L b l 5 : F + 1áF

L b l 4 : F + 1áF

L b l 3 : F + 1áF

L b l 2 : F + 1áF

L b l 1 : 1áA : 1áB

ClrHome:0áG : 0áH : 0áK

D i sp sub ( "PARABOLA SQUARE

ROOTSABSOLUTE VALSEMICIRCLE

G 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


Repeat G=82

O u t p u t ( 3 , 1 , " 1 . T R AN 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 ON " , 3 D + 1 , 3 ) )

O u t p u t ( 6 , 1 , " 4 . G O " )

getKeyáG :

I f G = 9 2 : 1 - TáT

I f G = 9 3 : 1 - RáR

I f G = 9 4 : 1 - DáD

End

I f T : T h e n

r a n d I n t ( — 7 , 7 )áH

r a n d I n t ( — 4 , 4 )áK

End

I f R : T h e n

I f r a n d < 0 . 5 : — 1áA

I f r a n d < 0 . 5 : — 1áB

End

I f D : T h e n

A * r a n d I n t ( 1 , 5 )áA

B * r a n d I n t ( 1 , 4 )áB

End

F n O f f

F n O n F

I f F = 7 : F n O n 8

DispGraph

L b l 9

Note 4F • Graphing Absolute-Value Functions

To use the absolute-value function, press NUM 1:abs(. For example,to graph y � x – 3, enter Y1�abs(X�3) into the Y� screen, set anappropriate window, and press .

[�9.4, 9.4, 1, �6.2, 6.2, 1]

GRAPH

MATH


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�(2�X2)*(X��1) will equal zero for all valuesof x less than �1 and equal 2 x2 for values of x greater than or equal to�1. 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 won’t graph anything when it’s dividing by 0, so the equationY1�(2�X2)�(X��1) will result in no graph when x is less than �1.

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�(4�X)*(X��1)�(X��3)�(2�X2)*(X��1)�(X�2) willcreate a function by connecting the line y � 4 x to 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)


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




3. Sketch a drawing/design in box below(tattoo, cartoon character, sports object or mascot, design or a scene—BE CREATIVE remember it should reflect something about you). Monday, October 15th Odd day and, Tuesday, October 16th Even day 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 slope b. 1 quadratic c. 1 square root d. 1 semi-circle e. 1 absolute value f. any 2 more functions of your choice

Transformation:

a. vertical translation (up/down) b. horizontal translation (left/right) c. vertical stretch or shrink d. horizontal stretch or shrink e. reflection over the x-axis f. reflection over the y-axis

4. Show me your completed picture—sketch on graph paper by Monday, October 15th Odd day and, Tuesday, October 16th Even 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. If you change must check with me first. You will need to do another sketch.

5. Write down and explore what you think the functions are for your drawing. Make notes on

your graph paper. Draw lines around your drawing and label what your windows would be for step 7. Friday, December 14th Even day and Monday, December 17th Odd day.


4. _____ Picture (10/15 or 10/16) 5. _____ Equations Labeled


6. Create a table with columns and rows titled as indicated and fill in the information for each numbered graph of your sketch. (you may use the chart on the back of this handout!) This will be need to be shown to me to get my initials by first 50% - Monday, February 4th Even day and Tuesday, February 5th Odd day 100% - Monday, March 4th Even day and Tuesday, March 5th Odd day

Write the individual Line of Code – example: DrawF (-0.5(x – 5)2 + 4) / (x>4) / (x<8) Write the equation given in the line of code and its domain – example: y= -0.5(x – 5)2 + 4 ; 4<x<8

Identify the parent function use f(x) notation – example: f(x)= x2

Identify transformations Draw a thumbnail sketch of the function - include relevant values on the x- and y- axes Identify the part of the design that the line of code draws

50% Due – Monday, February 4th Even At least 4 to 6 graphs done Tuesday, February 5th Odd

100% Due – Monday, March 4th Even All must be done for full credit Tuesday, March 5th Odd

Graph Number

Parent Function Equations in Calculator Form (y= )

Restrictions (Domain)

1

Quadratic f(x) = x2 y = -0.5(x – 5)2 + 4 ; x ≥ 4 and x ≤ 8

Line of Code DrawF (-0.5(x – 5)2 + 4) / (x>4) / (x<8)

Transformations Thumbnail Drawing with Label stretched by a ½ reflection over the x- axis moved to the right five (5) units moved up four (4) units

Top of Car


Graph Number



Line of Code

Transformations Thumbnail Drawing with Label

Graph Number



Line of Code


Graph Number



Line of Code



Graph Number



Line of Code


Graph Number



Line of Code


Graph Number



Line of Code



Graph Number



Line of Code


Graph Number



Line of Code


Graph Number



Line of Code



Graph Number



Line of Code


Graph Number



Line of Code


Graph Number



Line of Code



7. Enter the program in your calculator. During the next step every time you come to see me please have me initial your paper. The steps will be as follows. Need to come and see me at least once during this time. Between March 4th or 5th and April 8th or 9th

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. 2nd line of program: AxesOff (Use [2nd] [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 (Refer to Step 5 for your numbers for your window.) (the minimum and

maximum x and y values that will display on your screen). Your commands should appear like the following (enter number first then where → is the STO or store key on 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)/((x ≥ 2) / (x ≤ 4))

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 / is the division sign

j. Use [CLEAR] to delete a line. Be careful… k. Use [2nd] [INS] to insert a blank line l. If you wish to shade in a part of your graph, you may use the Shade command ([2nd] [PRGM]

7: Shade) as follows:

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

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

following:

: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. Type up your program as you go and title this PROGRAM.

50 % Due: Monday, April 8th Even 100% Due: Monday, April 29th Even Tuesday, April 9th Odd Tuesday, April 30th Odd


9. Cut out your design, cut a piece of construction paper/colored paper, and glue your design to the 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 neat copy of your table showing all of the specified information (and an initialed copy which

could 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 backing

Here is how your grade will be determined:

Project Component Drawing on graph paper (must be initialed)

Points15

Drawing with notes (must be initialed) 10Equations (Table) (must be initialed) 40Program (line of codes from calculator) 20Personal Reflection 10Final Design (colored and glued to construction paper) 10Presentation 20Creativity and Neatness 5 TOTAL 130

This project will be presented on these dates: Due Dates: Monday, May 6, 2013 Even Days

Tuesday, May 7, 2013 Odd Days Check list for you to make sure you have it all…

PROGRAM TABLE PRESENTATION OF PROGRAM & DRAWING

USED ALL 5 FUNCTIONS

PARENT FUNCTIONS

UNIQUE, ASTHETIC

USED ALL 6 TRANSFORMATIONS

THUMBNAIL SKETCH

PRESENTATION – EXPLAINED WELL

SET DOMAINS TRANSFORMATIONS AND DWG PIECE

SHARED PERSONAL REFLECTION

LINE OF CODE EQUATIONS IN “Y=” FORM

DOMAINS PERSONAL REFLECTION (you can place at the bottom of Table)


Projects submitted LATE will be penalized one letter grade for each day that they are late. If you are not 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!

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, etc—ANY TIME. Just COME ASK!! Don’t wait until the last minute!—it can get a bit crazy!

Boolean Project Presentation

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

1) Clear your equation editor

2) Operate from a clean home screen 3) Walk us through your program (PRGM, EDIT),

Identify the 8 parent functions:

a. 2 linear equation

b. quadratic equation c. square root equation

d. semi-circle function

e. absolute value function

f. any 2 more functions of your choice

Identify all six transformations:

a. vertical translation

b. horizontal translation

c. vertical stretch/shrink

d. horizontal stretch/shrink e. reflect over the x-axis

f. 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.


Boolean Project Rubric Program - submitted typed 20 Drawing - artistic and accurate (first one and final) 35 Personal 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 4 Defined individual line of codes 4 Identified corresponding equations 4 Identified parent functions and transformations 6 Gave thumbnail sketches 4 Connected functions to drawing pieces 4

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

(25) TOTAL 130

Documents

Algebra II Boolean Project—2012 - 13 - Kamehameha …blogs.ksbe.edu/brcajudo/files/2009/11/2012_13_-Boolean_Project... · Algebra II Boolean Project—2012 - 13 ... 6.2, 18.6, 1]