Graphing Calculator Resource Manual

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3 Table of Contents I. Basics. Page 2 1. Contrast 2. Settings 3. Parentheses 4. Computation 5. Editing 6. The MATH Menu 7. Other Home Screen Operations 8. Catalog II. Graphing and Tables.. Page 6 1. Y= Menu 2. Graphing Window 3. ZOOM Menu 4. Style 5. Computations with Graphs 6. Technical Issues of Graphing with the TI Tables III. Matrices..Page Entering a Matrix 2. Computations with Matrix 3. Solving Systems with Inverse Matrices IV. Statistics. Page List Basics 2. Data Entry 3. One Variable Statistics 4. Graphs with One Variable Statistics 5. Graphs with Two Variable Stats V. CBR Page Functions of the Ranger 2. Set Up Instructions 3. Using 1: SETUP/SAMPLE 4. PLOT MENU 5. Applications 6. TOOLS VI. Linking Page Linking Lists on the TI Linking Programs on theti Linking Applications on the TI-83 Plus VII. Computer Resources.. Page Connecting the TI-83 to a Computer 2. Reasons to Connect to a Computer. Page 1 of 27 Columbus Public Schools 8/22/04

4 I. Basics 1. Contrast You can adjust the contrast on the screen by pressing 2 nd, releasing the key and then pushing and holding the up arrow to make the screen darker or holding the down arrow to make it lighter. As you hold down the arrow, you should see a number in the upper right hand corner of the screen. When you have the brightness at the desired level, the number indicates the strength of the batteries. When the number is 9, the batteries are almost dead. Students will often complain that their batteries are dead when the problem is really that the contrast needs to be adjusted. 2. Settings For most work with the TI-83, the MODE should be set like the list on the right. To change an entry, use the arrow keys to highlight the choice and then hit ENTER. If you wish to set the calculator to display a given number of decimal places, highlight the number in the Float line. You should also check the FORMAT menu. It is accessed by pushing 2 nd and then ZOOM. If students have been playing programmed games on the calculator, these settings are often changed by the programs, and the axes are not displayed until Axes On is selected in the FORMAT menu. If you wish, you can change the calculator to the defaults (everything darkened at the left by choosing MEM (2 nd +) and #7 RESET and then #2 Defaults. The RADIAN/DEGREE is the only difference from the previous settings. This only matters if you will be working with trigonometric functions. Any time you access a menu, you return to the home screen (the basic command screen) by selecting QUIT (2 nd MODE) or by hitting CLEAR. 3. Parentheses The TI-83 differs from the TI-82 by inserting the opening parenthesis for the arguments of many functions. If the function is the end of the statement, the closing parenthesis is not necessary. If other steps follow the end of the function, the closing parenthesis is essential. Page 2 of 27 Columbus Public Schools 8/22/04

5 4. Computation Computation is basically the same as on a scientific calculator with a few exceptions. The negative sign (-), which is on the bottom row next to ENTER, is used before entering the number. This symbol is not interchangeable with the blue key in the right hand column. The square root (2 nd x 2 ) is also used before the number. To square a number, enter the number and then choose x 2. To find the reciprocal of a number, enter the number and then the key x -1. Computations are completed by hitting ENTER. If you wish to use the last answer in a computation, just enter the operation symbol. The calculator pastes Ans for the number. You may also recall the last answer by typing ANS (2 ND (-)) at any position in the line. To raise a number to any power, enter the number, then the ^ and then the power. Press ENTER. Trigonometric computations work basically the same as on scientific calculator. For basic computation, the MODE must be in degrees. The trigonometric function precedes the angle on the home screen. To find the angle, given the trig value, use 2 nd to access the inverse trig function. The calculator will provide complex roots if the MODE is at a+bi in the next to last row. It will also perform computations with complex numbers. The i is 2ND decimal point. 5. Editing You can clear the home screen by choosing CLEAR. You can replace a character in an entry (before you hit ENTER) by using the arrows to move until the character to be replaced is highlighted and then hitting the correct key. You can delete a character by using the arrows until the character you wish to delete is highlighted and then choosing DEL You can insert a character in front of another by using the arrows until the character you wish to place the new character in front of is highlighted, choosing INS (2 nd DEL) and then hitting the key or keys you wish to insert. Page 3 of 27 Columbus Public Schools 8/22/04

6 You can enter a letter or any other green character above the keys on the keypad by hitting ALPHA and then the key of the character. If you wish to enter several letters, choose A-LOCK (2 ND ALPHA) and the calculator will display the ALPHA characters until you hit ALPHA to turn off A-LOCK. You can access the previous entry by choosing ENTRY (2 ND ENTER). You can then edit it by using the steps above. You can do this repeatedly to recall earlier work. 6. The MATH Menu Many other functions for computation are in the MATH menu. Any command in the list can be selected by using the arrows to move to the command and hitting ENTER or just by typing the number of the command. The arrow on 7 indicates that there are more functions that can be accessed by using the down arrow. 1: FRAC changes a decimal on the home screen into a fraction. 2: DEC changes a fraction on the home screen into a decimal. 3: 3 cubes the number on the home screen 3 4: ( takes the cube root of the number on the home screen. 5: x takes any root. Enter the root on the home screen, choose 5: x, and then enter the argument of the function. Many commands for computation are accessed through the MATH key. The absolute value function is also accessed by the MATH key and is obtained by arrowing to NUM and choosing #1:abs(. The MATH key also accesses most commands needed for probability. Use the right or left arrow to highlight PRB. 1: rand yields a random decimal between 0 and 1. WARNING: NEW CALCULATORS, WHICH HAVE NEVER USED THIS FUNCTION, WILL GIVE THE SAME NUMBER BECAUSE THE PROGRAM IS INITIALLY SET WITH A SEED. LET STUDENTS PLAY WITH THIS BEFORE YOU START COMPARING NUMBERS. Page 4 of 27 Columbus Public Schools 8/22/04

7 2:nPr is used for the permutations of n objects taken r at a time. Enter the number for n on the home screen, hit MATH, choose PRB, select 2:nPr, enter the number for r, and hit ENTER. 3:nCr is used for combinations and works the same way as combinations. 4:! Computes the factorial of a number. Enter the number on the home screen, hit MATH, choose PRB, and select 4:! and hit ENTER. 5:randInt( yields random integer(s) within given bounds. The command randint(a,b) will give one random integer between a and b. The command randint(a,b,c,) will give c random integers between a and b. Continuing to hit ENTER will repeat the command without entering it again. 7. Other Home Screen Operations You can copy the last answer to a computation by keying ANS (2 ND (-)) You can store a value to memory by entering the value and then choosing STO, the letter where you wish to store it, and then hitting ENTER. If you wish to store the previous answer, you do not have to reenter it, just choose STO and then the letter. You can use the colon (ALPHA decimal point) to string several commands together. This is called concatenation. 8. Catalog Most commands can be accessed in the CATALOG (2 ND 0). After choosing CATALOG, hit the key with the first letter of the command you wish to access. (The calculator will move to the first command that begins with that letter. Then use the down arrow to move to the desired command. Hit ENTER to paste the command on the home screen. This is the easiest place to access absolute value, the first command in the CATALOG. Most of the symbols are also in the CATALOG at the end of the commands. You can access them by going the end of the CATALOG and then using down arrow or staying at the beginning of the CATALOG and using the up arrow. Hit ENTER when the triangle is next to the command or symbol of your choice to paste it onto the home screen. Page 5 of 27 Columbus Public Schools 8/22/04

8 II. Graphing and Tables 1. Y= Menu When the calculator is in the function mode, the Y=menu is used to enter functions which can be used for graphing, tables, and evaluating from the home screen. Be sure that the statplots at the top of the Y= menu are not highlighted. If any of them are highlighted, use the up arrow and right and left arrows to select the entry and hit ENTER to turn them off. Having a STATPLOT turned on is often the source of the error message at the right when graphing. If the statplot does not cause the error message, it may still show up on the graph of the function. On the TI-83, you may enter up to 10 functions in Y1 through Y0. (Hint, sometimes students will have something entered in Y7, Y8, Y9, or Y0 and have a "mystery" graph on the graphing screen. Be sure to check at the bottom of the menu.) To write the equation for a function, the function must be written in y= form. Use Y= and move to any of the function names and type the right hand side of the equation. In the function mode, the variable in your equation must be x. For x, it is easiest to use the X,T,Θ,n key in the third row. When you enter the equation, the equal sign is automatically highlighted. This means that the equation is active and will appear on the graph and/or table. If you wish to deactivate the equation without deleting the equation, left arrow to the = and hit ENTER. The equation remains in the menu but will not appear on graphs or tables. On the screen at the right, Y1 will not be graphed. To reactivate the equation, repeat the process. When entering rational functions, be sure to place the entire numerator and the entire denominator in parentheses. 2. Graphing Window You can choose the boundaries for the graph by choosing WINDOW. XMIN gives the lowest x-value for the display, Xmax, the largest value. Ymax and Ymin give the smallest and largest y-values. Xscl and Yscl give the intervals at which the calculator will display tick marks. If you choose 0 for Xscl and Yscl, there will be no tick marks. These scl settings have no effect on the graph of a function. Xres controls the number of pixels that will be active in the graph. Except for very complicated graphs that graph very slowly, it should be left at 1. After you have selected Page 6 of 27 Columbus Public Schools 8/22/04

9 the window, enter an equation in the Y= menu and hit GRAPH to display the graph in the chosen window. Use the arrows to move about the graphing screen. Notice the x- values displayed at the bottom of the screen. For most windows, these are unwieldy decimals, Choose TRACE. Use the right and left arrows. The x-values are the same as those above. The y-values are the function values of the x-values. The function being traced on should appear in the upper left corner of the screen. To trace on the other function, hit the down arrow. Notice that when you switch functions, the same x-coordinate is displayed. After choosing TRACE, if you type a number for the x-coordinate between Xmin and Xmax and hit ENTER, the calculator will display the function value. 3. ZOOM Menu The ZOOM menu includes options for preset windows or for automatically changing a window in predetermined ways. When you choose ZOOM 4, 6, or 7, the calculator immediately sketches the graph. You do not need to hit ENTER. 4: ZDecimal gives the window at the right. When you trace in this window, the x-coordinates tracing are one-place decimals. The y-coordinates are the function values of the x-coordinates. 6: ZStandard gives the viewing window at the right. These x and y values are convenient, but the x-values when tracing are decimals with many places. 7: ZTrig gives two different windows depending upon whether the MODE is set at degrees or radians. When in degrees, the window is shown at the right. When the calculator is in radians, the Xmin is and Xmax is , approximately 2π to 2π. 1: ZBox is used to select a region of the graph to zoom-in on. Choose ZBox and move the cursor to the point that you wish to be the upper left corner of your new window and push ENTER. Next, move the cursor to the point that you wish to be the lower right hand corner of your new window and hit ENTER. The window is adjusted to the rectangle you selected. Page 7 of 27 Columbus Public Schools 8/22/04

10 2: ZIn is used to zoom-in around a specific point and is used in conjunction with Set Factors that is discussed in ZOOM MEMORY. Choose 2: ZIn, move the cursor to the point that you wish to be the center of the new graph and hit ENTER. 3: ZOut is used to zoom-out around a specific point and works like ZIn 5: ZSquare adjusts the window so that x and y-axes have the same aspect ratio. This is not true for any of the other windows except ZDecimal. For example, in ZStandard, the graph of the semicircle y = 36 x 2 looks like half of an ellipse. To adjust the window, move the cursor to the point that you wish to be the center of the windows and select 5: ZSquare. The resulting graph is in a window with the same Ymin and Ymax, but the Xmin and Xmax are changed so the aspect is 1:1. 8: ZInteger takes a window and zooms out around the point where the cursor is left. When tracing, the x-coordinates are integers. 9: ZoomStat provides a window that fits the data entered lists for STATPLOTS. This is explained in the Statistics section. MEMORY, accessed by using the right arrow on the ZOOM menu gives four options. 1: ZPrevious returns the window to the previous window if you had used a ZOOM operation to change the window, 2: ZoomSto allows you save a window. 3: ZoomRcl allows you to restore the saved window. 4: SetFactor sets the factors that determine what XMIN and XMAX and YMIN and YMAX will be multiplied by when you use ZIn or ZOut. Page 8 of 27 Columbus Public Schools 8/22/04

11 4. Style The TI-83 can display graphs in seven styles. The style is assigned by using the left arrow to move to the left of Y=. You can change the style by hitting ENTER to toggle through the options. The styles are: Connected Heavy Shade Above Shade Below Path Animate Dotted 5. Computations with Graphs Most computations with graphs are accessed through the CALC menu (2 nd TRACE). You need to enter your equation into the Y= menu. To find the x-intercept of a graph, choose CALC, 2: zero. The Left Bound prompt requires you to use the right and left arrows to move the cursor to the left of the zero you are trying to find and then hit ENTER. A triangle appears above to indicate your choice. The right bound prompt requires use the right and left arrows to move the cursor to the right of the zero and hit ENTER. Another triangle marks your choice. Finally, Guess, requires you to move the cursor close to the zero. Hit ENTER to find the zero. Page 9 of 27 Columbus Public Schools 8/22/04

12 To find the point at which a maximum occurs, choose CALC, 4: maximum. The left bound, right bound, and Guess commands work just as they did to find the x-intercept. 3:minimum works the same way. It is also possible to find extreme values from the MATH menu. Choose 6: fmin or 7: fmax. The command is pasted on the home screen. Enter the function, the variable in your function, a lower bound for the extremum, and an upper bound for the extremum. You may key in the function or access the function name if it is entered in Y=. To access the function name, hit VARS and right arrow to Y-VARS. Choose 1: Function, and then 1:Y1 (or whichever equation you wish to evaluate). Y1 will be pasted on the home screen. 5: intersect finds the point of intersection of two graphs. The First curve prompt is asking if the graph marked by the cursor is one of the curves you are looking for. This is necessary in case there are more than two functions being graphed. To indicate that the answer is "Yes," press ENTER. If the answer were No, you would press the up or down arrows until the desired curve is marked. The Second curve prompt works the same way. Guess works as it did previously. Page 10 of 27 Columbus Public Schools 8/22/04

13 A function can be evaluated in four ways. 1. Using the CALC (2 nd TRACE), choose 1: value and enter the x-value to be evaluated. Hit ENTER. The calculator will show the equation being evaluated in the top left hand corner. If you have more than one equation graphed, you can move to another graph by hitting either the up or down arrow. 2. While in TRACE, press the x-value to be evaluated and hit ENTER. You can move to another graph by using the arrows. 3. From the home screen, paste the Y variable onto the home screen as above. Choose VARS, and right arrow to Y-VARS. Choose 1: Function, and then 1:Y1 (or whichever equation you wish to evaluate). Y1 will be pasted on the home screen. Enter the x-value to be evaluated in parentheses and hit ENTER. By hitting ENTRY (2 ND ENTER), you can get the statement back for editing and easily find more values. 4. By using the TABLE. This is explained in Using Tables. 6. Technical Issues of Graphing with the TI-83 The TI-83 graphs functions by choosing x-values for each pixel across the screen. Because there are 95 horizontal pixels available across the screen, for any window chosen, the region between Xmin and Xmax is divided into 94 equal regions. There are 63 vertical pixels and for any window chosen, the region between Ymin and Ymax is divided into 62 regions. This is the reason that ZOOM 4:ZDecimal with Xmin of -4.7 and Xmax of 4.7 and Ymin of 3.1 and Ymax of 3.1 gives nice x-values when using the arrow keys to move about the screen. When you graph a function, the x-coordinates of the divisions are used to find function values of the 95 function values, and the points are placed on the graphing screen. The point is placed on the screen with the x-coordinate assigned to the pixel and the y- coordinate of the pixel that is nearest to that actual function value. However, when you use TRACE or any of the CALC functions, the actual function value is displayed. Xscl and Yscl do not affect the graphing of the function. Xscl does matter when you are making a histogram as will be discussed in the statistics section. However, if you choose a large window and a small Xscl and Yscl, the x- and y-axes will be heavy. You can fix that by choosing larger values for Xscl and Yscl. The function grapher cannot graph v ertical lines, because they are not functions. You can draw a vertical line by using the DRAW (2 ND PRGM) and choosing 4:Vertical. When the calculator returns to the graphing screen, hitting the right and left arrows displays a vertical line and the x-coordinate of the line. When you hit ENTER, the line is drawn on your graph. If you wish to draw more vertical lines, you can do so by using the arrows to move to the next position. When you have drawn all the vertical lines that you want, hit Page 11 of 27 Columbus Public Schools 8/22/04

14 GRAPH to return to the graphing screen. The line will remain until you change the window or return to the DRAW menu and choose 1:ClrDraw. The calculator graphs by connecting pixels. That means that the calculator will connect points even if there is a point of discontinuity between them. For example, the graph of y = 3 has an infinite discontinuity at x = 2, but if you graph the equation in the x 2 standard viewing window 6: ZStandard, the calculator connects the last point before the asymptote, ( , ), to the first point after the asymptote, ( , ), so that the graph appears to be continuous. This is because the calculator did not select x = 2, the x- coordinate of the point of discontinuity, as one of the values to evaluate. If you graph the same equation using 4:Zdecimal, x = 2 is chosen as one of the values to evaluate. Because this yields an expression that is undefined, there is a break in the graph. If you change the Ymin and Ymax without changing Xmin and Xmax, you can get a better view of the graph while retaining the discontinuity. Similarly, you can view the removable discontinuity at x = 2 in y = x 2 4 by graphing it in the x 2 4:Zdecimal window. The hole is visible, and if you trace to x = 2, the y-coordinate is blank. 7. Tables Tables display the y-values for functions that are entered into the Y= menu. (If the function is turned off as described in graphing, it will not appear in the table.) Enter the functions in the Y= menu, and then choose TBLSET (2 WINDOW). TblStart determines the x-value at the beginning of the table. Tbl determines the increments in x. To get the table to automatically display a list of values, set Indpnt and Depend to Auto. To view the table, choose TABLE (2 ND GRAPH). The table will display the x and the first two y-values. ND Page 12 of 27 Columbus Public Schools 8/22/04

15 To view more y-values, right arrow to the function you wish to view. To view additional x-values, place the cursor in the X column and arrow up or down. If you move the cursor up to the Y on the table, you can view the function at the bottom of the screen. By using the Indpnt: Ask setting on TBLSET, you may ask the calculator for definite x-values. When you choose TABLE, you may enter the x-values that you want. It is evaluated by hitting ENTER. You may continue to enter as many x-values as you want. If both Indpnt and Depend are set at Ask, no y-value is displayed when you enter the x-value. When you click on the Y column, the calculator displays the value. It is possible to view both graph and table at the same time using Split Screen. To view Split Screen, go to MODE, arrow to the bottom, and highlight Horiz. When in this mode, the top of the split screen always displays the graph. The lower portion will display either the home screen, the Y= menu, or the table, depending on which you select. On the MODE menu, the last entry at the right G T, shows the graph on the left and the table on the right. As you TRACE, the x-coordinate on the graph and the table move together. This does not happen on the Horiz split screen. Table values are function values determined by the equations in Y= menu. This is different from displaying data. Data is entered into lists, which are described in the Statistics section. Page 13 of 27 Columbus Public Schools 8/22/04

16 III. Matrices 1. Entering a Matrix Push MATRIX (2 ND x -1 ) and right arrow to EDIT. You may or may not have something under the MATH column. It depends on whether matrices have been previously entered on the calculator. You may enter up to 10 matrices, named [A] through [J]. It is important to note the brackets are part of the name and must be used to access the matrix. Choose the name of the matrix by selecting the number or highlighting the number of the matrix and then hit ENTER. Put the number of rows at the flashing cursor and hit ENTER, Put the number of columns at the second flashing cursor and hit ENTER. The calculator automatically sets up the format for the entries. If the matrix has been used previously, the old numbers will be replaced. If the matrix has not been used previously, the entries will be zeros. Put the entries into the proper position. The calculator automatically moves to the next position when you hit ENTER. WARNING: The last entry is not saved if you do not hit enter. Return to the home screen by hitting QUIT (2 ND MODE). To enter another matrix, push MATRIX ( 2 ND x -1 ) again and right arrow to EDIT. Choose a different matrix and enter the information. Be sure to hit ENTER at the end of the matrix and then QUIT. 2. Computations with Matrix You complete arithmetic operations from the home screen with the regular computation keys. Choose MATRIX and the name of the first matrix. Hit ENTER. [A] is pasted on the home screen. Choose the operation and then go back to MATRIX and choose the name of the second matrix. Hit ENTER. If you attempt an impossible computation because of the order of the matrices, the calculator will display an error message. Page 14 of 27 Columbus Public Schools 8/22/04

17 You also find the inverse of a matrix on the home screen by using the x -1 key. If you wish, you can change the answer to fractions with MATH 1: Frac. The dotted lines indicate that there are more entries. You can view these by using the right and left arrows. Other matrix operations are accessed through pushing MATRIX and arrowing to MATH. Most of the commands are followed by (, indicating that the name of the matrix should be entered after the (. To find the determinant of a matrix, choose MATRIX, arrow to MATH choose 1: det( and fill in the name of the matrix. Hit ENTER. To transpose a matrix, hit MATRIX, arrow to MATH AND choose 2: T. Hit ENTER. To generate an identity matrix, use MATRIX, arrow to MATH, and choose 5: identity( followed by the number of rows and columns, e.g. 3 for a 3 3 matrix. 3. Solving Systems with Inverse Matrices. Store the coefficients in matrix [A] and the constants in matr ix [B]. The solution is [A] -1 [B]. Example: Go to MATRIX, EDIT, and enter the coefficient matrix in [A]. Then enter the constant matrix in [B]. Then on the home screen, enter [A] -1 [B] and hit ENTER. 3x y+ 2z = 13 2x+ 2y z = -1 x + 3y + 4z = 11 Page 15 of 27 Columbus Public Schools 8/22/04

18 IV. Statistics 1. List Basics Data is entered into Lists that are accessed through the STAT menu. Push STAT and choose 1:Edit. You should see L1, L2, and L3 and by using the right arrow, you should also see L4, L5, and L6. If you cannot see all of these lists, hit STAT again and choose 5: SetUpEditor. When SetUpEditor is pasted onto the home screen, hit ENTER. To clear a list, place the cursor into the list you wish to clear, and use the up arrow to highlight the name of the list and hit CLEAR. When you use the down arrow to return to the data, the list is cleared. WARNING: Be sure that you use CLEAR, not DEL. DEL will remove the list from the list editor. If that happens, it can be restored by using the SetUpEditor as described above. You can clear all the lists by hitting MEM (2 ND +) and choosing 4:ClrAllLists, and hitting ENTER. 2. Data Entry To enter data into a list, use the cursor to move to the desired list. Make sure the cursor is below the list name and enter the first number. Hit ENTER to move to the next position, put in the second number, hit ENTER, and continue until you have entered all the data. If you use the up arrow to highlight L1, the calculator will display the items in the list. By hitting ENTER, you can scroll through the entire list If you wish to delete one of the numbers in the list, highlight it either in the column or the in the edit line at the bottom and hit DEL. If you omit a number, you can insert it by highlighting the entry above the place you wish to insert the new number or in the edit line, highlight the number before the place you nd wish to insert the new number. Hit INS (2 DEL). You can also enter data into a list from the home screen. Begin with a left brace { (2 nd ( ), enter the numbers into the list separating them with commas. When all the numbers are entered, nd nd end with the right brace } (2 ) ) and type STO L2 (2 2). Hit ENTER. Page 16 of 27 Columbus Public Schools 8/22/04

19 You can also view the data in the list on the home screen by typing L1 (2 nd 1) and then ENTER. You can also scroll through this view. You can create new lists from the data in other lists. To enter data into L3 that is the sum of L1 and twice L2, open the list editor (hit STAT, choose 1: Edit), and move the cursor into L3. Use the up arrow to highlight L3. Type L1 (2 nd 1) + 2L2 (2 nd 2). Hit ENTER. In this case, the list can be edited. Notice that changing the 3 to 5 in L2 did not change L3. You can make the TI-83+ act like a spreadsheet so that the new list would change when one of the original lists is changed. To create L3 which is the difference of twice L2 and L1 squared and will automatically change if either L1 or L2 is changed, arrow up so that L3 is highlighted. Enter "2L2-L1 2 ". The quotation marks (ALPHA +) cause the list to behave like a spreadsheet. The diamond at the upper right corner of L3 denotes that it was created as a spreadsheet. Notice that change 3 to 5 in L2 changed the value in L3. To combine lists using either of these methods, the lists must contain the same number of elements. If they do not, the calculator will display this error message. 3. One Variable Statistics To compute single variable statistics on the data in one list, use STAT, arrow to CALC, and choose 1:1-Var Stats. If you are using L1, you do not need to enter the name of the list. The arrow next to n=7 indicates that there are more items accessed by using the down arrow. For any other list, you must enter the name of the list. Page 17 of 27 Columbus Public Schools 8/22/04

20 4. Graphs with One Variable Statistics Before beginning a STATPLOT, be sure that either there are no equations in Y= or that they are all turned off. To make any statistical graph, hit STATPLOT. The calculator displays the status of the 3 available statplots. In the example at the right, Plot 1 is active and is a box and whisker plot. Plot 2 is turned off and is a histogram. Plot 3 is turned off and is a modified box and whisker plot. By choosing 4: PlotsOff, you can turn off all STATPLOTS. By choosing 5: PlotsOn, you can turn on all of the STATPLOTS. The modified box and whisker plot shows an y outliers as separate points and does not use them to compute the median and the quartile boundaries. To change the status of a STATPLOT, select the plot and hit ENTER. To change a setting, highlight the desired setting and hit ENTER. To change the name of the list use L1 through L6 on the keypad. Freq only appears with one variable data. You usually leave Freq at 1 but you can use it to enter each data value only once, placing its frequency in the list designated in Freq. The Mark chooses the way the outlier will be designated on the graph on a modified box-and-whisker plot. To make a box-and-whisker plot, hit STATPLOT (2 nd Y=), and select the plot number. Turn the STATPLOT ON. Use the arrows to move to Type and select the correct icon. (The regular box-and-whisker plot is the middle one on the bottom row.) In Xlist, use the keypad to enter the name of the list where you have entered your data. Leave Freq at 1. (If you are making a modified box-and-whisker plot, choose the Mark that will show the position of the cursor when you trace.) For a box-andwhisker plot, use Z oomstat to choose the window. When you trace on a box and whisker plot, the calculator displays the maximum value, the 3 rd quartile boundary, the median, the first quartile boundary, a nd the minimum value. Page 18 of 27 Columbus Public Schools 8/22/04

21 To make a histogram, hit STATPLOT (2 nd Y=), and select the plot number. Turn the STATPLOT ON. Use the arrows to move to Type and select the correct icon. Enter the Xlist from the keypad. As with the box and whisker plots, you usually leave Freq at 1 but you can use it to enter each data value only once, placing its frequency in the list designated in Freq. Choosing ZoomStat will select a suitable window, but the width of the interval for each bar is determined by Xscl. This is the only graph where the choice of Xscl matters. Changing Xscl to create a different interval may necessitate that you change other window parameters as well. When you trace on a histogram, the cursor moves to the center of each interval. The min is the left boundary. Because the right boundary is not included in the region, it is shown by max<. The n shows the number of elements in the region. The last icon on the STATPLOT menu represents a normal probability plot that plots each observation X in Data List versus the corresponding quantile z of the standard normal distribution. If the plotted points lie close to a straight line, then the plot indicates that the data are normal. 5. Graphs with Two Variable Stats The first icon on Type of the Statplot represents a scatterplot. The second icon represents an XY line graph where the data points are connected in the order they appear in the lists. To make a scatter plot, enter the data into two lists. Access the menu by hitting STATPLOT (2 nd Y=) and choosing PLOT1, PLOT2, or PLOT3. Select the first icon in TYPE. Enter the names of the lists from the keypad. The Mark will determine how the points are displayed on the graph. The two lists must have the same number of elements. If they do not you will get this error message when you attempt to graph. Page 19 of 27 Columbus Public Schools 8/22/04

22 You can choose a window by considering the domain and range of your data and choosing values for Xmin, Xmax, Ymin, and Ymax. After selecting the window, hit GRAPH. You can also just choose 9: ZOOMSTAT from the ZOOM menu. You can enter an equation into the Y= menu and fit the curve by trial and error. The calculator also calculates regression equations and pastes them into the Y= menu. It is a good idea to clear the home screen before beginning the STAT CALC. Hit the STAT key, arrow to CALC. Choose the regression that appears to fit the data. In this case, the data suggests 4: LinReg (ax+b). Choose 4. The calculator pastes LinReg (ax+b) on the home screen. Before you hit enter, type in the names of the lists, separated by commas, and the Y= position where you want the equation placed. The Y= names are in the VARS menu. Hit VARS, arrow to Y-VARS, choose 1: FUNCTION, and the then number of the position where the equation will be placed. Hit ENTER. The calculator displays the regression equation on the home screen. When you look at Y=, the equation has been entered into Y1. The r and r 2 are measures of the fit of the line to the data points. The closer r is to one, the better the fit; r and r 2 may not be displayed. If they are not displayed and you wish to see them, choose CATALOG and move to DiagnosticOn and hit ENTER. If they are on and you do not want them displayed, choose DiagnosticOff. Remember that you can move more quickly through the CATALOG by hitting the D key. Page 20 of 27 Columbus Public Schools 8/22/04

23 V. Calculator Based Ranger 1. Functions of the Ranger The ranger is a pre-programmed motion detector that allows students to collect, view, and analyze motion data. The ranger collects time/distance data and displays graphs of time vs. distance, velocity, or acceleration. The ranger has built in applications for matching time/distance and time/velocity graphs and for collecting ball bounce data. 2. Set Up Instructions The TI-83 Plus should be ready to use the Ranger. To check, hit the APPS key. Although there may be other applications in the list as well, you should find CBL/CBR in the list. To run the application, choose CBL/CBR, press any key, and then choose 3: RANGER. If it is not in the list, you can use the following directions for installing the Ranger program on the TI-83, or you can link to another TI-83 Plus to install the CBL/CBR application. See Linking/Applications in the next section. A TI-82 or TI-83 may or may not be ready to use the Ranger. To check, hit the PRGM key. If RANGER is in the list, it is installed on the calculator. If RANGER is not in the list, connect the calculator to the Ranger with a link cord. On the calculator, push LINK (2 nd X,T,Θ,n). Use the right arrow to move to RECEIVE. Hit ENTER. While the calculator displays Waiting, open the Ranger to display the buttons on the inside. Push the 82/83 button. The calculator displays Receiving and then the screen at the right. The program should now appear in the PRGM list. To run the program select RANGER and hit ENTER. Hit ENTER one more time to access the main menu. Page 21 of 27 Columbus Public Schools 8/22/04

24 The Ranger program is identical as an application on the TI-83 Plus and as a program on any of the calculators. Choosing 2: SET DEFAULTS sets the menu to these settings. 3. Using 1: SETUP/SAMPLE You move through the menu using the arrow keys. Except for TIME, you toggle through the options for each category by hitting ENTER. REALTIME: YES means that the data will be collected and displayed simultaneously. The time is set at 15 seconds and cannot be changed. The YES/NO toggles by hitting ENTER. REALTIME: NO means that the data will be collected and the graph will be displayed at the end of the chosen time. TIME(S) With the REALTIME: NO set, change the time by arrowing to TIME and hitting ENTER. When the question marks appear, enter the number of seconds that the data will be collected. The number of seconds can vary from 1 to 99. DISPLAY: determines whether the graph will display distance, time, or acceleration. You toggle through these by hitting ENTER. BEGIN ON: gives the option of starting to gather data by hitting ENTER on the calculator or hitting the TRIGGER on the Ranger. DELAY causes the sampling to begin 10 seconds after pressing ENTER. SMOOTHING evens out the graph. You HEAVY. UNITS allows you to toggle between meters and feet. can choose NONE, LIGHT, MEDIUM, or To collect the data, use the up arrow so that the triangle is next to START NOW. Hit ENTER and follow the instructions on the calculator. In real time, the graph will appear as the graph is collected. When not in real time, the Ranger will transfer the data to the calculator. At the end of collection the calculator will then display the graph. After the calculator displays the graph, hit ENTER and the calculator will display the PLOT MENU. This is the same PLOT MENU that is accessed by 4:PLOT MENU on the MAIN MENU. Page 22 of 27 Columbus Public Schools 8/22/04

25 4. PLOT MENU The PLOT MENU allows you to select different graphs to view. 1: DIST- TIME selects the distance/time graph. The graph already displayed is a distance/time graph because you chose DISTANCE for DISPLAY on the SETUP/SAMPLE menu. Choosing 2: VEL-TIME displays a velocity/time graph for the same data. Choosing 3: ACC-TIME displays an acceleration/time graph for the same data. Choosing 4:PLOT TOOLS gives the PLOT TOOL menu. Option 1: SELECT DOMAIN allows you to select a portion of the graph to isolate. When you choose 1: SELECT DOMAIN, the calculator prompts you to select a left bound by using the arrows to brace to the left-most point you wish to include in the data. When you hit ENTER the calculator draws a vertical line and prompts you to locate the right bound. When you move the cursor to the right-most point you wish to include in your data, hit ENTER again, the calculator draws another vertical line and then displays the graph of the new data set. The PLOT TOOLS menu also allows you to smooth the data, if you wish. On the PLOT MENU, 5:REPEAT SAMPLE allows you to collect the data again. 6: MAIN MENU returns you to the original Ranger menu. While in the RANGER program you cannot access the statistical or graphical functions of your calculator. By choosing 6: QUIT, you exit the program and can access all normal calculator functions. The calculator shows the location of the data you have gathered, so that you can analyze it. For example, the final graph looks vaguely parabolic, so you could try to model it using quadratic regression, Page 23 of 27 Columbus Public Schools 8/22/04

26 5. Applications 3:APPLICATIONS are built-programs designed for frequently used motion detector activities. When you select APPLICATIONS, the calculator prompts you to choose either meters or feet for measuring distance. When you make your selection, there are three choices. 1:DIST MATCH shows a simple distance vs. time graph that students can attempt to match. After the student attempts to match the graph, you may repeat it with 1:SAME MATCH or choose 2:New MATCH. 2:VEL MATCH works just like the distance match, except that the students are trying to match the velocity walked to the graph. This is a lot more difficult. 3:BALL BOUNCE is a program designed to collect distance/time data from a bouncing ball. It works best with a large ball like a volleyball or soccer ball. The program automatically reflects the data so that the distance at the maximum of each parabola is actually the distance when the ball is at its maximum height. You can access the PLOT MENU by hitting ENTER. 6. TOOLS 5:TOOLS on the main menu has options for sharing data and for controlling the Ranger. 1:GET CBR DATA transfers the data previously collected on a Ranger to any TI-83, 2:GET TI83P DATA will transfer Ranger data between two TI-83 calculators. It is also possible to link calculators and transfer L1, L2, L3, L4, and L5 to share Ranger data. See the linking section. 3:CBR STATUS checks the battery and lists any errors that may have occurred. 4:STOP/CLEAR CBR stops the Ranger and/or clears all data on it. Page 24 of 27 Columbus Public Schools 8/22/04

27 VI. Linking 1. Linking Lists on the TI-83 Connect the calculators with a link cord. On the receiving calculator, hit LINK (2 nd X,T,Θ,n) and right arrow to RECEIVE. Hit ENTER. The calculator will display Waiting On the nd sending calculator hit LINK (2 X,T,Θ,n) and choose 4:List. Select the lists to be transferred by hitting ENTER when the list is highlighted. Right arrow to TRANSMIT and hit ENTER. The calculator displays a log of lists transferred. The receiving calculator recognizes that it already has lists of these names and offers choices. To receive the data into the list, choose 2:Overwrite, any data already in the list will be deleted and the new data will be placed in the list. You will have to do this for each list being received. A TI-83 can send data to a TI-82 in the same way, except you choose 5:Lists to TI-82. The TI-82 has a different menu for sending. 1:Select ALL+ selects all lists, programs, variables, equations, etc. to be sent. You can deselect anything you do not wish to send by highlighting it and hitting ENTER. By choosing 2:Select All nothing is selected and you choose the items you wish to send by highlighting and hitting ENTER. 2. Linking Programs on theti-83 The linking procedure is the same on the receiving calculator. On the sending calculator, choose 3:PRGM and select the programs to be transferred by highlighting and hitting ENTER. Programs are shared on the TI-82 by selecting them just like the lists. Most programs cannot be shared between a TI-82 and the TI-83 because of slight differences in the programming language. 3. Linking Applications on the TI-83 Plus Only the TI-83 has applications. You can transfer "free" applications from the link menu just like lists. Some applications come pre-loaded on the TI-83 Plus. Others are available on the education.ti.com website. Many of them can be downloaded at no cost. Others are available for purchase. There are also some third party applications available from other sources. See the Computer Resources section for more information. Page 25 of 27 Columbus Public Schools 8/22/04

28 VII. Computer Resources 1. Connecting the TI-83 to a Computer TI-Graph Link Cables are used to connect TI calculators to a computer. There are three types of TI-Graph Link Cables. The original gray cable connects to a com port of a Windows computer, or with the included adapter, to the serial port of a Macintosh. On a Window machine, this cable can be used only with Graph Link software. On a Mac, this cable can be used with either the Graph Link or TI-Connect software. The black cable that connects to a Com port of a PC. This cable works only with Windows computers and works with either the Graph Link or TI-Connect software. The silver cable that connects to a USB port of a Windows or Macintosh computer. This cable works with both Windows and Mac computers. It works only with TI-Connect Software. The cables are available at Best Buy, Office Depot, OfficeMax, Radio Shack, Staples, Target, and Wal-Mart and through many instructional dealers. Check the TI website, to locate dealers. The software is available for free download from the TI website, On a Macintosh computer, you will need TI-Connect. On a Windows computer, you may need TI-Connect or Graph Link for the TI-83 or Graph Link for the TI-83 plus, depending on the type of calculator and cable you are using (see above). Page 26 of 27 Columbus Public Schools 8/22/04

29 2. Reasons to Connect to a Computer. You can back up your calculator or save programs or data for later use You can write or edit calculator programs and transfer them to you calculator. You can download and install the latest Operating System for your calculator. (Once this is installed on one calculator, you can install it on others by linking calculators.) You can download ( and install Applications. Most of these applications are free and are helpful for review activities with students. You can download ( programs from the TI archives. You can download many games from the TI website and many other sites. Page 27 of 27 Columbus Public Schools 8/22/04

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