TI-30XS MultiView™ A Guide for Teachers Developed by Texas Instruments Incorporated Activities developed by Gary Hanson, Aletha Paskett, and Margo Lynn Mankus Illustrated by Jay Garrison and David Garrison
About the authors Gary Hanson and Aletha Paskett are math teachers in the Jordan Independent School District in Sandy, Utah. They developed several of the activities and assisted in evaluating the appropriateness of the examples in the How to use the TI-30XS MultiView™ section of this guide. Margo Lynn Mankus currently works in Mathematics and Technology Education at the State University of New York at New Paltz.
Table of contents CHAPTER PAGE About the teacher guide v About the TI-30XS MultiView™ calculator vi Name that rule Algebraic expressions 12 Probability 89 13 Function table 97 3 14 Powers, roots, and reciprocals 101 7 15 Logarithms and exponential functions 109 16 Pi 113 13 17 Angle settings and conversions 117 21 18 Polar and rectangular conversions 121 19 Trigonometry 123 20 Hyperbolics 131 Appendix A Quick reference to keys A-1 How to use the TI-30XS MultiView calculator 1
iv TI-30XS MultiView: A Guide For Teachers © 2006 TEXAS INSTRUMENTS INCORPORATED
About the teacher guide How the teacher guide is organized • This guide is for the TI-30XS MultiView™ and TI-30XB MultiView scientific calculators. All subsequent references in this guide refer to the TI-30XS MultiView, but are also applicable for the TI-30XB MultiView. An introductory page describing the calculator keys presented in the example, the location of those keys on the TI-30XS MultiView, and any pertinent notes about their functions.
About the TI-30XS MultiView™ calculator Home screen Mode On the Home screen, you can enter mathematical expressions and functions, along with other instructions. The answers are displayed on the Home screen. The TI-30XS MultiView screen can display a maximum of four lines with a maximum of 16 characters per line. For entries and expressions of more than 16 characters, you can scroll left and right (! and ") to view the entire entry or expression. Use pto choose modes.
About the TI-30XS MultiView™ (Continued) Menus Resetting the TI-30XS MultiView Certain keys display menus: H, %I, v, %t, % , %h, and %{. Press " or $ to scroll and select a menu item, or press the corresponding number next to the menu item. To return to the previous screen without selecting the item, press -. To exit a menu or application and return to the Home screen, press %Q. Pressing & and - simultaneously or pressing % and then selecting 2 (Yes) resets the calculator.
viii TI-30XS MultiView: A Guide For Teachers © 2006 TEXAS INSTRUMENTS INCORPORATED
Activities Star Voyage — Scientific notation Heart Rates — 1-variable statistics At the movies — Data formulas at the box office Name that rule — Algebraic expressions © 2006 TEXAS INSTRUMENTS INCORPORATED 3 7 13 21 TI-30XS MultiView: A Guide For Teachers 1
2 TI-30XS MultiView: A Guide For Teachers © 2006 TEXAS INSTRUMENTS INCORPORATED
Star voyage — scientific notation Math Concepts Overview Students investigate scientific notation by changing numbers into scientific notation, and then using them in calculations. Materials • scientific notation • TI-30XS MultiView™ • addition • pencil • division • student activity Introduction Set up the activity by telling your students: The standard form for scientific notation is a ¿ 10 n,where a is greater than or equal to 1 and less than 10, and n is an integer. 1.
Star voyage — scientific notation (Continued) Hint: Make sure the TI-30XS MultiView calculator is in MathPrint™ mode to work this problem. Activity Present the following problem to students: You are a captain of a starship in the distant future. You have been assigned to go to Alpha Centauri and you have 5 years to get there. The distance from our sun to Alpha Centauri is 2.5 x 10 13 miles. The distance from the earth to our sun is approximately 9.3 x 10 7 miles.
Star voyage — scientific notation Name ___________________________ Date ___________________________ Problems 1. Write the following numbers in scientific notation. Standard Notation Scientific Notation a. 93 000 000 __________________________ b. 384 000 000 000 __________________________ c. 0.00000000000234 __________________________ d. 0.0000000157 __________________________ 2. Using the TI-30XS MultiView™ calculator, change the following numbers into scientific notation using SCI mode.
Star voyage — scientific notation Name ___________________________ Date ___________________________ Problem You are a captain of a starship in the distant future. You have been assigned to go to Alpha Centauri and you have 5 years to get there. The distance from our sun to Alpha Centauri is 2.5 x 1013 miles. The distance from the earth to our sun is approximately 9.3 x 107 miles.
Heart rates — 1-variable statistics Overview Students use the data editor and statistics function of the TI-30XS MultiView™ calculator to investigate the effect of exercise on heart rate. Math Concepts Materials • mean, minimum, maximum, and range • TI-30XS MultiView • stopwatch or a watch with a second hand • student activity Introduction Students may be placed in smaller groups for this activity to minimize the amount of data to be entered.
Heart rates — 1-variable statistics (Cont.) 4. Check the statistics calculations. After students display Òx (Sigma x), explain that Òx is the sum of all the heart rates. Ask students: • • • How many heartbeats were entered from all of the student in one minute? This is Òx. How many students were entered? This is n. How can we calculate the average heart rate? This is Ï. • Σx ------ = 62.27272727 n Is the average heart rate higher or lower than you expected? 5.
Heart rates — 1-variable statistics Name ___________________________ Date ___________________________ Problem What do you think the average heart rate is for someone your age? What about after exercising? Procedure 1. Use this table to record your class or group data (resting). Heartbeats per minute (resting) Frequency 2. What is the class (group) average? ________________________________________ 3. Answer the following questions from the data: a.
Heart rates — 1-variable statistics Name ___________________________ Date ___________________________ 4. Use this table to record your class or group data (running). Heartbeats per minute (running) Frequency 5. What is the class (group) average? _______________________________________ 6. Answer the following questions from the data: a. What is the total number of heartbeats for the minute? Write the symbol and the number from the calculator. ______________________ b.
Heart rates — 1-variable statistics Name ___________________________ Date ___________________________ 7. Use this table to record your class or group data (jumping). Heartbeats per minute (jumping) Frequency 8. What is the class (group) average? _______________________________________ 9. What is the total number of heartbeats for the minute? ____________________ 10. Answer the following questions from the data: a.
Heart rates — 1-variable statistics Name ___________________________ Date ___________________________ 11. Make a bar graph for each of the 3 sets of data you collected. Resting Running Jumping 12. How are the bar graphs the same? How are they different? _________________ _______________________________________________________________________ _______________________________________________________________________ 13.
At the movies — data formulas at the box office Overview Students investigate a table of values and observe patterns in the table. Students use v on the TI-30XS MultiView™ calculator to enter data into a list and test their generalizations. Math Concepts Materials • patterns • algebraic expressions • linear functions • variables • • • • TI-30XS MultiView pencil graph paper student activity Introduction The warm up question is given to help you launch the student sheet activity.
At the movies (Continued) Point out that the Money column looks like the multiplication table for the number 4. This connects them back to something familiar. Remind the students that they know that Kyle earns $4 per week. This is the rate of Kyle's savings and it can be written in fractional form as $4 rate = 1 week Ask the students to fill in more of the table describing how much Kyle will save.
At the movies (Continued) Ask the students the following: "If you calculate W weeks times $4, you get a number. What does that number mean to Kyle?" You are prompting the student to say Money (M) and lead them into writing the formula or sentence in two variables, M = W x 4. Typically, you write the number and then the letter with implied multiplication. Remind students that multiplication is commutative so M = W x 4 = 4 x W = 4W.
At the movies (Continued) The students now have taken data from words to a table of values, to a pattern they can view, to writing an algebraic expression. The next step is to show them a view of how the number pattern plots on a graph. What is the shape of M = 4W? Have students plot the first 4 points in the table. Notice the points fall on a straight line. You can mention that they can describe the increase of Money (M) as "for every 1 week (W) Kyle works, his amount of money (M) increases by $4.
At the movies (Continued) Procedure Students should write the algebraic equation from the pattern showing in their table: M = P x 11.50 or using implicit multiplication, M = 11.50 P. Students check their formula using the data editor ( v) on the TI-30XS MultiView™ calculator, as in the warm up example. 1. Have the students check to see how the calculator is set up. ³ Make sure the calculator mode is set as shown. 1. Press p. 2. Enter the first three values in L1 {1, 2, 3}. 3.
Name ___________________________ At the movies Date ___________________________ Problem A blockbuster movie is opening this weekend. On the news, you hear that tickets will be $11.50 per person. The reporter says that a family of two will spend $23 and a family of three will spend $34.50. They show a graphic with this information in a table format. Number of People Amount of Money 1 $11.50 2 $23.00 3 $34.
Name ___________________________ At the movies Date ___________________________ 2. What pattern do you see from your table? Using the information in your table, write a formula (an algebraic expression) which describes the amount of money (M) depending on the number of people (P) that buy a ticket to the show. M = ___________________________ 3. Check your formula using the data list editor ( v) on the TI-30XS MultiView™ calculator. a.
Name ___________________________ At the movies Date ___________________________ 5. Your boss wants you to make a presentation to the people who invest money in MultiPlex. The investors want to see numbers and graphs in your presentation! Fill in the table below using the data editor on your calculator. Graph the points from this table. This is another way that an accountant can show how the amount of money (M) depends on the number of people (P).
Name that rule! Overview Students guess the algebraic expression (function) from a table of values in a game format. Students use o on the TI-30XS MultiView™ calculator to enter an expression as a function (y=) in order to play the game. Math Concepts Materials • algebraic expressions • functions • • • • TI-30XS MultiView pencil student activity strips of paper and paper bag Introduction Students will warm up for this activity by evaluating expressions and filling out a table of values.
Name that rule! (Continued) to provide an alternate way of thinking about evaluating an expression for different values of x. Here, an input of x = 1 gives an output of y = 1 + 3 = 4. Discuss that the expression, x + 3, can be thought of as the rule to find y. Later in the game, the students will think backwards to guess the "rule." If needed, discuss how students follow the rules to their favorite board games. They need to follow the rules in order to play.
Name that rule! (Continued) Rules for group play • • • • • • • • • • • • • Form groups of three to four students. Assign one student to be the Ruler of the game. The Ruler is in charge of the calculator for the game. The Ruler picks an algebraic expression from a paper bag (or any container) and keeps it hidden from the other players, or the Ruler writes an algebraic expression on a piece of paper for the game and gets approval to use the expression from the teacher.
Name that rule! (Continued) Algebraic expression list Copy these or other expressions on pieces of paper so the Ruler of each team of players can pick the expression to play. You can also have the Ruler write an expression which you can approve before the start of a game. Having the student write an expression gives them ownership and is an assessment of their knowledge. Pick a list or mix the lists depending on the level of your students. Expand the lists depending on your students' level.
Name that rule! Name ___________________________ Date ___________________________ Problem We follow rules every day. Can you follow the rules to your favorite board game? Do you have to carefully follow the rules to play? We also follow rules when we work with numbers and expressions. Example: If x = 1, then x + 3 = 1 + 3 = 4 The expression x + 3 has one variable, x. Depending on the value of x, x + 3 will be equal to different numbers. You can think of x + 3 as a rule.
? Name That Rule! ? Think backwards! Guess the rule from a table of values! Player names: ? ? Ruler: Your teacher will give you the instructions on how to play. Use the table to keep track of the x and y values for every player’s turn during the game. Use the Guess columns to check the rule. If a player's rule is not correct, continue playing.
How to use the TI-30XS MultiView™ calculator TI-30XS MultiView basic operations Clearing and correcting Basic math Order of operations and parentheses Numeric notation Fractions Decimals and decimal places Constant Memory and stored variables Data editor and list formulas Statistics Probability Function table Powers, roots, and reciprocals Logarithms and exponential functions Pi Angle settings and conversions Polar and rectangular conversions Trigonometry Hyperbolics © 2006 TEXAS INSTRUMENTS INCORPORATED
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TI-30XS MultiView™ basic operations Keys 1. & turns on the calculator. 2. % turns on the 2nd indicator and accesses the function shown above the next key you press. 3. % ' turns off the calculator and clears the display. 4. < completes the operation or executes the command. 5. % i recalls the most recently calculated result and displays it as Ans. 6. n toggles the answer between fraction and decimal, exact square root and decimal, and exact pi and decimal formats. 1 7.
TI-30XS MultiView™ basic operations (Continued) Notes • The examples on the transparency masters assume all default settings (See page vi). • n can be used in an entry before pressing <. Pressing n more than once in a current entry may result in a Syntax error. To achieve the desired result, you can: – Enter the expression, press n <, and then press n again after the result is displayed.
Second, off, arrows, enter • Enter 46 – 23. • Change 46 to 41. Change 23 to 26 and complete the operation. %' ! " #$< • Enter 2/5 + 3/10 and complete the operation. • Turn the TI-30XS MultiView™ calculator off and back on. The Home screen is blank; scroll up to view history.
Reset Reset the calculator. Press % Display % 2 - Pressing & and - at the same time also resets the calculator immediately. No menu or message is displayed. Using % or & and returns all settings to their defaults and clears the memory.
Mode p Use pto choose modes. Press $ # ! " to choose a mode, and < to select it. Press - or %Q to return to the Home screen and perform your work using the chosen mode settings. Default mode settings are shown highlighted. p DEG RAD GRAD Sets the angle mode to degrees, radians, or gradians. NORM SCI ENG Sets the numeric notation mode. Numeric notation modes affect only the display of results, and not the accuracy of the values stored in the calculator, which remain maximal.
Mode (continued) NORM displays results with digits to the left and right of the decimal, as in 123456.78. p SCI expresses numbers with one digit to the left of the decimal and the appropriate power of 10, as in 1.2345678x105 (which is the same as 123456.78). ENG displays results as a number from 1 to 1000 times 10 to an integer power. The integer power is always a multiple of 3. Note: C is a shortcut key to enter a number in scientific notation format.
Mode (continued) 0 1 2 3 4 5 6 7 8 9 (fixed decimal point) specifies the number of digits (0 through 9) to display to the right of the decimal. p CLASSIC MATHPRINT sets the display input and output. CLASSIC displays inputs and outputs in a single line. MATHPRINT displays most inputs and outputs in textbook format. Use MathPrint mode for better visual confirmation that math expressions have been entered correctly and to better reinforce the correct math notation.
Menus Certain keys display menus: H, %I, v, %t, % , %h, and %{. Some keys may display more than one menu. Press " and $ to scroll and select a menu item, or press the corresponding number next to the menu item. To return to the previous screen without selecting the item, press -. To exit a menu or application and return to the Home screen, press %Q. The Home screen is blank; scroll up to view history.
Menus (Continued) v (Press v once to display the Data editor screen. Press again to display the menu.) CLEAR 1: Clear L1 2: Clear L2 3: Clear L3 4: Clear ALL FORMULA 1: Add/Edit Frmla 2: Clear L1 Frmla 3: Clear L2 Frmla 4: Clear L3 Frmla 5: Clear ALL Press v while you are in the Add/ Edit Frmla option of the FORMULA menu to display this menu: Ls 1: L1 2: L2 3: L3 %t STATS 1: 1-Var Stats 2: 2-Var Stats 3: StatVars This menu option displays after you calculate 1-var or 2-var stats.
Last answer (Ans) Use Last answer (Ans) to calculate 2 %i 2 5 + 12 .
Answer toggle Press n to toggle the display result between fraction and decimal answers, exact square root and decimal, and exact pi and decimal.
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2 Clearing and correcting Keys Notes 1. - clears characters and error messages. Press - once to clear an uncompleted entry; press it again to clear the display. You can scroll up and use - to clear entries in history. - backs up one screen in applications. • The examples on the transparency masters assume all default settings. • Pressing - does not affect the memory, statistical registers, angle units, or numeric notation. 2. % f lets you insert a character at the cursor. 3.
Delete and insert Enter 4569 + 285, and then change it to 459 + 2865. Complete the problem.
Clear - Enter 21595. Clear the 95. Clear the entry.
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3 Basic math Keys 1. T adds. Notes 2. U subtracts. 3. V multiplies. • The examples on the transparency masters assume all default settings. • The TI-30XS MultiView™ allows implied multiplication. Example: 3 (4+3) = 21 • Do not confuse M with U. U allows subtraction. • Use parentheses to group the negation sign with the number if needed. Example: M22 = M4, and (M2)2 = 4. • Results of percent calculations display according to the decimal notation mode setting. 4. W divides. 5.
Add, subtract, multiply, divide, equals TUVW < Find: 2 + 54 ½ 6 = 16 x 21 = --1- x 10 = 2 12 x (5 + 6) = Press Display 2 T 54 U 6< 16 V 21 < 1q2"V 10 < 12 V D 5 T 6E< 46 TI-30XS MultiView: A Guide For Teachers © 2006 TEXAS INSTRUMENTS INCORPORATED
Negative numbers The temperature in Utah was M3Ä C at 6:00 a.m. By 10:00 a.m. the temperature had risen 12Ä C. What was the temperature at 10:00 a.m.? Press M Display M3T 12 < The temperature at 10:00 a.m. was 9Ä C.
Percent Mike makes $80 per week. He saves 15% of his earnings. How much does Mike save per week? Press %_ Display 15 %_V 80 < Mike saves $12 per week.
Order of operations and parentheses Keys 4 Notes 1. D opens a parenthetical expression. • The examples on the transparency masters assume all default settings. • The transparency master showing the Equation Operating System (EOS™) demonstrates the order in which the TI-30XS MultiView™ calculator completes calculations. • Operations inside parentheses are performed first. Use D E to change the order of operations and, therefore, change the result. Example: 1 + 2 x 3 = 7 (1 + 2) x 3 = 9 2.
Equation Operating System (EOS™) 1 (first) Expressions inside D E 2 Functions that need a E and precede the expression, such as >, A, and some menu items 3 Fractions 4 Functions entered after the expression, such as F and angle unit modifiers (¡, ¢, £, r, g) 5 Exponentiation (G) and roots (%c) Note: In Classic mode, exponentiation using the G key is evaluated from left to right. The expression 2^3^2 is evaluated as (2^3)^2, with a result of 64.
Equation Operating System (EOS™) (Continued) 6 7 8 9 10 11 (last) Negation (M) Permutations (nPr) and combinations (nCr) Multiplication, implied multiplication, and division Addition and subtraction Conversions (%O, %j, %R, and ´DMS) < completes all operations and closes all open parentheses.
Order of operations TVD E 1+2x3= Press Display 1T2V 3< 1 + (2 x 3) = Press Display 1TD2V3 E< (1 + 2) x 3 = Press Display D1T2E V3< 52 TI-30XS MultiView: A Guide For Teachers © 2006 TEXAS INSTRUMENTS INCORPORATED
Order of operations (Continued) 5 – 4 ( 1 ) ( 3 ) = (Classic mode) 2 Press Display p$$$ <%b5 F U4D1E D3E< 5 – 4 ( 1 ) ( 3 ) = (MathPrint™ mode) 2 Press Display p$$$ "<%b5 F U4D1E D3E< n © 2006 TEXAS INSTRUMENTS INCORPORATED TI-30XS MultiView: A Guide For Teachers 53
54 TI-30XS MultiView: A Guide For Teachers © 2006 TEXAS INSTRUMENTS INCORPORATED
5 Numeric notation Keys 1. p lets you choose from the following Notes • The examples on the transparency masters assume all default settings. • You can enter a value in scientific notation regardless of the numeric notation mode setting. For a negative exponent, press M before entering it. • Results requiring more than 10 digits are automatically displayed in scientific notation. • For the decimal notation mode, refer to Chapter 7, Decimals and decimal places.
Engineering, scientific, floating decimal Enter 12543, which will be in floating decimal notation and normal numeric notation (both default settings in p). Alternate the display result between normal, scientific, and engineering notations by changing settings on the mode screen.
Engineering, scientific, floating decimal (Continued) p p$< -< © 2006 TEXAS INSTRUMENTS INCORPORATED TI-30XS MultiView: A Guide For Teachers 57
Scientific notation With the TI-30XS MultiView™ calculator in Norm and MathPrint™ modes (both defaults), enter the following problem in scientific notation using the C key. C The Earth is approximately 1.5 x 108 kilometers from the Sun. Jupiter is approximately 7.8 x 108 kilometers from the Sun.
6 Fractions Keys 1. %N lets you enter mixed numbers and fractions. The unit must be an integer. The numerator and denominator can contain decimals. To enter a mixed number, enter an integer for the unit, and then press %N to enter a numerator. In MathPrint™ mode, pressing %N before entering an integer displays a fraction template, and allows only one digit to be entered for the unit. 2. q lets you enter a simple fraction. Pressing q before or after a number can result in differing behavior.
Fractions (Continued) • • • • To paste a previous entry in the denominator, place the cursor in the denominator, press % # to scroll to the desired entry, and then press < to paste the entry to the denominator. To paste a previous entry in the numerator or unit, place the cursor in the numerator or unit, press # or % # to scroll to the desired entry, and then press < to paste the entry to the numerator or unit. Fractional results and entries are automatically simplified to their lowest terms.
Fractions At the party, you ate --5- of the 6 1- of the pepperoni pizza and ---10 sausage pizza. The pizzas are the same size. If you put the pieces together, how much of one whole pizza did you eat? Press q Display 5 q 6 " T1 q 10 < 14 of the size of one whole You ate ---15 pizza.
Mixed numbers 3- pounds at birth. A baby weighed 4 -8 In the next 6 months, she gained 23 --- pounds. How much does she 4 weigh? Press %N %O Display 4 %N 3 $8"T2 %N 3 $ 4< %O < After 6 months, the baby weighs 7 --1- pounds.
Converting fractions and decimals Juan swims 20 laps in 5.72 minutes. Mary swims 20 laps in 5 3 --- minutes. 4 Change Mary's time to a decimal to determine who swims faster. Press %j Display 5 %N 3 $4" %j < Juan swims faster than Mary since he swims 20 laps in 5.72 minutes. Change 2.25 to its fractional equivalent.
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Decimals and decimal places 7 Keys Notes 1. 8 enters a decimal point. • 2. p lets you set the number of decimal places. Press $ $ and then " to the choice of decimal desired. Press < to select it. The examples on the transparency masters assume all default settings. • Press p $ $ < to return to standard notation (floating decimal). • The decimal mode setting affects most decimal results and the mantissa of scientific and engineering notation results.
Decimal Round 12.345 to the hundredths place, to the tenths place, and then to floating notation.
8 Constant Keys Notes 1. % l turns the constant feature on and off, and lets you define a constant number, operation, or expression for a shortcut when repeating a set of keystrokes. K displays when the constant mode is on. • The examples on the transparency masters assume all default settings. • All operations, functions, and values work in constant mode. • To enter a constant: 2. < places the contents of K at the end of the expression in the display. 1. Press % l.
Constant Three people babysit for $5.25 each per hour. The first person works 16 hours. The second person works 12 hours. The third person works 17 hours. How much did each person earn? Press %l Display %l V 5.
Constant (Continued) %l %l (Constant mode is off.
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Memory and stored variables 9 Keys 3. % { clears all variables. 1. L lets you store values to variables. Press Lto store a variable, and press z to select the variable to store. Press < to store the value in the selected variable. If this variable already has a value, that value is replaced by the new one. 4. % h displays a menu of the variables x, y, z, t, a, b, and c, and lets you view their stored values before pasting to the display. 2. z accesses variables.
Store, variables Following are your scores for tests and homework in your math class. Lz %h Test scores: 96, 76, 85. Homework scores: 92, 83, 97, 86. 1. Find your test grade as the average of your test scores. 2. Find your homework grade as the average of your homework scores. 3. Your teacher will compute your final grade as the average of your test grade and your homework grade. What is your final grade? Your teacher will round to the nearest whole number if needed.
Store, variables (Continued) Lz %h W3< Lz < 92 T 83 T 97 T 86 < W4< Tz< W2< Your final grade is 88 rounded to the nearest whole number.
Store, recall You are going to ship a gift to each of two friends. You see the gifts at two web sites for the same price. The shipping charges are different at each site. The packages weigh 4.5 pounds and 3.2 pounds. Store A will ship a package for €2 plus €1.40 per pound. Store B will ship the package for €3 plus €1.10 per pound. Which store will charge the least for shipping each gift? Press L %h Display 485L z< 2 T z D1 8 40 E < 3 T z D1 8 10 E < Store A charges €8.30 and store B charges €7.95.
Store, recall (Continued) L %h 382L z< ##### #<< ##### #<< Store A charges €6.48 and store B charges €6.52. Store A charges less to ship the gift that weighs 3.2 pounds.
Store, recall (Continued) Shop A B C Purchases shirts ties belt suspenders Qty 2 3 1 1 Cost €13.98 ea. €7.98 ea. €6.98 €9.
Store, recall (Continued) L %h 6 8 98 T 9 8 98 < Lz zz< %h 1 T% h 2T% h3< You spent: €27.96 at shop A, €23.94 at shop B, €16.96 at shop C. You spent €68.86 at all three shops.
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Data editor and list formulas 10 Keys Notes 1. v displays a data editor with three lists. Each list can contain up to 42 items. To enter data, navigate to a list and enter a number. Press the arrow keys to navigate list elements. • The examples on the transparency masters assume all default settings. • List formulas accept all calculator functions. • In formulas, use D and E around variables or list names to ensure the desired order of operations.
Entering data and formulas On a November day, a weather report on the Internet listed the following temperatures. v Paris, France 8ÄC Moscow, Russia ½1ÄC Montreal, Canada 4ÄC Convert these temperatures from degrees Celsius to degrees Fahrenheit. Reminder: F= 9 --- C+32.
Entering data and formulas (Continued) v < Notice L2 is highlighted, since it is the result of a formula. The degrees Fahrenheit are: Paris, France 46.4ÄF Moscow, Russia 30.2ÄF Montreal, Canada 39.2ÄF If Sydney, Australia is 21ÄC, find the temperature in degrees Fahrenheit. !$$$ 21 < The temperature in Sydney, Australia is 69.8ÄF.
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11 Statistics StatVars menu: Keys 1. v lets you enter data points (x for 1-Var stats; x and y for 2-Var stats). (See Chapter 10, Data editor and list formulas, for more details on v.) n v or w Sx or Sy 2. %t displays a menu from which you can select 1-Var, 2-Var or StatVars. sx or sy 1-Var Analyzes data from 1 set of data with 1 measured variable—x. 2-Var Analyzes paired data from 2 sets of data with 2 measured variables—x, the independent variable, and y, the dependent variable.
Entering 1-Var stat data Five students took a math test. Using their scores, enter the data points—85, 85, 97, 53, 77.
Viewing the statistics Find the number of data points (n), the mean (v), the sample standard deviation (Sx), the population standard deviation (sx), the sum of the scores (Gx), the sum of the squares (Gx2), and the five-number summary of the data, minX, Q1, Q2, and maxX.
Removing data points Drop the lowest test score by editing the data in L1 in the data editor. Make sure you update the frequency list, L2, if needed. Find the new mean (v). Finally, clear the data from all of the lists.
Entering 2-Var stat data The table below shows the number of pairs of athletic shoes sold by a small shoe store. The table shows the total number of pairs of shoes sold for two months and the total number of pairs of Brand A shoes sold during the same months. Enter this data in the data editor. Month April May %t v Total No.
Viewing the statistics Assuming that the rate of shoe sales is a constant, you can use two data points to predict the June sales of Brand A if we know the total June sales. Use a line of best fit to find the June sales of Brand A if the store sells a total of 32 pairs in June. Hint: Find y'(32). Press %t Display %t 2$$ < $ (scroll down to y') < 32 E < 18 pairs of Brand A will be sold in June if the total sales are 32 pairs.
12 Probability Keys Notes 1. H displays the following menu of functions. • The examples on the transparency masters assume all default settings. nPr Calculates the number of possible permutations. • nCr Calculates the number of possible combinations. A combination is an arrangement of objects in which the order is not important, as in a hand of cards. • ! Calculates the factorial of a number. A permutation is an arrangement of objects in which the order is important, as in a race.
Combination (nCr) You have space for 2 books on your bookshelf. You have 4 books to put on the shelf. Use this formula to find how many ways you could place the 4 books in the 2 spaces. H 4 nCr 2 A B C AB AB and BA count as only 1 BA CA combination DA Press D AC BC CB DB AD BD CD DC Display 4H$ <2< There are 6 unique combinations of 2 books chosen from 4 different books.
Permutation (nPr) Four different people are running in a race. Use this formula to find how many different ways they can place 1st and 2nd. 4 nPr 2 A B C AB and BA count as 2 permutations AB BA CA DA Press H D AC BC CB DB AD BD CD DC Display 4H <2 < There are 12 different permutations for the 1st and 2nd place results of the race.
Factorial (!) State license plates contain different numbers and letters to create a unique identification number for each car. Make your own license plates each containing a 4-digit number. Using the digits 1, 3, 7, and 9 without repetition, how many 4-digit numbers can you form? You can use a tree diagram to create the following list of license plates.
Random (rand) H Generate a sequence of random numbers. Press Display H" << < Results will vary.
Setting a random (rand) seed Set 1 as the current seed and generate a sequence of random numbers. Press H Display 1LH "< < H"< < < Note: Your results will be the same as this example if you use the same number to store to random seed.
Random integer (randint) Create your own calculator spinner. Your spinner will pick numbers from 2 through 10. H Hint: Generate a random integer from 2 through 10. Press Display H "$ < 2 %` 10 E <<< Results will vary.
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13 Function table Keys • 1. o allows you to display a defined function in a tabular form. To set up a function table: The examples on the transparency masters assume all default settings. • Enter the function (expression) at the y= prompt. Functions can contain stacked fractions and most built-in functions such as sine, cosine, ex, and so forth. Functions can not contain n or the functions rand and randint. • To change a value on the table setup screen, press - and then enter a new value.
Using auto Find the vertex of the parabola y = x(36 - x) using a table of values. o Reminder: The vertex of the parabola is a point on the line of symmetry of the parabola. Notice that (0, 0) and (36, 0) are x-intercepts and the parabola is open (concave) down. The vertex will be between x = 0 and x = 36. Press Display ozD 36 U z E< 0$4$ <$ <$$$ $$ Notice that the vertex must be between x = 16 and x = 20 since the y-values are the same.
Using auto (Continued) o -15 $ 1 $$ <$ $ $$ On your own: Start at 17 and change the step size to 0.25. What happens around x = 18? Can you locate the vertex? Why? After searching close to x = 18, the point (18, 324) appears to be the vertex of the parabola since it appears to be the turning point of the set of points of this function.
Using ask-x A charity collected $3,600 to help support a local food kitchen. $450 will be given to the food kitchen every month until the funds run out. How many months will the charity support the kitchen? Reminder: If x = months and y = money left, then y = 3600 - 450x. Press Display o o Press - if necessary to clear a previous function. 3600 U450 z< -0 $ -1 $ " <$< Input good guesses for the number of months, x. < The charity will be able to support the food kitchen at this rate for 8 months.
14 Powers, roots, and reciprocals Keys Notes 1. F squares the value. • The examples on the transparency masters assume all default settings. 3. % c calculates the specified root (x) of the value. • To use G, enter the base, press G, and then enter the exponent. 4. a calculates the reciprocal. • In Classic mode, exponentiation using the G key is evaluated from left to right. The expression 2^3^2 is evaluated as (2^3)^2, with the result of 64. 2. % b calculates the square root. 5.
Squares Use this formula to find the size of the tarpaulin needed to cover the entire baseball infield. FG A = x2 = 27.42 square meters Press Display 27 8 4 F< or 27 8 4 G 2< The area of the tarpaulin is 750.76 square meters.
Square roots Use this formula to find the length of the side of a square clubhouse if 3m2 of carpet would cover the floor. Round your answer to 0 decimal places. x = L = x %b 3 meters 3m2 of carpet Press Display %b3 < n p$$ "< -< The length of a side of the square clubhouse is 2 meters rounded to 0 decimal places.
Cubes Use this formula to find the volume of a cube with sides 2.3 meters long. Change your answer to a fraction. G V = L3 = 2.33 cubic meters L Press Display 283G 3< n The volume of the cube is 12.167 cubic meters.
Powers Fold a piece of paper in half, in half again, and so on until you cannot physically fold it in half again. How many sections would there be after 10 folds? After 15 folds? Press G Display 2 G 10 < 2 G 15 < Fold the paper in half once and you will see two sections. Fold the paper in half again and you will see four sections. Folding again yields 8 sections, and so on. After 10 folds there will be 1,024 sections.
Roots If the volume of a cube is 125 cm3, what is the length of each side? %c L = 3 125 cm L Press Display 3 %c 125 < The length of each side is 5 cm.
Reciprocals The chart below shows the amount of time spent building model ships. Ships Sailing Steam Luxury Time Spent Building 10 hrs. 5 hrs. 5 1/3 hrs.
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Logarithms and exponential functions 15 Keys Notes 1. A calculates the common logarithm (base 10). • The examples on the transparency masters assume all default settings. 2. % ] calculates 10 raised to the power of the value entered as the exponent (common antilogarithm). • E ends a logarithmic function. • In MathPrint™ mode, press " to exit the exponent function. 3. B calculates the natural logarithm (base e, where e ≈ 2.718281828459). 4.
Common logarithm, natural logarithm Find log 23 rounded to 4 decimal places. Then find ln 23 rounded to 4 decimal places and return to floating decimal notation.
Common antilogarithm, natural antilogarithm Find antilog 3.9824 rounded to 4 decimal places. Then find antiln 3.9824 rounded to 4 decimal places. When finished, return to floating decimal notation.
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16 Pi Keys Notes 1. g displays the value of pi rounded to 10 digits (3.141592654). • The examples on the transparency masters assume all default settings. • In MathPrint™ mode, include a decimal number inside the expression with pi to receive a decimal output. For example, if you enter 2À, the TI-30XS MultiView™ calculator displays 2À. If you enter 2.0À, the calculator displays the decimal version, 6.28319. • You can use n to toggle the answer between decimal and pi formats.
Circumference Use this formula to find the amount of border you need if you want to put a circular border all the way around the tree. g C = 2Àr = 2 x À x 1.5m Press Display 2VgV 185< n The border length is 3À m. You will need approximately 9.4 m for the border.
Area Use this formula to find how much of a lawn would be covered by the sprinkler. Round your answer to the nearest whole number, and then return to floating decimal mode.
Area (Continued) p$$ <- g < The area that will be covered by the sprinkler is approximately 50 square meters.
Angle settings and conversions If you specify an angle unit modifier from the Angle menu, the calculation is performed in that angle type, but the result will be given in the angle mode setting. Keys 1. %I displays a choice of two submenus that enable you to specify the angle unit modifier as degrees (º), minutes ('), seconds ("); radian (r); gradian (g), or convert units using ´DMS. You can also convert between rectangular coordinate form (R) and polar coordinate form (P).
Degrees, minutes, and seconds to decimal Find the measure of the third angle of a triangle if one angle measures 45Ä 30Å and the other angle measures 36Ä 15Å. Express the angle measure in degrees, minutes, and seconds. Press %I Display 45 % I 1 30 % I 2 T 36 % I1 15 % I 2< 180 % I 1U%i < %I6 < The measure of the third angle is 98Ä 15Å.
Decimal to degrees, minutes, and seconds You are visiting Beijing, China. Your GPS gives your location (latitude and longitude) as 39.55Ä N 116.20Ä E. Change your location information to degrees, minutes and seconds. Press %I Display 39.55 % I< %I# << 116.20 % I< %I# << Your location in Beijing, China is 39Ä 33Å N 116Ä 12Å E.
Degrees, radians, and gradians Calculate the following: %I cos(180 degrees) cos(À radians) cos(200 grad) Remember: 180 degrees = À radians = 200 grad.
Polar and rectangular conversions 18 Keys Notes 1. %I displays the choice of two submenus that let you convert rectangular coordinates (x,y) to polar coordinates (r,q) or vice versa. You can also specify the angle unit modifier. (See Chapter 17, Angle settings and conversions, for more information.) • The example on the transparency master assumes all default settings. • Before starting calculations, set the angle mode as necessary. R μPr( Converts rectangular coordinate to polar coordinate r.
Polar to rectangular Convert the polar ordered pair (7, 30Ä) to rectangular coordinates. Press %I Display %I " $$ < 7 %` 30 E < %I " $$$< 7 %` 30 E< The rectangular ordered pair is (x, y) = (6.062177826, 3.5.
19 Trigonometry Keys Notes 1. > calculates the sine of an angle. • The examples on the transparency masters assume all default settings. • Before starting a trigonometric calculation, be sure to select the appropriate angle mode setting (DEG, RAD, or GRAD—See Chapter 17, Angle settings and conversions). The calculator interprets values according to the current angle-unit mode setting.
Tangent Use this formula to find the distance from the lighthouse to the boat. Round your answer to the nearest whole number, and then return to floating decimal mode. @ 78 D = --------------TAN 27 D Press Display 78 q @27 %I< E< p$ $ "< -< p$$< -< The distance from the lighthouse to the boat is approximately 153 m.
Inverse tangent Use this formula to find the angle of depression, x. Round your answer to the nearest tenth, and then return to floating decimal mode. %\ 600x = TAN-1 ------------ 2500 Press Display %\ 600 q 2500 " E< p$ $ " "< -< p$ $ <-< The angle of depression is x = 13.5Ä rounded to the nearest tenth.
Cosine Use this formula to find the distance, D, from the base of the ladder to the house. Round your answer to the nearest whole number, and then return to floating decimal mode. ? D = 5 x COS(74) meters D Press Display 5 V ? 74 E< p$ $ "< -< p$ $ <-< The distance is approximately 1 meter.
Inverse cosine Use this formula to find the angle of the ski jump, x. Round your answer to the nearest tenth, and then return to floating decimal mode. %[ 453x = COS-1 --------500 Press Display %[ 453 q 500 " E< p$ $ " "< -< p$ $ <-< The angle of the ski jump is x = 25.0Ä rounded to the nearest tenth.
Sine Use this formula to find the length of the ramp, D. Round your answer to the nearest whole number, and then return to floating decimal mode. 1.5 - meters D = ------------------sin ( 12° ) > D Press Display 185q> 12 E < p$ $ "< -< p$ $ <-< The length of the ramp is D = 7 m rounded to the nearest whole number.
Inverse sine Use this formula to find the angle of the conveyor belt, x. Round your answer to the nearest tenth, and then return to floating decimal mode. 13 x = SIN-1 ------ meters 20 Press %Z Display %Z 13 q 20 " E < p$ $ " "< -< p$ $ <-< The angle of the conveyer belt is x = 40.5Ä rounded to the nearest tenth.
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20 Hyperbolics Keys Notes 1. % Y accesses the hyperbolic function (sinh, cosh, tanh; and sinh-1, cosh-1, tanh-1)of the next trig key that you press. • The example on the transparency masters assumes all default settings. • Hyperbolic calculations are not affected by the angle mode setting-whether or not the calculator is in RAD (radian), GRAD (gradian), or DEG (degree) modes.
Sinh, cosh, and tanh Find the sinh(2) and the sinh-1(2). Repeat for cosh and tanh. What do you notice? Press %Y Display %Y> 2 E< %Y% Z%i E< %Y? 2 E< %Y% [%i E< %Y@ 2 E< %Y% \%i E< 132 TI-30XS MultiView: A Guide For Teachers © 2006 TEXAS INSTRUMENTS INCORPORATED
A Quick reference to keys KEY FUNCTION !" ! " move the cursor left and right so you can scroll an entry on the Home screen. #$ Press % ! or % " to scroll to the beginning or end of a current entry. # $ move the cursor up and down to navigate menu items, view entries in the data editor and function table, and view previous entries on the Home screen. % # moves the cursor to the oldest entry on the Home screen, and to the top entry of the active column in Data editor.
A Quick reference to keys (Continued) KEY FUNCTION %I Displays the following menus. DMS lets you specify the unit of an angle. R ¶P lets you convert rectangular coordinates to polar coordinates, or vice versa. DMS R ¶P 1: Ä 1: R ´Pr( 2: Å 2: R ´PÁ( 3: Æ 3: P ´Rx( 4: r 4: P ´Ry( 5: g 6: ´DMS C C is a shortcut key to enter a number in scientific notation format. %b Calculates the square root. %_ Appends the % sign to a number.
Quick reference to keys (Continued) A KEY FUNCTION %[ Calculates the inverse cosine. @ Calculates the tangent of an angle. %\ Calculates the inverse tangent. v Lets you enter the statistical data points for 1-Var stats and 2-Var stats. vv Press v once to display the data editor screen. Press again to display the Clear and Formula menus. Lets you access list names when in the Formula menu. J Deletes the character at the cursor.
A Quick reference to keys (Continued) KEY FUNCTION %t Displays the following menu from which you can select 1-Var, 2-Var, or StatVars. 1-Var Analyzes data from 1 set of data with 1 measured variable–x. 2-Var Analyzes paired data from 2 sets of data with 2 measured variables–x, the independent variable, and y, the dependent variable. StatVars After choosing 1-var or 2-var stats, displays data values. StatVars displays the following menu of stat variables with their current values.
Quick reference to keys (Continued) KEY FUNCTION % Displays the RESET menu. A RESET 1: No 2: Yes Press 1 (No) to return to the previous screen without resetting the calculator. Press 2 (Yes) to reset the calculator. The message MEMORY CLEARED is displayed. You can press & and - simultaneously to reset the calculator immediately. No menu or message is displayed. L Lets you store values to variables. Press Lto store a variable, and press z to select the variable to store.
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B Display indicators INDICATOR MEANING 2nd 2nd function. HYP Hyperbolic function. FIX Fixed-decimal setting. (See the Mode section in Chapter 1, TI-30XS MultiView™ basic operations, and Chapter 7, Decimals and decimal places.) SCI, ENG Scientific or engineering notation. (See the Mode section in Chapter 1, TI-30XS MultiView basic operations.) DEG, RAD, GRAD Angle mode (degrees, radians, or gradians). (See the Mode section in Chapter 1, TI-30XS MultiView basic operations.
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C Error messages When the TI-30XS MultiView™ calculator detects an error, it returns an error message with the type of error. To correct the error, note the error type and determine the cause of the error. If you cannot recognize the error, use the following list, which describes error messages in detail. Press - to clear the error message. The previous screen is displayed with the cursor at or near the error location. Correct the expression.
Error messages (Continued) MESSAGE MEANING SYNTAX The command contains a syntax error—entering more than 23 pending operations, 8 pending values, or having misplaced functions, arguments, conversions, variables, parentheses, or commas. If using q, try using W. INVALID FUNCTION You entered an invalid function in the function table. LOW BATTERY Replace the battery. Note: This message displays briefly and then disappears. Pressing does not clear this message.
Texas Instruments support and service D For general information Home Page: education.ti.com KnowledgeBase and e-mail inquiries: education.ti.com/support Phone: (800) TI-CARES / (800) 842-2737 For U.S., Canada, Mexico, Puerto Rico, and Virgin Islands only International Information: education.ti.com/international For technical support KnowledgeBase and e-mail inquiries: education.ti.com/support Phone (not toll-free): (972) 917-8324 For product (hardware) service Customers in the U.S.
D-2 TI-30XS MultiView: A Guide For Teachers © 2006 TEXAS INSTRUMENTS INCORPORATED
E Battery information Battery precautions • Do not leave batteries within the reach of children. • Do not mix new and used batteries. Do not mix brands (or types within brands) of batteries. • Do not mix rechargeable and non-rechargeable batteries. • Install batteries according to polarity (+ and -) diagrams. • Do not place non-rechargeable batteries in a battery recharger. • Properly dispose of used batteries immediately. • Do not incinerate or dismantle batteries.
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